Table of contents

This paper gives a brief overview of some of the theory behind inflationary cosmology, and discusses prospects for constraining inflation using observations. Particular care is given to the question of falsifiability of inflation or of subsets of inflationary models.

I discuss cosmological models either derived from, or inspired by, string theory or M-theory. In particular, I discuss solutions in the low-energy effective theory and the role of the dilaton, moduli and antisymmetric form fields in the dimensionally reduced effective action. The pre-big-bang model is an attempt to use cosmological solutions to make observational predictions. I then discuss the effective theory of gravity found in recent braneworld models where we live on a 3-brane embedded in a five-dimensional spacetime and how the study of cosmological perturbations may enable us to test these ideas.

This paper gives a brief qualitative description of the possible evolution of the early universe between the end of an inflationary epoch and the end of big-bang nucleosynthesis. After a general introduction, establishing the minimum requirements cosmologists impose on this cosmic evolutionary phase, namely, successful baryogenesis, the production of cosmic dark matter and successful light-element nucleosynthesis, a more detailed discussion on some recent developments follows. This latter includes the physics of preheating, the putative production of (alternative) dark matter and the current status of big bang nucleosynthesis.

I briefly review the cosmological constant problem and the issue of dark energy (or quintessence). Within the framework of quantum field theory, the vacuum expectation value of the energy momentum tensor formally diverges as k⁴. A cutoff at the Planck or electroweak scale leads to a cosmological constant which is, respectively, 10¹²³ or 10⁵⁵ times larger than the observed value, Λ/8πG ≃ 10⁻⁴⁷ GeV⁴. The absence of a fundamental symmetry which could set the value of Λ to either zero or a very small value leads to the cosmological constant problem. Most cosmological scenarios favour a large time-dependent Λ-term in the past (in order to generate inflation at z ≫ 10¹⁰), and a small Λ-term today, to account for the current acceleration of the universe at z ≲ 1. Constraints arising from cosmological nucleosynthesis, CMB and structure formation constrain Λ to be sub-dominant during most of the intermediate epoch 10¹⁰ < z < 1. This leads to the cosmic coincidence conundrum which suggests that the acceleration of the universe is a recent phenomenon and that we live during a special epoch when the density in Λ and in matter are almost equal. Time varying models of dark energy can, to a certain extent, ameliorate the fine-tuning problem (faced by Λ), but do not resolve the puzzle of cosmic coincidence. I briefly review tracker models of dark energy, as well as more recent brane inspired ideas and the issue of horizons in an accelerating universe. Model independent methods which reconstruct the cosmic equation of state from supernova observations are also assessed. Finally, a new diagnostic of dark energy—statefinder— is discussed.

The theory of cosmic inflation offers an attractive resolution of some of the great paradoxes in cosmology: why the universe is so large, flat and uniform on large scales, and how density variations arose. Inflation has rightly dominated cosmological thinking for the past two decades, helping stimulate the development of high-precision observational programmes. The survival of simple inflationary models in the face of an impressive observational onslaught has been interpreted as convincing evidence of the correctness of the basic idea. In this paper, I review inflation, but highlight its weaknesses, explaining my reasons for believing that a more complete theory may supersede inflation without necessarily incorporating it.

The aim of this paper is to give a brief survey of the current state of cosmic microwave background experiments and results. The effects of systematics and experimental uncertainties are emphasized and a summary of our current knowledge of cosmological parameters is given, using the latest data. Some future experiments are also discussed.

Over the past five years two teams have used type Ia supernovae to trace the expansion of the universe to a look-back time more than 70% of the age of the universe. These observations show an accelerating universe which is best explained by a cosmological constant, or other form of dark energy with an equation of state near w = p/ρ = −1. There are many possible lurking systematic effects. However, while difficult to completely eliminate, none of these appears large enough to challenge current results. However, as future experiments attempt to better characterize the equation of state of the matter leading to the observed acceleration, these systematic effects will ultimately limit progress.

We present the current status of cosmological weak lensing studies. Theoretical expectations and observational results are discussed in the framework of standard cosmology and CDM scenarios. We show that present-day surveys already provide important clues and new constraints on cosmological parameters and on the biasing. Finally, the potentials of the next generation cosmic shear surveys are discussed.

Observational tests for the cosmological principle are reviewed. Assuming the FRW metric we then summarize estimates of cosmological parameters from various datasets, in particular the cosmic microwave background and the 2dF galaxy redshift survey. These and other analyses suggest a best-fit Λ-cold dark matter model with Ω_m = 1 − Ω_l ≈ 0.3 and H₀ ≈ 70 km s⁻¹ Mpc⁻¹. It is remarkable that different measurements converge to this 'concordance model', although it remains to be seen if the two main components of this model, the dark matter and the dark energy, are real entities or just 'epicycles'. We point out some open questions related to this fashionable model.

The purpose of this paper is to give a brief account of what we hope to learn from the future CMB experiments, essentially from the point of view of primordial cosmology. After recalling what we have already learnt, the principles of parameter extraction from the data are summarized. The discussion is then devoted to the information we could gain about the early universe in the framework of the inflationary scenario or in more exotic scenarios such as brane cosmology.

I describe some of the principal landmarks coming up in the medium to long term future of observational extragalactic astronomy. Rather than attempting to compile an exhaustive catalogue, I have instead made a completely biased sample of some of the developments across the electromagnetic spectrum (including x-ray, optical, infra-red, submillimetre and radio) that seemed most exciting to me. Among the 'greatest hits' I have picked are XEUS, GAIA, NGST, OWL, ALMA and SKA.

Issues related to bringing together the principles of general relativity and quantum theory are discussed. After briefly summarizing the points of conflict between the two formalisms I focus on four specific themes in which some contact has been established in the past between general relativity and quantum field theory: (i) the role of the Planck length in the microstructure of spacetime, (ii) the role of quantum effects in cosmology and the origin of the universe, (iii) the thermodynamics of spacetimes with horizons, and especially the concept of entropy related to spacetime geometry, (iv) the problem of the cosmological constant.

Cosmology has come of age as an observational science, based on the tremendous progress in satellite- and ground-based experiments that measure the vital statistics of our universe. Perhaps the most dramatic advances have come in observations of the cosmic microwave background radiation, but there have also been major developments in galaxy surveys and supernovae observations. A new era of high-precision cosmology has dawned, and we can expect further major advances in our observational knowledge of the universe. This has raised difficult but exciting challenges for cosmological theory, which is struggling to keep pace with observational advances. In this context, it is clearly useful to provide opportunities for observational and theoretical developments to be brought together and critically reviewed.

This was the motivation for the conference The Early Universe and Cosmological Observations: a Critical Review, which was organized as a follow-on meeting after GR16, the triennial conference of the International Society of General Relativity and Gravitation (held in Durban, South Africa, July 2001). The meeting reviewed current theoretical models of the early universe and the observational tests of such models. Starting with summaries of the major achievements of the standard model of cosmology and the impact of the tremendous growth in cosmological data, the meeting then turned its attention to open issues and what still needs to be done in these areas. This was followed by a critical review of the subject, highlighting unresolved problems and some of the more fundamental issues which inevitably underlie the relation of theory to observation. The scientific organizing committee (B Bassett, B Carter, T Damour, P Dunsby, G Ellis, R Maartens and N Turok) also attempted to design the conference so as to maximize open discussion and interaction between participants.

The conference programme was divided into three parts.

(a) Theoretical models of the early universe

Inflationary cosmology: theory and phenomenology A Liddle String-inspired cosmology D Wands From (p)reheating to nucleosynthesis K Jedamzik The cosmological constant problem and quintessence V Sahni Critical review of inflation N Turok Panel discussion: Braneworld cosmology - is it here to stay? N Deruelle, R Maartens and J-P Uzan

(b) Observational tests of early universe models

CMB anisotropies: recent measurements and interpretation A Lasenby Measuring global curvature and cosmic acceleration with supernovae B Schmidt Cosmological weak lensing Y Mellier Observational tests of FRW world models O Lahav Large galaxy surveys D Schlegel Dark matter: theories and observation N Turok

(c) Fundamental open questions: the future

How much will we learn from the CMB? D Langlois The future of extragalactic observations P Coles The future of large-scale structure studies J Frieman Combining general relativity and quantum theory T Padmanabhan Panel discussion: The nature of cosmology - critical reflections N Deruelle, J Ehlers, G Ellis and M MacCallum

This issue of Classical and Quantum Gravity contains nearly all of the plenary talks of the conference. The panel discussion on braneworld cosmology reflected the strong impact on cosmology of recent ideas emerging from string theory/M theory. In braneworld models, the observable universe is a 3-space (the `brane') moving in a higher-dimensional spacetime (the `bulk'), where the extra spatial dimensions are not all necessarily small or even compact. Standard model matter is confined to the brane, but gravity propagates in the bulk. The panellists emphasized that, whether or not the braneworld models survive in the longer term, they are useful to investigate, since they can give a qualitative insight into how M theory affects the dynamics of the universe. Furthermore, in a similar way to inflationary models, braneworld models develop the synergy between cosmology and particle physics.

The closing panel discussion on the nature of cosmology considered several questions arising from the more geometric approach to general relativity. Many of these points are summarized in the article Comments: Cosmology, 2001 by G Ellis at the end of this issue.

The conference was attended by more than 70 local and international researchers and students from about 10 countries. It was hosted by the Cosmology research group at the University of Cape Town, and held from 23 to 25 July 2001. Financial support was provided by the National Research Foundation of South Africa, the University of Cape Town Research Committee, ICTP (Trieste) and the French Embassy. The interest and generosity of these institutions is gratefully acknowledged. All participants will join us in thanking the local organizing committee, and especially D Loureiro, for their great efforts and excellent organization.

Peter Dunsby and George EllisUniversity of Cape Town, South Africa

Roy MaartensUniversity of Portsmouth, UK