We investigate a model that modifies general relativity on cosmological scales, specifically by having a `glitch' in the gravitational constant between the cosmological (super-horizon) and Newtonian (sub-horizon) regimes, as motivated e.g. in the Hořava-Lifshitz proposal or in the Einstein-aether framework. This gives a single-parameter extension to the standard ΛCDM model, which is equivalent to adding a dark energy component, but where the energy density of this component can have either sign. Fitting to data from the Planck satellite, we find that negative contributions are, in fact, preferred. Additionally, we find that roughly one percent weaker superhorizon gravity can somewhat ease the Hubble and clustering tensions in a range of cosmological observations, although at the expense of spoiling fits to the baryonic acoustic oscillation scale in galaxy surveys. Therefore, the extra parametric freedom offered by our model deserves further exploration, and we discuss how future observations may elucidate this potential cosmic glitch in gravity, through a four-fold reduction in statistical uncertainties.
The International School for Advanced Studies (SISSA) was founded in 1978 and was the first institution in Italy to promote post-graduate courses leading to a Doctor Philosophiae (or PhD) degree. A centre of excellence among Italian and international universities, the school has around 65 teachers, 100 post docs and 245 PhD students, and is located in Trieste, in a campus of more than 10 hectares with wonderful views over the Gulf of Trieste.
SISSA hosts a very high-ranking, large and multidisciplinary scientific research output. The scientific papers produced by its researchers are published in high impact factor, well-known international journals, and in many cases in the world's most prestigious scientific journals such as Nature and Science. Over 900 students have so far started their careers in the field of mathematics, physics and neuroscience research at SISSA.
ISSN: 1475-7516
Journal of Cosmology and Astroparticle Physics (JCAP) covers all aspects of cosmology and particle astrophysics and encompasses theoretical, observational and experimental areas as well as computation and simulation. An electronic-only journal, JCAP is jointly owned by IOP Publishing and SISSA.
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Nicole F. Bell et al JCAP04(2024)006
The capture of dark matter, and its subsequent annihilation, can heat old, isolated neutron stars. In order for kinetic heating to be achieved, the captured dark matter must undergo sufficient scattering to deposit its kinetic energy in the star. We find that this energy deposit typically occurs quickly, for most of the relevant parameter space. In order for appreciable annihilation heating to also be achieved, the dark matter must reach a state of capture-annihilation equilibrium in the star. We show that this can be fulfilled for all types of dark matter-baryon interactions. This includes cases where the scattering or annihilation cross sections are momentum or velocity suppressed in the non-relativistic limit. Importantly, we find that capture-annihilation equilibrium, and hence maximal annihilation heating, can be achieved without complete thermalization of the captured dark matter. For scattering cross sections that saturate the capture rate, we find that capture-annihilation equilibrium is typically reached on a timescale of less than 1 year for vector interactions and 104 years for scalar interactions.
Marco Cirelli et al JCAP03(2011)051
We provide ingredients and recipes for computing signals of TeV-scale Dark Matter annihilations and decays in the Galaxy and beyond. For each DM channel, we present the energy spectra of at production, computed by high-statistics simulations. We estimate the Monte Carlo uncertainty by comparing the results yielded by the Pythia and Herwig event generators. We then provide the propagation functions for charged particles in the Galaxy, for several DM distribution profiles and sets of propagation parameters. Propagation of e± is performed with an improved semi-analytic method that takes into account position-dependent energy losses in the Milky Way. Using such propagation functions, we compute the energy spectra of e±, and at the location of the Earth. We then present the gamma ray fluxes, both from prompt emission and from Inverse Compton scattering in the galactic halo. Finally, we provide the spectra of extragalactic gamma rays. All results areavailable in numerical form and ready to be consumed.
J. Ambjørn and Y. Watabiki JCAP12(2023)011
We show that by allowing our Universe to merge with other universes one is lead to modified Friedmann equations that explain the present accelerated expansion of our Universe without the need of a cosmological constant.
Peter Ade et al JCAP02(2019)056
The Simons Observatory (SO) is a new cosmic microwave background experiment being built on Cerro Toco in Chile, due to begin observations in the early 2020s. We describe the scientific goals of the experiment, motivate the design, and forecast its performance. SO will measure the temperature and polarization anisotropy of the cosmic microwave background in six frequency bands centered at: 27, 39, 93, 145, 225 and 280 GHz. The initial configuration of SO will have three small-aperture 0.5-m telescopes and one large-aperture 6-m telescope, with a total of 60,000 cryogenic bolometers. Our key science goals are to characterize the primordial perturbations, measure the number of relativistic species and the mass of neutrinos, test for deviations from a cosmological constant, improve our understanding of galaxy evolution, and constrain the duration of reionization. The small aperture telescopes will target the largest angular scales observable from Chile, mapping ≈ 10% of the sky to a white noise level of 2 μK-arcmin in combined 93 and 145 GHz bands, to measure the primordial tensor-to-scalar ratio, r, at a target level of σ(r)=0.003. The large aperture telescope will map ≈ 40% of the sky at arcminute angular resolution to an expected white noise level of 6 μK-arcmin in combined 93 and 145 GHz bands, overlapping with the majority of the Large Synoptic Survey Telescope sky region and partially with the Dark Energy Spectroscopic Instrument. With up to an order of magnitude lower polarization noise than maps from the Planck satellite, the high-resolution sky maps will constrain cosmological parameters derived from the damping tail, gravitational lensing of the microwave background, the primordial bispectrum, and the thermal and kinematic Sunyaev-Zel'dovich effects, and will aid in delensing the large-angle polarization signal to measure the tensor-to-scalar ratio. The survey will also provide a legacy catalog of 16,000 galaxy clusters and more than 20,000 extragalactic sources.
Wendy L. Freedman and Barry F. Madore JCAP11(2023)050
One of the most exciting and pressing issues in cosmology today is the discrepancy between some measurements of the local Hubble constant and other values of the expansion rate inferred from the observed temperature and polarization fluctuations in the cosmic microwave background (CMB) radiation. Resolving these differences holds the potential for the discovery of new physics beyond the standard model of cosmology: Lambda Cold Dark Matter (ΛCDM), a successful model that has been in place for more than 20 years. Given both the fundamental significance of this outstanding discrepancy, and the many-decades-long effort to increase the accuracy of the extragalactic distance scale, it is critical to demonstrate that the local measurements are convincingly free from residual systematic errors. We review the progress over the past quarter century in measurements of the local value of the Hubble constant, and discuss remaining challenges. Particularly exciting are new data from the James Webb Space Telescope (JWST), for which we present an overview of our program and first results. We focus in particular on Cepheids and the Tip of the Red Giant Branch (TRGB) stars, as well as a relatively new method, the JAGB (J-Region Asymptotic Giant Branch) method, all methods that currently exhibit the demonstrably smallest statistical and systematic uncertainties. JWST is delivering high-resolution near-infrared imaging data to both test for and to address directly several of the systematic uncertainties that have historically limited the accuracy of extragalactic distance scale measurements (e.g., the dimming effects of interstellar dust, chemical composition differences in the atmospheres of stars, and the crowding and blending of Cepheids contaminated by nearby previously unresolved stars). For the first galaxy in our program, NGC 7250, the high-resolution JWST images demonstrate that many of the Cepheids observed with the Hubble Space Telescope (HST) are significantly crowded by nearby neighbors. Avoiding the more significantly crowded variables, the scatter in the JWST near-infrared (NIR) Cepheid PL relation is decreased by a factor of two compared to those from HST, illustrating the power of JWST for improvements to local measurements of H0. Ultimately, these data will either confirm the standard model, or provide robust evidence for the inclusion of additional new physics.
Marica Branchesi et al JCAP07(2023)068
The Einstein Telescope (ET), the European project for a third-generation gravitational-wave detector, has a reference configuration based on a triangular shape consisting of three nested detectors with 10 km arms, where each detector has a 'xylophone' configuration made of an interferometer tuned toward high frequencies, and an interferometer tuned toward low frequencies and working at cryogenic temperature. Here, we examine the scientific perspectives under possible variations of this reference design. We perform a detailed evaluation of the science case for a single triangular geometry observatory, and we compare it with the results obtained for a network of two L-shaped detectors (either parallel or misaligned) located in Europe, considering different choices of arm-length for both the triangle and the 2L geometries. We also study how the science output changes in the absence of the low-frequency instrument, both for the triangle and the 2L configurations. We examine a broad class of simple 'metrics' that quantify the science output, related to compact binary coalescences, multi-messenger astronomy and stochastic backgrounds, and we then examine the impact of different detector designs on a more specific set of scientific objectives.
Simone Aiola et al JCAP12(2020)047
We present new arcminute-resolution maps of the Cosmic Microwave Background temperature and polarization anisotropy from the Atacama Cosmology Telescope, using data taken from 2013–2016 at 98 and 150 GHz. The maps cover more than 17,000 deg2, the deepest 600 deg2 with noise levels below 10μK-arcmin. We use the power spectrum derived from almost 6,000 deg2 of these maps to constrain cosmology. The ACT data enable a measurement of the angular scale of features in both the divergence-like polarization and the temperature anisotropy, tracing both the velocity and density at last-scattering. From these one can derive the distance to the last-scattering surface and thus infer the local expansion rate, H0. By combining ACT data with large-scale information from WMAP we measure H0=67.6± 1.1 km/s/Mpc, at 68% confidence, in excellent agreement with the independently-measured Planck satellite estimate (from ACT alone we find H0=67.9± 1.5 km/s/Mpc). The ΛCDM model provides a good fit to the ACT data, and we find no evidence for deviations: both the spatial curvature, and the departure from the standard lensing signal in the spectrum, are zero to within 1σ; the number of relativistic species, the primordial Helium fraction, and the running of the spectral index are consistent with ΛCDM predictions to within 1.5–2.2σ. We compare ACT, WMAP, and Planck at the parameter level and find good consistency; we investigate how the constraints on the correlated spectral index and baryon density parameters readjust when adding CMB large-scale information that ACT does not measure. The DR4 products presented here will be publicly released on the NASA Legacy Archive for Microwave Background Data Analysis.
A. Abdul Halim et al JCAP01(2024)022
The combined fit of the measured energy spectrum and shower maximum depth distributions of ultra-high-energy cosmic rays is known to constrain the parameters of astrophysical models with homogeneous source distributions. Studies of the distribution of the cosmic-ray arrival directions show a better agreement with models in which a fraction of the flux is non-isotropic and associated with the nearby radio galaxy Centaurus A or with catalogs such as that of starburst galaxies. Here, we present a novel combination of both analyses by a simultaneous fit of arrival directions, energy spectrum, and composition data measured at the Pierre Auger Observatory. The model takes into account a rigidity-dependent magnetic field blurring and an energy-dependent evolution of the catalog contribution shaped by interactions during propagation. We find that a model containing a flux contribution from the starburst galaxy catalog of around 20% at 40 EeV with a magnetic field blurring of around 20° for a rigidity of 10 EV provides a fair simultaneous description of all three observables. The starburst galaxy model is favored with a significance of 4.5σ (considering experimental systematic effects) compared to a reference model with only homogeneously distributed background sources. By investigating a scenario with Centaurus A as a single source in combination with the homogeneous background, we confirm that this region of the sky provides the dominant contribution to the observed anisotropy signal. Models containing a catalog of jetted active galactic nuclei whose flux scales with the γ-ray emission are, however, disfavored as they cannot adequately describe the measured arrival directions.
P.S. Bhupal Dev et al JCAP04(2024)045
We study the full-sky distribution of the radio emission from the stimulated decay of axions which are assumed to compose the dark matter in the Galaxy. Besides the constant extragalactic and CMB components, the decays are stimulated by a Galactic radio emission with a spatial distribution that we empirically determine from observations. We compare the diffuse emission to the counterimages of the brightest supernovæ remnants, and take into account the effects of free-free absorption. We show that, if the dark matter halo is described by a cuspy NFW profile, the expected signal from the Galactic center is the strongest. Interestingly, the emission from the Galactic anti-center provides competitive constraints that do not depend on assumptions on the uncertain dark matter density in the inner region. Furthermore, the anti-center of the Galaxy is the brightest spot if the Galactic dark matter density follows a cored profile. The expected signal from stimulated decays of axions of mass ma ∼ 10-6 eV is within reach of the Square Kilometer Array for an axion-photon coupling gaγ ≳ (2-3) × 10-11 GeV-1.
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Zhi-Qiang You et al JCAP05(2024)031
Peculiar velocity encodes rich information about the formation, dynamics, evolution, and merging history of binary black holes. In this work, we employ a hierarchical Bayesian model to infer the peculiar velocity distribution of binary black holes. We use the data from GWTC-3 and assume a Maxwell-Boltzmann distribution for the peculiar velocities, but do not consider the dependence of peculiar velocity on the masses of black hole binaries. The constraint on the peculiar velocity distribution parameter, v0, is weak and uninformative. However, the determination of peculiar velocity distribution can be significantly improved with next-generation ground-based gravitational wave detectors. For the Einstein Telescope, the relative uncertainty of v0 will reduce to ∼ 10% using 103 golden binary black hole events. Our statistical approach thus provides a robust and prospective inference for determining the peculiar velocity distribution.
Zhenyu Zhang et al JCAP05(2024)032
Based on the horizon-scale magnetofluid model developed in [1], we investigate the millimeter-wave images of a geometrically thick accretion disk or a funnel wall, i.e., the magnetofluid that encloses the base of the jet region, around a Kerr black hole. By employing the numerical method to solve the null geodesic and radiative transfer equations, we obtain the optical appearances at various observational angles and frequencies, generated by the thermal synchrotron radiation within the magnetofluid. For the thick disk, we specifically examine the impact of emission anisotropy on images, concluding that anisotropic synchrotron radiation could play an important role in the observability of the photon ring. For the funnel wall, we find that both the outflow and inflow funnel walls exhibit annular structures on the imaging plane. The outflow funnel wall yields a brighter primary image than the photon ring, whereas the inflow one does not. Based on our investigation, the inflow funnel wall model can not be ruled out by current observations of M87*.
Trupti Patil et al JCAP05(2024)033
We do a detailed analysis of a well-theoretically motivated interacting dark energy scalar field model with a time-varying interaction term. Using current cosmological datasets from CMB, BAO, Type Ia Supernova, H(z) measurements from cosmic chronometers, angular diameter measurements from Megamasers, growth measurements, and local SH0ES measurements, we found that dark energy component may act differently than a cosmological constant at early times. The observational data also does not disfavor a small interaction between dark energy and dark matter at late times. When using all these datasets in combination, our value of H0 agrees well with SH0ES results but in 2.5σ tension with Planck results. We also did AIC and BIC analysis, and we found that the cosmological data prefer coupled quintessence model over ΛCDM, although the chi-square per number of degrees of freedom test prefers the latter.
G. Zagatti et al JCAP05(2024)034
Cosmic birefringence is the in-vacuo, frequency independent rotation of the polarization plane of linearly polarized radiation, induced by a parity-violating term in the electromagnetic Lagrangian. We implement a harmonic estimator for the birefringence field that only relies on the CMB E to B mode cross-correlation, thus suppressing the effect of cosmic variance from the temperature field. We derive constraints from Planck public releases 3 and 4, revealing a cosmic birefringence power spectrum consistent with zero at about 2σ up to multipole L = 1500. Moreover, we find that the cross-correlations of cosmic birefringence with the CMB T-, E- and B-fields are also well compatible with null. The latter two cross-correlations are provided here for the first time up to L = 1500.
Virgile Dandoy et al JCAP05(2024)035
Dark matter direct (and indirect) detection experiments usually can only determine a specific combination of a power of the coupling and the dark matter density. This is also true for axion haloscopes which are sensitive to the product g2aγγρDM, the combination of axion-photon coupling squared and the dark matter density. In this note we show, that in the lucky case when we intersect with a so-called axion minicluster of a suitable size, we can utilize the spectral information available in haloscopes to determine the gravitational potential of the minicluster. We can then use this to measure separately the coupling and the density of the minicluster.
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Trupti Patil et al JCAP05(2024)033
We do a detailed analysis of a well-theoretically motivated interacting dark energy scalar field model with a time-varying interaction term. Using current cosmological datasets from CMB, BAO, Type Ia Supernova, H(z) measurements from cosmic chronometers, angular diameter measurements from Megamasers, growth measurements, and local SH0ES measurements, we found that dark energy component may act differently than a cosmological constant at early times. The observational data also does not disfavor a small interaction between dark energy and dark matter at late times. When using all these datasets in combination, our value of H0 agrees well with SH0ES results but in 2.5σ tension with Planck results. We also did AIC and BIC analysis, and we found that the cosmological data prefer coupled quintessence model over ΛCDM, although the chi-square per number of degrees of freedom test prefers the latter.
G. Zagatti et al JCAP05(2024)034
Cosmic birefringence is the in-vacuo, frequency independent rotation of the polarization plane of linearly polarized radiation, induced by a parity-violating term in the electromagnetic Lagrangian. We implement a harmonic estimator for the birefringence field that only relies on the CMB E to B mode cross-correlation, thus suppressing the effect of cosmic variance from the temperature field. We derive constraints from Planck public releases 3 and 4, revealing a cosmic birefringence power spectrum consistent with zero at about 2σ up to multipole L = 1500. Moreover, we find that the cross-correlations of cosmic birefringence with the CMB T-, E- and B-fields are also well compatible with null. The latter two cross-correlations are provided here for the first time up to L = 1500.
Bin Xu and Wei Xue JCAP05(2024)038
We present a semiclassical non-perturbative approach for calculating the preheating process at the end of inflation. Our method involves integrating out the decayed particles within the path integral framework and subsequently determining world-line instanton solutions in the effective action. This enables us to obtain the effective action of the inflaton, with its imaginary part linked to the phenomenon of particle creation driven by coherent inflaton field oscillations. Additionally, we utilize the Bogoliubov transformation to investigate the evolution of particle density within the medium after multiple inflaton oscillations. We apply our approach to various final state particles, including scalar fields, tachyonic fields, and gauge fields. The non-perturbative approach provides analytical results for preheating that are in accord with previous methods.
Pablo Martínez-Miravé et al JCAP05(2024)002
The large distances travelled by neutrinos emitted from the Sun and core-collapse supernovae together with the characteristic energy of such neutrinos provide ideal conditions to probe their lifetime, when the decay products evade detection. We investigate the prospects of probing invisible neutrino decay capitalising on the detection of solar and supernova neutrinos as well as the diffuse supernova neutrino background (DSNB) in the next-generation neutrino observatories Hyper-Kamiokande, DUNE, JUNO, DARWIN, and RES-NOVA. We find that future solar neutrino data will be sensitive to values of the lifetime-to-mass ratio τ1/m1 and τ2/m2 of (10-1–10-2) s/eV. From a core-collapse supernova explosion at 10 kpc, lifetime-to-mass ratios of the three mass eigenstates of (105) s/eV could be tested. After 20 years of data taking, the DSNB would extend the sensitivity reach of τ1/m1 to 108 s/eV. These results promise an improvement of about 6–15 orders of magnitude on the values of the decay parameters with respect to existing limits.
Sveva Castello et al JCAP05(2024)003
Upcoming galaxy surveys provide the necessary sensitivity to measure gravitational redshift, a general relativistic effect that generates a dipole in galaxy clustering data when correlating two distinct populations of galaxies. Here, we study the constraining power of gravitational redshift within the framework of the effective theory of interacting dark energy. This formalism describes linear cosmological perturbations in scalar-tensor theories of gravity with a limited number of free functions, and allows each particle species to be coupled differently to the gravitational sector. In this work, we focus on Horndeski theories with a non-minimal coupling of dark matter to the scalar degree of freedom, yielding a breaking of the weak equivalence principle for this cosmic component, a scenario that is yet untested. We show that the dipole generated by gravitational redshift significantly breaks degeneracies and tightens the constraints on the parameters of the effective theory compared to the standard redshift-space distortion analysis solely based on the even multipoles in the galaxy correlation function, with an improvement of up to ∼ 50% for populations with a galaxy bias difference equal to 1. We make the Python package EF-TIGRE (Effective Field Theory of Interacting dark energy with Gravitational REdshift) developed for this work publicly available (https://github.com/Mik3M4n/EF-TIGRE).
Hyat Huang et al JCAP05(2024)007
A beyond Horndeski theory is considered that admits wormholes, black holes and naked singularities. In this theory the shadow images of the black holes and the exotic compact objects (ECOs), illuminated by an optically and geometrically thin disk, are investigated. The results show that the three kinds of objects cast unlike shadow images, in particular, because the different objects possess a different number of light rings. The different boundaries of the accretion disk also affect the images. This may provide further insight into the nature of the shadow images of massive compact objects.
Giovanni Antinozzi et al JCAP05(2024)017
We present a forecast for the upcoming Einstein Telescope (ET) interferometer with two new methods to infer cosmological parameters. We consider the emission of Gravitational Waves (GWs) from compact binary coalescences, whose electromagnetic counterpart is missing, namely Dark Sirens events. Most of the methods used to infer cosmological information from GW observations rely on the availability of a redshift measurement, usually obtained with the help of external data, such as galaxy catalogues used to identify the most likely galaxy to host the emission of the observed GWs. Instead, our approach is based only on the GW survey itself and exploits the information on the distance of the GW rather than on its redshift. Since a large dataset spanning the whole distance interval is expected to fully represent the distribution, we applied our methods to the expected ET's far-reaching measuring capabilities. We simulate a dataset of observations with ET using the package darksirens, assuming an underlying ΛCDM cosmology, and including the possibility to choose between three possible Star Formation Rate density (SFR) models, also accounting for possible population III stars (PopIII). We test two independent statistical methods: one based on a likelihood approach on the theoretical expectation of observed events, and another applying the cut-and-count method, a simpler method to compare the observed number of events with the predicted counts. Both methods are consistent in their final results, and also show the potential to distinguish an incorrect SFR model from the data, but not the presence of a possible PopIII. Concerning the cosmological parameters, we find instead that ET observations by themselves would suffer from strong degeneracies, but have the potential to significantly contribute to parameter estimation if used in synergy with other surveys.
Marta Monelli et al JCAP05(2024)018
Polarization of the cosmic microwave background (CMB) can help probe the fundamental physics behind cosmic inflation via the measurement of primordial B modes. As this requires exquisite control over instrumental systematics, some next-generation CMB experiments plan to use a rotating half-wave plate (HWP) as polarization modulator. However, the HWP non-idealities, if not properly treated in the analysis, can result in additional systematics. In this paper, we present a simple, semi-analytical end-to-end model to propagate the HWP non-idealities through the macro-steps that make up any CMB experiment (observation of multi-frequency maps, foreground cleaning, and power spectra estimation) and compute the HWP-induced bias on the estimated tensor-to-scalar ratio, r. We find that the effective polarization efficiency of the HWP suppresses the polarization signal, leading to an underestimation of r. Laboratory measurements of the properties of the HWP can be used to calibrate this effect, but we show how gain calibration of the CMB temperature can also be used to partially mitigate it. On the basis of our findings, we present a set of recommendations for the HWP design that can help maximize the benefits of gain calibration.
Liam Pinchbeck et al JCAP05(2024)020
We present GammaBayes, a Bayesian Python package for dark matter detection with the Cherenkov Telescope Array (CTA). GammaBayes takes as input the CTA measurements of gamma rays and a user-specified dark-matter particle model. It outputs the posterior distribution for parameters of the dark-matter model including the velocity-averaged cross section for dark-matter self interactions 〈σv〉 and the dark-matter mass mχ. It also outputs the Bayesian evidence, which can be used for model selection. We demonstrate GammaBayes using 525 hours of simulated data, corresponding to 108 observed gamma-ray events. The vast majority of this simulated data consists of noise, but 100000 events arise from the annihilation of scalar singlet dark matter with mχ = 1 TeV. We recover the dark matter mass within a 95% credible interval of mχ ∼ 0.96–1.07 TeV. Meanwhile, the velocity averaged cross section is constrained to 〈σv〉 ∼ 1.4–2.1 × 10-25 cm3 s-1 (95% credibility). This is equivalent to measuring the number of dark-matter annihilation events to be NS ∼ 1.1-0.2+0.2 × 105. The no-signal hypothesis 〈σv〉 = 0 is ruled out with about 5σ credibility. We discuss how GammaBayes can be extended to include more sophisticated signal and background models and the computational challenges that must be addressed to facilitate these upgrades. The source code is publicly available here.
Philippa S. Cole et al JCAP05(2024)022
Primordial black holes (PBHs) can be produced by a range of mechanisms in the early universe. A particular formation channel that connects PBHs with inflationary phenomenology invokes enhanced primordial curvature perturbations at small scales. In this paper, we examine how rapidly the background can transition between different values of the parameters of the Hubble hierarchy in the context of single-clock inflation, which must ultimately derive from a consistent derivative expansion for the background inflaton field. We discuss artefacts associated with instant or very rapid transitions, and consider the impact on the steepest power spectrum growth and the formation of PBHs. In particular, we highlight the robustness of the k4 steepest growth previously found for single-field inflation with conservatively smoothed transitions and limits on how much the amplitude of the power spectrum can grow, and demonstrate that the PBH mass distribution is sensitive to the artefacts, which go away when the transitions are smoothed. We also show that the mass distribution is relatively insensitive to the steepness of the growth and subsequent decay of the power spectrum, depending primarily on the peak amplitude and the presence of any plateaus that last more than an e-fold. The shape of the power spectrum can of course be constrained by other tracers, and so understanding the physical limitations on its shape remains a pertinent question.