Table of contents

This special issue contains the proceedings of the 2nd International Conference on Quantum Theories and Renormalization Group in Gravity and Cosmology (IRGAC 2006), which was held in Cosmocaixa, Barcelona, on 11–15 July 2006 (http://ns.ecm.ub.es/IRGAC2006/index.htm).

A few words to clarify the framework and main purposes of this conference are in order. In the course of the last decade we have witnessed a progressively increasing interaction between high energy physics/particle physics and cosmology/astrophysics. Cosmology, in particular, is rapidly becoming an experimental branch of precision physics. It is no longer a realm of theoretical (sometimes philosophical) speculation; theoretical models can be tested, and new and more accurate data in the near future will restrict our conceptions of the Universe to within a few per cent accuracy. Particle physics, on the other hand, is not only the science of highest experimental accuracy, but also the natural theoretical arena where one can try to get a fundamental understanding of the basic laws of Nature, from the lowest to the highest scales available. There is no doubt that the present observational data (obtained from different and independent experimental sources, ranging from measurements of distant high redshift supernovae to the universal microscopic anisotropies of the cosmic microwave background) confirm the process of accelerated expansion of the Universe. This fundamental fact, which is nowadays amply recognized and endorsed by the international scientific community, has revitalized and boosted more than ever the relationship between the fields of high energy physics and cosmology. It is generally accepted that the physical cause of the accelerated expansion of the Universe is the existence of a (positive) cosmological constant, or in general of a `dark energy' fluid which pervades uniformly all corners of the known part of the Universe, and mimics a positive cosmological term in Einstein's equations. We also know, from experimental observations, that it constitutes roughly 70% of the critical density. But we really don't know what it is yet; we need some microphysical input on the ultimate nature of this substratum. What is the explanation for that bulk 70% of the cosmological energy budget? Is it really the ground state energy associated with the quantum field theory vacuum? Is it, instead, the current value of the energy density of some slowly evolving homogeneous and isotropic scalar field (the so-called quintessence)? Perhaps a hint of a modified gravitational theory? Or just the most likely vacuum state of the string theoretical 'landscape', consisting of some 10¹⁰⁰⁰ metastable (non-supersymmetric) vacua? Whatever it may be, it is currently the cause of one of the most troublesome headaches of modern cosmology, if not of the whole of theoretical physics: the so-called 'cosmological constant problem'—the deepest mystery of fundamental physics ever!

IRGAC is a series of international conferences intended to enhance the interdisciplinary collaboration among scientists working in precisely the above research fields. The ultimate aim is to combine their efforts to address, in the most efficient way, basic problems in cosmology which at the same time appear as fundamental problems of physics, such as the aforementioned cosmological constant problem, the nature of the dark energy, and the dark matter problem in the Universe. A central topic in this series of conferences is to establish what are the current state of the art and outlook for the quantum theories of gravitation and cosmology, in particular the role played by the latest theoretical developments in theoretical high energy physics, both in quantum field theory and string theory (including the general methods of the renormalization group, common to both) in our search for a satisfactory explanation of those fundamental problems. Equally important is to confront the theoretical status with the current experimental situation, i.e. to keep an eye on the future experiments that are planned to gather observational data on the cosmological parameters with unprecedented accuracy. Undoubtedly, some balanced phenomenology ingredient in a field like this is not only highly desirable, but actually indispensable to enable researchers to assess by themselves during the conference the real impact of the theoretical ideas versus experiments and observations, and vice versa.

IRGAC 2006 in Barcelona was a follow-up to the first conference held in Ouro Preto, Brazil, in 2003 (under the slightly different acronym of IRGA 2003) [1]. The present, and more complete, name for this series (note the ending 'C') intends to stress the cosmology component of the meeting, and it is intended to stay in future editions. In this respect it is worth emphasizing that 2006 represented the 25th anniversary of the formulation of the inflationary paradigm, which nowadays appears as a theoretical conception perfectly compatible with, if not the most likely explanation for, the spatial flatness of our Universe as measured by the CMB data. This 25th anniversary was obviously a unique opportunity to accentuate and enhance the cosmology background of IRGAC 2006: see the full scientific program athttp://ns.ecm.ub.es/IRGAC2006/Program.htm.

As the chairman organizer of the conference, I was particularly interested to count, on this very special occasion, on the participation of the three outstanding cosmologists who first proposed the idea of inflation: Alan Guth, Andrei Linde and Alexei Starobinsky. I am very grateful to the three of them for being so positive in accepting my invitation to participate. I am especially grateful to Alan Guth for his early interest in our conference, expressed some two years before it took place. Needless to say, I am pleased to extend these thanks to the rest of the speakers and participants, without whom this conference would not have attained the high degree of scientific performance and successful level of participation that it finally achieved (namely 140 registered participants from 25 different countries). As chairman, I was proud of these achievements, especially if we take into account that IRGAC 2006 was just the second edition of the series. Certainly this constitutes a great motivation and provides a strong boost to encourage future editions. I would like to take this opportunity to thank the many participants who, either through email or personally during the conference, expressed their satisfaction with the logistics, smoothness and scientific success of the conference. At the same time, my sincere apologies for any shortcomings that the participants might have experienced.

There were many talks at IRGAC 2006: to be precise 97; of these 34 were plenary and 63 parallel. Clearly, the level of participation was high. Three conference rooms were ordered in Cosmocaixa for simultaneous parallel talks. We are especially proud to have arranged for a substantial number of these parallel talks to be given by students and young researchers from different countries. At the same time we could offer to many of them (although, regretfully, not to all of them) some financial support. We also set out a substantially reduced fee for all students who participated in the conference.

I wish to thank all the members of the International Advisory Committee of IRGAC 2006 for honouring us with their help and support: I Antoniadis (CERN), M Asorey (Zaragoza), L Bergstrom (Stockholm), S Deser (Brandeis), E Fernández (IFAE), D Z Freedman (MIT), A Guth (MIT), J Isern (CSIC), R Jackiw (MIT), V F Mukhanov (Munich), R D Peccei (UCLA), A Schwimmer (Weizmann Institute), I L Shapiro (UFJF), J Silk (Oxford), A Starobinsky (Landau Institute), R Tarrach (UB), P K Townsend (Cambridge), A Vilenkin (Tufts), S Weinberg (Austin) and C Wetterich (Heidelberg). Particular thanks go to Manuel Asorey and Ilya Shapiro (the previous organizers) for their advice. I am especially obliged to Ilya Shapiro for his encouragement to organize the conference in Barcelona and for his continuous support. To organize an event like this is not a completely trivial task. I counted on the collaboration of the other members of the Local Organizing Committee, to whom I am also very grateful: J Garriga, E Gaztañaga, J Gomis, J A Grifols, J I Latorre and E Verdaguer.

The efficient performance of the huge secretariat work would not have been possible without the superb collaboration of our secretary, Ariadna Frutos, to whom I am indebted for her intense and competent dedication. Many thanks also go to the Cosmocaixa staff, and especially to Paquita Ciller for her unfailing positive attitude and for her taking care of so many things. It is fair to say that the Cosmocaixa support to the IRGAC 2006 event was magnificent. I also wish to thank Rolf Tarrach for his crucial advice at the initial stages of the organization of the conference, in particular for introducing me to the Cosmocaixa staff.

The funding for IRGAC 2006 came from different sources: Ministerio de Educación y Ciencia, Generalitat de Catalunya, Consejo Superior de Investigaciones Científicas, Universitat de Barcelona, Universitat Autònoma de Barcelona, Institut de Física d'Altes Energies, Obra Social Fundació `La Caixa', and last but not least IOP Publishing, as publishers of these proceedings as a special issue of Journal of Physics A: Mathematical and Theoretical, where all the contributions have been rigorously refereed according to the high standards of the journal.

My hearty thanks are also addressed to some of our PhD students and postdocs of the Department d'Estructura i Constituents de la Matèria, and of the Departament de Fisica Fonamental, of the Universitat de Barcelona, for their invaluable help and collaboration in solving innumerable niceties and logistical problems that appeared during the frantic days of the conference. Thank you very much to all of them: Daniel Arteaga, Diego Blas, Joan Camps, Noela Fariña, Javier Grande, Laia Jornet, David López Val, Guillem Pérez and Hrvoje Štefančić.

I cannot finish without mentioning Dolors (my wife) and Clara (my daughter) who suffered during the many months I had to devote to the detailed organization of this event, a task that I had to combine of course with the research work and the ordinary duties of any university professor. In fact, although the conference took place during just those five (sunny) days of July 2006 mentioned above, the first preliminary searches for speakers had begun in mid-2004, and now I still find myself writing this preface in May 2007—roughly three years' intermittent work for just a one-week event! No complaints whatsoever, of course. I just feel immensely gratified knowing in my heart that most of the participants, if not all of them, truly enjoyed IRGAC 2006 in Barcelona. The challenge was worth it!

Matter is distributed very homogeneously and isotropically on scales larger than a few hundred Mpc. The measurements of the microwave background temperature fluctuations show that at recombination the universe was extremely homogeneous and isotropic (with accuracy ∼10⁻⁴) on all scales up to the present horizon (Spergel et al 2006 Preprint astro-ph/0603449; MacTavish et al 2005 Preprint astro-ph/0507503). On the other hand, there is a large scale structure in the observable universe and one of the central issues of contemporary cosmology is the explanation of the origin of primordial inhomogeneities, which serve as the seeds for structure formation. Before the advent of inflationary cosmology the initial perturbations were postulated and their spectrum was designed to fit observational data. In this way practically any observation could be 'explained', or more accurately described, by arranging the appropriate initial conditions. In contrast, inflationary cosmology truly explains the origin of primordial inhomogeneities and predicts their spectrum (Mukhanov and Chibisov 1981 JETP Lett.33 532; Mukhanov and Chibisov 1982 Sov. Phys.—JETP56 258). Thus it becomes possible to test this theory by comparing its predictions with observations. According to cosmic inflation, primordial perturbations originated from quantum fluctuations. These fluctuations have substantial amplitudes only on scales close to the Planckian length, but during the inflationary stage they are stretched to galactic scales with nearly unchanged amplitudes. Thus, inflation links the large-scale structure of the universe to its microphysics. The resulting spectrum of inhomogeneities is not very sensitive to the details of any particular inflationary scenario and has nearly universal shape. This leads to concrete predictions for the spectrum of cosmic microwave background anisotropies.

In this paper, we review the actual situation of electroweak breaking theories concerning their capabilities to generate the baryon asymmetry of the universe at the electroweak phase transition. First of all we consider the case of the standard model which, in spite of possessing all necessary ingredients, is unable to produce the observed amount of baryon asymmetry. This fact is enough to motivate the existence of physics beyond the standard model. We then present the situation in the minimal supersymmetric extension of the standard model (MSSM) where, only if the Higgs is on the verge of experimental detection and the right-handed stop is lighter than the top quark, the baryon asymmetry of the universe could be likely generated in agreement with observations. Otherwise one should go beyond the MSSM, either by splitting supersymmetry or by assuming the existence of new fields strongly coupled to the Higgs sector. One such model is provided as an example.

The cosmological constant problem emerges when quantum field theory is applied to the gravitational theory, due to the enormous magnitude of the induced energy of the vacuum. The unique known solution of this problem involves an extremely precise fine tuning of the vacuum counterpart. We review a few of the existing approaches to this problem based on the account of the quantum (loop) effects and pay special attention to those involving the renormalization group.

The possibility of a minimal physical length in quantum gravity is discussed within the asymptotic safety approach. Using a specific mathematical model for length measurements ('COM microscope'), it is shown that the spacetimes of quantum Einstein gravity based upon a special class of renormalization group trajectories are 'fuzzy' in the sense that there is a minimal coordinate separation below which two points cannot be resolved.

The axion solution of the strong CP problem provides a number of possible windows to physics beyond the standard model, notably in the form of searches for solar axions and for galactic axion dark matter, but in a broader context also inspires searches for axion-like particles in pure laboratory experiments. We briefly review the motivation for axions, astrophysical limits, their possible cosmological role, and current searches for axions and axion-like particles.

The deflection of light from distant sources by the foreground mass distribution can be quantified and mined for interesting cosmological information. Within the last decade, observers have moved from making the first detections of this phenomenon to planning ambitious future surveys. These surveys may teach us much about fundamental physics such as dark energy and neutrino mass. After a qualitative review of some of this, we present new results regarding the accuracy with which cluster masses can be determined through a detailed study of the way in which the clusters distort the cosmic microwave background.

In this work, we will review the main properties of braneworld models with low tension. Starting from very general principles, it is possible to obtain an effective action for the relevant degrees of freedom at low energies (branons). Using the cross sections for high-energy processes involving branons, we set bounds on the different parameters appearing in these models. We also show that branons provide a WIMP candidate for dark matter in a natural way. We consider cosmological constraints on its thermal and non-thermal relic abundances. We derive direct detection limits and compare those limits with the preferred parameter region in the case in which the EGRET excess in the diffuse galactic gamma rays is due to dark matter annihilation. Finally, we will discuss the constraints coming from the precision tests of the standard model and the muon anomalous magnetic moment.

This is a non-technical summary of the subtleties of quantum corrections on extra-dimensional theories: should one first renormalize and then mode expand, or first expand in four-dimensional modes and then renormalize?

Zeta function regularization techniques are optimally suited for the calculation of the contribution of fluctuations of the vacuum energy of the quantum fields pervading the universe to the cosmological constant (cc). The order of magnitude calculations of the absolute contributions of all fields is known to lead to a value which is off by over 120 orders, as compared with the results obtained from observational fits, known as the new cc problem. This is difficult to solve and many authors still stick to the old problem to try to prove that basically its value is zero with some perturbations thereof leading to the (small) observed result (Burgess C P et al 2006 Preprints hep-th/0606020, 0510123, Padmanabhan T 2006 Preprint gr-qc/0606061, etc). We also address this issue in a somewhat similar way, by considering the additional contributions to the cc that may come from the possibly non-trivial topology of space and from specific boundary conditions imposed on braneworld and other seemingly reasonable models that are being considered in the literature (mainly with other purposes too)—kind of a Casimir effect at cosmological scale. If the ground value of the cc would be indeed zero, we would then be left with this perturbative quantity coming from the topology or BCs. We review the status of this approach, in particular the fact that the computed number is of the right order of magnitude (and has the right sign, what is also non-trivial) when compared with the observational value, in some of the aforementioned examples.

Lowering the string scale in the TeV region provides a theoretical framework for solving the mass hierarchy problem and unifying all interactions. The apparent weakness of gravity can then be accounted for by the existence of large internal dimensions, in the submillimetre region, and transverse to a braneworld where our universe must be confined. I review the main properties of this scenario and its implications for observations at both particle colliders, and in non-accelerator gravity experiments. Such effects are for instance the production of Kaluza–Klein resonances, graviton emission in the bulk of extra dimensions, and a radical change of gravitational forces in the submillimetre range. I also discuss localization of gravity in the presence of infinite size extra dimensions that can modify Newton's law at cosmological distance scales.

We explain simple semi-classical rules to estimate the lifetime of any given highly excited quantum state of the string spectrum and apply them to identify new long-lived string states. Using analytic formulae for the string evolution after joining and interconnection, we study examples of fundamental cosmic string collisions leading to gravitational collapse. We find that the interconnection of two strings of equal and opposite maximal angular momenta and arbitrarily large mass generically leads to the formation of black holes. (Based on the works (Iengo and Russo 2006 J. High Energy Phys.JHEP02(2006)041, Iengo and Russo 2006 J. High Energy Phys.JHEP08(2006)079).)

We explore a well-motivated class of inflationary models from the particle physics point of view: those with a flat tree-level potential, where the radiative corrections cause the slow rolling of the inflaton and the running of the spectral index n. This includes typical SUSY inflation models (e.g. D-hybrid inflation). In the small-coupling regime the predictions for the size and running of n are remarkably neat and model independent, e.g. −dn/d ln k = (n − 1)² ≪ 1. The fit to WMAP data gives the number of e-folds, N_e, as an output: N_e = 26⁺³⁰₋₈, which is very encouraging. On the other hand, to account for the WMAP preliminary indication of a running n crossing n = 1, we find it extremely natural to incorporate non-renormalizable operators (only the dominant one is relevant), which automatically increase the running as demanded. The analysis is still very model independent and predicts a rapidly changing n at the initial scales, which then gets stabilized below n = 1.

The relation between entanglement entropy and the computational difficulty of classically simulating quantum mechanics is briefly reviewed. Matrix product states are proven to provide an efficient representation of one-dimensional quantum systems. Further applications of the techniques based on matrix product states, some of their spin-off and their recent generalizations to scale invariant theories and higher dimension systems are also discussed.

The accelerating expansion of the Universe presents an exciting, fundamental challenge to the standard models of particle physics and cosmology. I highlight some of the outstanding challenges in both developing theoretical models and interpreting without bias the observational results from precision cosmology experiments in the next decade that will return data to help reveal the nature of the new physics. Examples given focus on distinguishing a new component of energy from a new law of gravity, and the effect of early dark energy on baryon acoustic oscillations.

The status of the problem of neutrino masses, mixing and oscillations is discussed. Future perspectives are briefly considered.

This paper is a review of aspects of supergravity theories that are relevant in superstring cosmology. In particular, it considers the possibilities and restrictions for 'uplifting terms', i.e., methods to produce de Sitter vacua. We concentrate on N = 1 and N = 2 supergravities, and the tools of superconformal methods, which clarify the structure of these theories. Cosmic strings and embeddings of target manifolds of supergravity theories in others are discussed briefly at the end.

A reconstruction scheme is developed for modified f(R) gravity with realistic matter (dark matter, baryons, radiation). Two versions of such theory are constructed: the first one describes the sequence of radiation and matter domination, deceleration–acceleration transition and acceleration era, and the second one is reconstructed from exact ΛCDM cosmology. The inclusion of a radiation dominated era in the cosmological sequence is qualitatively a new result. The asymptotic behaviour of the first model at late times coincides with the theory containing positive and negative powers of curvature while the second model approaches general relativity without a singularity at zero curvature.

The correspondence between domain-wall and cosmological solutions of gravity coupled to scalar fields is explained. Any domain-wall solutions that admit a Killing spinor are shown to correspond to a cosmology that admits a pseudo-Killing spinor; whereas the Killing spinor obeys a Dirac-type equation with Hermitian 'mass'-matrix, the corresponding pseudo-Killing spinor obeys a Dirac-type equation with a anti-Hermitian 'mass'-matrix. We comment on some implications of (pseudo)supersymmetry.

I review the use of type-Ia supernovae (SNe) for cosmological studies. After briefly recalling the main features of type-Ia SNe that lead to their use as cosmological probes, I briefly describe current and planned type-Ia SNe surveys, with special emphasis on their physics reach in the presence of systematic uncertainties, which will be dominant in nearly all cases.

Observation of the universe in the VHE gamma-ray domain with the new generation of Cherenkov telescopes is producing new measurements with a direct implication for cosmology. The present results and the future prospects will be discussed.

The vacuum dependence on boundary conditions in quantum field theories is analysed from a very general viewpoint. From this perspective, the renormalization prescriptions not only imply the renormalization of the couplings of the theory in the bulk but also the appearance of a flow in the space of boundary conditions. For regular boundaries, this flow has a large variety of fixed points and no cyclic orbit. The family of fixed points includes Neumann and Dirichlet boundary conditions. In one-dimensional field theories, pseudo-periodic and quasi-periodic boundary conditions are also RG fixed points. Under these conditions massless bosonic free field theories are conformally invariant. Among all fixed points only Neumann boundary conditions are infrared stable fixed points. All other conformal invariant boundary conditions become unstable under some relevant perturbations. In finite volumes, we analyse the dependence of the vacuum energy along the trajectories of the renormalization group flow providing an interesting framework for dark energy evolution. In contrast, the renormalization group flow on the boundary does not affect the leading behaviour of the entanglement entropy of the vacuum in one-dimensional conformally invariant bosonic theories.

I review recent progress in defining a probability measure in the inflationary multiverse. General requirements for a satisfactory measure are formulated and recent proposals for the measure are clarified and discussed.

Dynamical dark energy (DE) has been proposed to explain various aspects of the cosmological constant (CC) problem(s). For example, it is very difficult to accept that a strictly constant Λ-term constitutes the ultimate explanation for the DE in our Universe. It is also hard to acquiesce in the idea that we accidentally happen to live in an epoch where the CC contributes an energy density value ρ_Λ = Λ/8πG right in the ballpark of the rapidly diluting matter density ρ_m ∼ 1/a³. It should perhaps be more plausible to conceive that the vacuum energy, ρ_Λ, is actually a dynamical quantity as the Universe itself. More generally, we could even entertain the possibility that the total DE is in fact a mixture of ρ_Λ and other dynamical components (e.g. fields, higher order terms in the effective action etc) which can be represented collectively by an effective entity X (dubbed the 'cosmon'). The 'cosmon', therefore, acts as a dynamical DE component different from the vacuum energy. While it can actually behave phantom-like by itself, the overall DE fluid may effectively appear as standard quintessence, or even mimic at present an almost exact CC behaviour. Thanks to the versatility of such cosmic fluid we can show that a composite DE system of this sort ('ΛXCDM') may have a key to resolving the mysterious coincidence problem.

The cosmic microwave background has provided an unprecedented cosmological window on the very early universe for probing the initial conditions from which structure evolved. Infinitesimal variations in temperature on the sky, first predicted in 1967 but only discovered in the 1990s, provide the fossil fluctuations that seeded the formation of the galaxies. The cosmic microwave background radiation has now been mapped with ground-based, balloon-borne and satellite telescopes. I describe its current status and future challenges.

I summarize the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region.

In this paper we provide a short review of the main results developed in Charmousis et al (2006 Preprint hep-th/0604086). We focus on linearized vacuum perturbations about the self-accelerating branch of solutions in the DGP model. These are shown to contain a ghost in the spectrum for any value of the brane tension. We also comment on Deffayet et al (2006 Preprint hep-th/0607099), where some counter arguments have been presented.

The SNe type Ia data admit that the universe today may be dominated by some exotic matter with negative pressure violating all energy conditions. Such exotic matter is called phantom matter due to the anomalies connected with violation of the energy conditions. If a phantom matter dominates the matter content of the universe, it can develop a singularity in a finite future proper time. Here we show that, under certain conditions, the evolution of perturbations of this matter may lead to avoidance of this future singularity (the big rip). At the same time, we show that local concentrations of a phantom field may form, among other regular configurations, black holes with asymptotically flat static regions, separated by an event horizon from an expanding, singularity-free, asymptotically de Sitter universe.

On the basis of a semi-classical analysis of vacuum energy in an expanding spacetime, we describe a non-singular cosmological model in which the vacuum density decays with time, with a concomitant production of matter. During an infinitely long period we have an empty, inflationary universe, with H ≈ 1. This primordial era ends in a fast phase transition, during which H and Λ decrease to nearly zero in a few Planck times, with the release of a huge amount of radiation. The late-time scenario is similar to the standard model, with the radiation phase followed by a long dust era, which tends asymptotically to a de Sitter universe, with vacuum dominating again. An analysis of the redshift-distance relation for supernovae Ia leads to cosmological parameters in agreement with other current estimations.

There is an evidence of a scale-invariant matter distribution up to scales over 10 Mpc. We review scaling (fractal or multifractal) models of large-scale structure and their observational evidence. We conclude that the dynamics of cosmological structure formation seems to be driven to a multifractal attractor. This supports previous studies, which we review, of structure formation by means of the renormalization group within a hydrodynamic formulation.

Minimal supersymmetric hybrid inflation based on a minimal Kähler potential predicts a spectral index n_s ≳ 0.98. On the other hand, WMAP three-year data prefer a central value n_s ≈ 0.95. We propose a class of supersymmetric hybrid inflation models based on the same minimal superpotential but with a non-minimal Kähler potential. Including radiative corrections using the one-loop effective potential, we show that the prediction for the spectral index is sensitive to the small non-minimal corrections, and can lead to a significantly red-tilted spectrum, in agreement with WMAP.

It has been persuasively argued that the number of effective degrees of freedom of a macroscopic system is proportional to its area rather than to its volume. This entails interesting consequences for cosmology. Here we present a model based on this 'holographic principle' that accounts for the present stage of accelerated expansion of the Universe and significantly alleviates the coincidence problem also for non-spatially flat cosmologies. Likewise, we comment on a recently proposed late transition to a fresh decelerated phase.

In this paper, I will present highlights of a recent model of dark energy and dark matter in which the present universe is 'trapped' in a false vacuum described by the potential of an axion-like scalar field (the acceleron) which is related to a new strong interaction gauge sector, SU(2)_Z, characterized by a scale Λ_Z ∼ 3 × 10⁻³ eV. This false vacuum model mimicks the ΛCDM scenario. In addition, there are several additional implications such as a new mechanism for leptogenesis coming from the decay of a 'messenger' scalar field, as well as a new model of 'low-scale' inflation whose inflaton is the 'radial' partner of the acceleron.

The models that unify dark matter and dark energy based upon the Chaplygin gas fail owing to the suppression of structure formation by the adiabatic speed of sound. Including string theory effects, in particular the Kalb–Ramond field, we show how nonadiabatic perturbations allow a successful structure formation.

The physical equivalence of Einstein and Jordan frames in scalar–tensor theories was explained by Dicke in 1962: they are related by a local transformation of units. We discuss this point in a cosmological framework. Our main result is the construction of a formalism in which all the physical observables are frame-invariant. The application of this approach to CMB codes is at present under analysis.

We analyse the direct detection of neutralino dark matter in the framework of the next-to-minimal supersymmetric standard model. Taking into account all the available constraints from LEPII and Tevatron, including bounds from the muon anomalous magnetic moment and flavour constraint as b → sγ, we compute the neutralino–nucleon cross section and compare the results with the sensitivity of dark matter detectors. We also study the relic abundance of neutralinos, comparing it with WMAP observations. We show that a light singlet-like Higgs can escape accelerator constraints allowing for scenarios with large cross sections and a very interesting phenomenology.

We generalize the adiabatic renormalization to theories with dispersion relations modified at energies higher than a new scale M_C. We obtain explicit expressions for the mean value of the stress tensor in the adiabatic vacuum, up to the second adiabatic order. We show that for any dispersion relation the divergences can be absorbed into the bare gravitational constants of the theory. We also point out that, depending on the renormalization prescription, the renormalized stress tensor may contain finite trans-Planckian corrections even in the limit M_C → ∞.

We study the quantum propagation of particles in cosmological backgrounds, by considering a doublet of massive scalar fields propagating in an expanding universe, possibly filled with radiation. We focus on the dissipative effects related to the expansion rate. At first order, we recover the expected result that the decay rate is determined by the local temperature. Beyond linear order, the decay rate has an additional contribution governed by the expansion parameter. This latter contribution is present even for stable particles in the vacuum. Finally, we analyse the long time behaviour of the propagator and briefly discuss applications to the trans-Planckian question.

The impact of finite temperature effects on axions in the context of cosmology is studied here for two interesting cases. We find that they may be significant for detailed and precise abundance and rate calculations of axions in the early universe.

It is quite plausible that colour superconductivity occurs in the inner regions of neutron stars. At the same time, it is known that strong magnetic fields exist in the interior of these compact objects. In this paper we discuss some important effects that can occur in the colour superconducting core of compact stars due to the presence of the stars' magnetic field. In particular, we consider the modification of the gluon dynamics for a colour superconductor with three massless quark flavours in the presence of an external magnetic field. We show that the long-range component of the external magnetic field that penetrates the colour-flavour locked phase produces an instability for field values larger than the charged gluons' Meissner mass. As a consequence, the ground state is restructured forming a vortex state characterized by the condensation of charged gluons and the creation of magnetic flux tubes. In the vortex state the magnetic field outside the flux tubes is equal to the applied one, while inside the tubes its strength increases by an amount that depends on the amplitude of the gluon condensate. This paramagnetic behaviour of the colour superconductor can be relevant for the physics of compact stars.

The dynamical system approach has recently acquired great importance in the investigation on higher order theories of gravity. In this talk I review some of the main results obtained with this method and I consider briefly a number of further developments.

We use nonequilibrium renormalization group (RG) techniques to analyse the thermalization process in quantum field theory, and, by extension, reheating after inflation. Even if at a high scale Λ the theory is described by a non-dissipative λφ⁴ theory, and the RG running induces nontrivial noise and dissipation. For long wavelength and slowly varying field configurations, the noise and dissipation are white and ohmic, respectively. The theory will then tend to thermalize to an effective temperature given by the fluctuation-dissipation theorem.

The coincidence problems and other dynamical features of dark energy are studied in cosmological models with variable cosmological parameters and in models with the composite dark energy. It is found that many of the problems usually considered to be cosmological coincidences can be explained or significantly alleviated in the aforementioned models.

Experimental evidence pointing to the late accelerated expansion of the Universe is often interpreted while assuming a particular dark energy model. We discuss a model-independent approach which relies on optimized estimates of the equation of state parameter at different redshift regions. In this context, recent supernova data favour the cosmological constant scenario over evolving dark energy. Furthermore, the apparent rapid variation in the equation of state parameter w appears to be a feature of certain datasets.

Two different realizations of a symmetry principle that impose a zero cosmological constant in an extra-dimensional set-up are studied. The symmetry is identified by multiplication of the metric by minus one. In the fist realization of the symmetry this is provided by a symmetry transformation that multiplies the coordinates by the imaginary number i. In the second realization this is accomplished by a symmetry transformation that multiplies the metric tensor by minus one. In both realizations of the symmetry the requirement of the invariance of the gravitational action under the symmetry selects out the dimensions given by D = 2(2n + 1), n = 0, 1, 2..., and forbids a bulk cosmological constant. Another attractive aspect of the symmetry is that it seems to be more promising for quantization when compared to the usual scale symmetry. The second realization of the symmetry principle is more attractive in that it is possible to make a possible brane cosmological constant zero in a simple way by using the same symmetry, and the symmetry may be identified by reflection symmetry in extra dimensions.

The leading order gravitational effect of nonlinear matter fluctuations in de Sitter spacetime is briefly analysed and it is found that the initial value problem for the perturbed Einstein equations possesses so-called linearization instabilities. Using previous results, I very briefly review how these linearization instabilities can be avoided by assuming strict de Sitter invariance of the quantum states of the linearized fluctuations. I then sketch how quantum anomalies do not block the invariance requirement. Finally, I explore tantalizing evidence that the same stringent symmetry requirement may also be present when gravitational wave backreactions are included.

In a 6D model, where the extra dimensions form a discretized curved disc, we investigate the mass spectra and profiles of gravitons and Dirac fermions. The discretization is performed in detail leading to a star-like geometry. In addition, we use the curvature of the disc to obtain the mass scales of this model in a more flexible way. We also discuss some applications of this setup such as generating small fermion masses.

We study Lagrangians with the minimal amount of gauge symmetry required to propagate spin-2 particles without ghosts or tachyons. In general, these Lagrangians also have a scalar mode in their spectrum. We find that, in two cases, the symmetry can be enhanced to a larger group: the whole group of diffeomorphisms or an enhancement involving a Weyl symmetry. We consider the nonlinear completions of these theories. The intuitive completions yield the usual scalar–tensor theories except for the pure spin-2 cases, which correspond to two inequivalent Lagrangians giving rise to Einstein's equations. A more constructive self-consistent approach yields a background-dependent Lagrangian.

The calculation of gravitational scattering of particles with various spin configurations in the framework of effective quantum field theory of general relativity is presented. We find that the long-range quantum and classical corrections to the spin-independent piece and the spin–orbit coupling piece of the scattering amplitude and the scattering potential are universal for different spin configurations, which leads us to propose this universality to be true for arbitrary spins. Furthermore, we give the leading corrections to the spin–spin coupling, and a comparison with scattering in QED is made.

We calculate dilaton and axion radiation generated in the collision of two straight initially unexcited strings and give a rough cosmological estimate of dilaton and axion densities produced via this mechanism in the early universe.

We investigate the effective action for a non-BPS brane in a time-dependent embedding. This action is considered as the action for tachyon and embedding coupled to the brane gravity. We derive the slow-roll parameters from this model.

We investigate the dynamics of Randall–Sundrum AdS₅ braneworlds with five-dimensional conformal matter fields. In the scenario with a compact fifth dimension the class of conformal fields with weight −4 is associated with exact five-dimensional warped geometries which are stable under radion field perturbations and describe on the brane the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytropic dark energy. We analyse the graviton mode fluctuations around this class of background solutions and determine their mass eigenvalues and wavefunctions from a Sturm–Liouville problem. We show that the localization of gravity is not sharp enough for large mass hierarchies to be generated. We also discuss the physical bounds imposed by experiments in particle physics, in astrophysics and in precise measurements of the low energy gravitational interaction.

In this talk we considered the Affleck–Dine mechanism with various types of the Kähler potential, and investigated whether or not the Affleck–Dine field could acquire a large VEV as an initial condition for successful baryogenesis. In addition to a negative Hubble-induced mass term, we found examples that large enough Hubble-induced A-terms could also develop the minima at a large amplitude of the field. It is concluded, therefore, that the Affleck–Dine mechanism works for broader classes of the theories. This talk is based on Kasuya and Kawasaki (2006 Phys. Rev. D 74 063507). Here I extend the discussion from a more generic standpoint, and find that essentially there are three cases that large enough A-terms develop minima at large field values.

We discuss a toy model where baryogenesis and cosmic acceleration are driven by a leptonic quintessence field coupled to the standard model sector via a massive mediating scalar field. It does not require the introduction of B–L-violating interactions below the inflationary scale. Instead, a B–L-asymmetry is stored in the quintessence field, which compensates for the corresponding observed baryon asymmetry.

A simple phenomenological description for the energy transfer between a variable cosmological constant (CC) and a gas of relic neutrinos in an expanding universe can account for a near coincidence between the neutrino and dark-energy densities to hold over a significant portion of the history of the universe. Although such a cosmological setup may promote neutrinos to mass-varying particles, both with slow and quick neutrino mass changing with the expansion of the universe naturally implemented in the model, it also works equally well for static neutrino masses. We also stress what sort of models for variable CC can potentially underpin the above scenario.

The aim of this paper is to give a basic introduction to deformation quantization (DQ) to physicists. We compare DQ to canonical quantization and path integral methods. It is described how certain issues such as the roles of associativity, coordinate invariance, dynamics and operator orderings are understood in the context of DQ. Convergence issues in DQ are mentioned. Additionally, we formulate the Klein–Gordon (KG) equation in DQ. Original results are discussed which include the exact construction of the Fedosov star-product on the dS and AdS spacetimes. Also, the KG equation is written down for these spacetimes.

We study a stationary 'black' brane in M/superstring theory. Assuming BPS-type relations between the first-order derivatives of metric functions, we present general stationary black brane solutions with a time-like Killing vector for the Einstein equations in D-dimensions. The solutions are given by a few independent harmonic equations (and plus the Poisson equation). General solutions are constructed by superposition of a complete set of those harmonic functions. Using the hyperspherical coordinate system, we explicitly give the solutions in 11-dimensional M theory for the case with M2⊥ M2⊥ M2 intersecting branes. Compactifying these solutions into five dimensions, we show that these solutions include the supersymmetric black ring solution. We prove that the solutions preserve the 1/8 supersymmetry if the gravi-electromagnetic field , which is a rotational part of gravity, is self-dual, or to add the additional constraint for the integral constants.

The combination of the Lorentz symmetry and the strong subadditive property of the entropy leads to a c-theorem for the entanglement entropy in (1+1) dimensions. We present a simple derivation of this theorem and compare the associated c-functions with the Zamolodchikov's ones for the case of free fields. We discuss the various difficulties which are obstacles to the naive generalizations of the entropic c-theorem to higher dimensions.

We study the spectrum of primordial fluctuations and the scale dependence of the inflaton spectral index due to self-interactions of the field. We compute the spectrum of fluctuations by applying nonequilibrium renormalization group techniques.

Quantum creation of the universe is described by the density matrix defined by the Euclidean path integral. This yields an ensemble of universes—a cosmological landscape—in a mixed quasi-thermal state which is shown to be dynamically more preferable than the pure quantum state of the Hartle–Hawking type. The latter is suppressed by the infinitely large positive action of its instanton, generated by the conformal anomaly of quantum matter. The Hartle–Hawking instantons can be regarded as posing initial conditions for Starobinsky solutions of the anomaly driven de Sitter expansion, which are thus dynamically eliminated by infrared effects of quantum gravity. The resulting landscape of hot universes treated within the cosmological bootstrap (the self-consistent back reaction of quantum matter) turns out to be limited to a bounded range of the cosmological constant, which rules out a well-known infrared catastrophe of the vanishing cosmological constant and suggests an ultimate solution to the problem of unboundedness of the cosmological action in Euclidean quantum gravity.

Actions governing the dynamics of the Nambu–Goldstone modes resulting from the spontaneous breaking of the SO(4, 2) and SU(2, 2|1) isometries of five-dimensional anti-de Sitter space (AdS₅) and SUSY AdS₅ × S₁ spaces, respectively, due to a restriction of the motion to embedded four-dimensional AdS₄ space and four-dimensional Minkowski space (M₄) probe branes are presented. The dilatonic Nambu–Goldstone mode governing the motion of the M₄ space probe brane into the covolume of the SUSY AdS₅ × S₁ space is found to be unstable. No such instability appears in the other cases. Gauging these symmetries leads to an Einstein–Hilbert action containing, in addition to the gravitational vierbein, a massive Abelian vector field coupled to gravity.

We consider a multigravity approach to spacetime foam. As an application we give indications on the computation of the cosmological constant, considered as an eigenvalue of a Sturm–Liouville problem. A variational approach with Gaussian trial wavefunctionals is used as a method to study such a problem. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of the Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.

Recently, attention has been given to modified gravity models, as they may represent alternatives to quintessence models for an explanation to today's acceleration of the universe. We review the main results developed in De Felice, Hindmarsh and Trodden (2006 J. Cosmol. Astropart. Phys. JCAP08(2006)005 (Preprint astro-ph/0604154)) and Calcagni, de Carlos and De Felice (2006 Nucl. Phys. B (Preprint hep-th/0604201)), where we showed that those theories that involve a coupling between a scalar field with the Gauss–Bonnet curvature combination, in general possess both ghosts degrees of freedom and classical instabilities. We believe these constraints put severe bounds on these types of modifications of gravity. We add a critical assessment of the present understanding of these bounds.

We consider the linearized nonsymmetric theory of gravitation (NGT) within the background of an expanding universe and near a Schwarzschild mass. We show that the theory always develops instabilities unless the linearized nonsymmetric Lagrangian reduces to a particular simple form. This form contains a gauge-invariant kinetic term, a mass term for the anti-symmetric metric field and a coupling with the Ricci curvature scalar. This form cannot be obtained within NGT. Based on the linearized Lagrangian we know to be stable, we consider the generation and evolution of quantum fluctuations of the anti-symmetric gravitational field (B-field) from inflation up to the present day. We find that a B-field with a mass m ∝ 0.03(H_I/10¹³ GeV)⁴ eV is an excellent dark matter candidate.

The quantum fluctuations of a black hole spacetime are studied within a low-energy effective field theory approach to quantum gravity. Our approach accounts for both intrinsic metric fluctuations and those induced by matter fields interacting with the gravitational field. Here we will concentrate on spherically symmetric fluctuations of the black hole horizon. Our results suggest that for a sufficiently massive evaporating black hole, fluctuations can accumulate over time and become significant well before reaching Planckian scales. In addition, we provide the sketch of a proof that the symmetrized two-point function of the stress-tensor operator smeared over a null hypersurface is actually divergent and discuss the implications for the analysis of horizon fluctuations. Finally, a natural way to probe quantum metric fluctuations near the horizon is briefly described.

We present a model based on the idea that Planck-scale effects may produce a small explicit breaking of global symmetries. The model contains a new complex scalar field Ψ, charged under a certain global U(1) symmetry, interacting with a new real scalar field χ, neutral under U(1). For exponentially small breaking, the model accounts for both early and late periods of acceleration of the universe.

Cooperstock and Tieu proposed a model of galaxy, based on ordinary GR, in which no exotic dark matter is needed to explain the flat rotation curves in galaxies. I will present the arguments against this model. In particular, I will show that in their model the gravitational field is generated not only by the ordinary matter distribution, but by a infinitely thin, massive and rotating disc as well. This is a serious and incurable flaw and makes the Cooperstock–Tieu metric unphysical as a galaxy model.

Precise knowledge of the atmospheric neutrino fluxes is a key ingredient in the interpretation of the results from any atmospheric neutrino experiment. In the standard atmospheric neutrino data analysis, these fluxes are theoretical inputs obtained from sophisticated numerical calculations. In this contribution, we present an alternative approach to the determination of the atmospheric neutrino fluxes based on the direct extraction from the experimental data on neutrino event rates. The extraction is achieved by means of a combination of artificial neural networks as interpolants and Monte Carlo methods.

The consideration of dark energy's quanta, required also by thermodynamics, introduces its chemical potential into the cosmological equations. Isolating its main contribution, we obtain solutions with dark energy decaying to matter or radiation. When dominant, their energy densities tend asymptotically to a constant ratio, explaining today's dark-energy–dark-matter coincidence, and in agreement with supernova redshift data.

A light scalar field, minimally or not-minimally coupled to the metric field, is a well-defined candidate for the dark energy, alleviating the fine-tuning problem intrinsic to the cosmological constant and avoiding the difficulties of parameterizations. We present a general description of the weak gravitational lensing valid for every metric theory of gravity, including vector and tensor perturbations for a non-flat spatial metric. Based on this description, we investigate two minimally coupled scalar-field quintessence models using VIRMOS-Descart and CFHTLS cosmic-shear data, and forecast the constraints for the proposed space-borne wide-field imager DUNE.

If inflation was preceded by a thermal era, then there will be a thermal distribution of gravitons at the time of inflation. Gravitons produced during inflation will be amplified by stimulated emission into the existing thermal gravitons. This will result in an enhancement of the B-mode signal at large angles and which could be observable in WMAP and Planck experiments. Non-observation of this signal will have important implications on standard inflation models and will rule out warm inflation.

We investigated a simple D-term inflation by taking into account higher order corrections in the potential, particularly, in the Kähler potential. These terms make an inflationary potential flatter than logarithmic in the case without these higher correction terms, through one-loop radiative corrections. As a result, the mass per unit length of cosmic strings formed after inflation can be suppressed and its corresponding Gμ is several ×10⁻⁷. In addition, the change of the potential slope simultaneously leads to a more tilted scalar spectral index n_s ≃ 0.96–0.97 than that in the model without these corrections n_s ≃ 0.98.