arXiv subjects

Andrew D. Gow

Publications and source records attributed to Andrew D. Gow.

11 recordsLinked to original sources

arXiv2025

Stochastic inflation beyond slow roll: noise modelling and importance sampling

We simulate the distribution of very rare, large excursions in the primordial density field produced in models of inflation in the very early universe which include a strong enhancement of the power spectrum. The stochastic $δ\mathcal{N}$ formalism is used to identify the probability distribution for the primordial curvature perturbation with the first-passage-time distribution, $P(δ\mathcal{N})$, and we compare our stochastic results with those obtained in the classical $δ\mathcal{N}$ approach. We extend the PyFPT numerical code to simulate the full 2D phase space, and apply importance sampling which allows very rare fluctuations to be simulated in $\mathcal{O}(10)$ minutes on a single CPU, where previous direct simulations required supercomputers. We demonstrate that the stochastic noise due to quantum fluctuations after a sudden transition to ultra-slow roll can be accurately modelled using an analytical Bessel-function ansatz to identify the homogeneous growing mode. The stochastic noise found in this way is a function of the field value only. This enables us to coarse grain the inflation field at the Hubble scale and include non-linear, stochastic evolution on all super-Hubble length scales.

astro-ph.CO↗

arXiv2024

Smooth vs instant inflationary transitions: steepest growth re-examined and primordial black holes

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 $k^4$ 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.

astro-ph.CO↗

arXiv2024

The separate-universe approach and sudden transitions during inflation

The separate-universe approach gives an intuitive way to understand the evolution of cosmological perturbations in the long-wavelength limit. It uses solutions of the spatially-homogeneous equations of motion to model the evolution of the inhomogeneous universe on large scales. We show that the separate-universe approach fails on a finite range of super-Hubble scales at a sudden transition from slow roll to ultra-slow roll during inflation in the very early universe. Such transitions are a feature of inflation models giving a large enhancement in the primordial power spectrum on small scales, necessary to produce primordial black holes after inflation. We show that the separate-universe approach still works in a piece-wise fashion, before and after the transition, but spatial gradients on finite scales require a discontinuity in the homogeneous solution at the transition. We discuss the implications for the $δN$ formalism and stochastic inflation, which employ the separate-universe approximation.

astro-ph.CO↗

arXiv2024

I'm in AGNi: A new standard for AGN pluralisation

We present a new standard acronym for Active Galactic Nuclei, finally settling the argument of AGN vs. AGNs. Our new standard is not only etymologically superior (following the consensus set by SNe), but also boasts other linguistic opportunities, connecting strongly with relevant theology and streamlining descriptions of AGN properties.

astro-ph.GA↗

arXiv2023

Primordial black holes from a curvaton scenario with strongly non-Gaussian perturbations

We investigate the production of primordial black holes (PBHs) in a mixed inflaton-curvaton scenario with a quadratic curvaton potential, assuming the curvaton is in de Sitter equilibrium during inflation with $\langle χ\rangle =0$. In this setup, the curvature perturbation sourced by the curvaton is strongly non-Gaussian, containing no leading Gaussian term. We show that for $m^2/H^2\gtrsim 0.3$, the curvaton contribution to the spectrum of primordial perturbations on CMB scales can be kept negligible but on small scales the curvaton can source PBHs. In particular, PBHs in the asteroid mass range $10^{-16}M_{\odot}\lesssim M\lesssim 10^{-10}M_{\odot}$ with an abundance reaching $f_{\rm PBH} = 1$ can be produced when the inflationary Hubble scale $H\gtrsim 10^{12}$ GeV and the curvaton decay occurs in the window from slightly before the electroweak transition to around the QCD transition.

astro-ph.CO↗

arXiv2023

Primordial black holes from single-field inflation: a fine-tuning audit

All single-field inflationary models invoke varying degrees of tuning in order to account for cosmological observations. Mechanisms that generate primordial black holes (PBHs) from enhancement of primordial power at small scales posit inflationary potentials that transiently break scale invariance and possibly adiabaticity over a range of modes. This requires additional tuning on top of that required to account for observations at scales probed by cosmic microwave background (CMB) anisotropies. In this paper we study the parametric dependence of various single-field models of inflation that enhance power at small scales and quantify the degree to which coefficients in the model construction have to be tuned in order for certain observables to lie within specified ranges. We find significant tuning: changing the parameters of the potentials by between one part in a hundred and one part in $10^8$ (depending on the model) is enough to change the power spectrum peak amplitude by an order one factor. The fine-tuning of the PBH abundance is larger still by 1-2 orders of magnitude. We highlight the challenges imposed by this tuning on any given model construction. Furthermore, polynomial potentials appear to require significant additional fine-tuning to also match the CMB observations.

astro-ph.CO↗

arXiv2023

Non-perturbative non-Gaussianity and primordial black holes

We present a non-perturbative method for calculating the abundance of primordial black holes given an arbitrary one-point probability distribution function for the primordial curvature perturbation, $P(ζ)$. A non-perturbative method is essential when considering non-Gaussianities that cannot be treated using a conventional perturbative expansion. To determine the full statistics of the density field, we relate $ζ$ to a Gaussian field by equating the cumulative distribution functions. We consider two examples: a specific local-type non-Gaussian distribution arising from ultra slow roll models, and a general piecewise model for $P(ζ)$ with an exponential tail. We demonstrate that the enhancement of primordial black hole formation is due to the intermediate regime, rather than the far tail. We also show that non-Gaussianity can have a significant impact on the shape of the primordial black hole mass distribution.

astro-ph.CO↗

arXiv2022

An accurate model for the primordial black hole mass distribution from a peak in the power spectrum

We examine the shape of the primordial black hole mass distribution arising from a peak in the primordial power spectrum. In light of improvements to the modelling, we revisit the claim that the effects of critical collapse produce a distribution that is not described by the commonly assumed lognormal, showing that this conclusion remains valid, particularly for narrow peaks where the shape of the mass distribution is insensitive to the peak properties and critical collapse determines a minimum width. We propose some alternative models that may better describe the shape, both for the narrow peak case and for much broader peaks where the effect of the peak shape is significant. We highlight the skew-lognormal and a generalised model motivated by the physics of critical collapse as the best of these possible alternatives. These models can be used as an accurate and fast approximation to the numerically calculated mass distribution, allowing for efficient implementation in an MCMC analysis. We advocate the use of one of these two models instead of the lognormal with sufficiently accurate data, such as future LIGO-Virgo observations, or when considering strongly mass dependent constraints on the PBH abundance.

astro-ph.CO↗

arXiv2021

The power spectrum on small scales: Robust constraints and comparing PBH methodologies

We compare primordial black hole (PBH) constraints on the power spectrum and mass distributions using the traditional Press Schechter formalism, peaks theory, and a recently developed version of peaks theory relevant to PBHs. We show that, provided the PBH formation criteria and the power spectrum smoothing are treated consistently, the constraints only vary by $\sim$10\% between methods (a difference that will become increasingly important with better data). Our robust constraints from PBHs take into account the effects of critical collapse, the non-linear relation between $ζ$ and $δ$, and the shift from the PBH mass to the power spectrum peak scale. We show that these constraints are remarkably similar to the pulsar timing array (PTA) constraints impacting the black hole masses detected by the LIGO and Virgo, but that the $μ$-distortion constraints rule out supermassive black hole (SMBH) formation and potentially even the much lighter mass range of $\sim$(1-100) $\mathrm{M}_\odot$ that LIGO/Virgo probes.

astro-ph.CO↗

arXiv2020

Bayesian analysis of LIGO-Virgo mergers: Primordial vs. astrophysical black hole populations

We conduct a thorough Bayesian analysis of the possibility that the black hole merger events seen in gravitational waves are primordial black hole (PBH) mergers. Using the latest merger rate models for PBH binaries drawn from a lognormal mass function we compute posterior parameter constraints and Bayesian evidences using data from the first two observing runs of LIGO-Virgo. We account for theoretical uncertainty due to possible disruption of the binary by surrounding PBHs, which can suppress the merger rate significantly. We also consider simple astrophysically motivated models and find that these are favoured decisively over the PBH scenario, quantified by the Bayesian evidence ratio. Paying careful attention to the influence of the parameter priors and the quality of the model fits, we show that the evidence ratios can be understood by comparing the predicted chirp mass distribution to that of the data. We identify the posterior predictive distribution of chirp mass as a vital tool for discriminating between models. A model in which all mergers are PBH binaries is strongly disfavoured compared with astrophysical models, in part due to the over-prediction of heavy systems having $\mathcal{M}_{\rm chirp} \gtrsim 40 \, M_\odot$ and positive skewness over the range of observed masses which does not match the observations. We find that the fit is not significantly improved by adding a maximum mass cut-off, a bimodal mass function, or imposing that PBH binaries form at late times. We argue that a successful PBH model must either modify the lognormal shape of the initial mass function significantly or abandon the hypothesis that all observed merging binaries are primordial. We develop and apply techniques for analysing PBH models with gravitational wave data which will be necessary for robust statistical inference as the gravitational wave source sample size increases.

astro-ph.CO↗

arXiv2020

Primordial black hole merger rates: distributions for multiple LIGO observables

We have calculated the detectable merger rate of primordial black holes, as a function of the redshift, as well as the binary's mass ratio, total mass and chirp mass (observables that have not previously been explored in great detail for PBHs). We consider both the current and design sensitivity of LIGO and five different primordial black hole mass functions, as well as showing a comparison to a predicted astrophysical black hole merger rate. We show that the empirical preference for nearly equal-mass binaries in current LIGO/Virgo data can be consistent with a PBH hypothesis once observational selection effects are taken into account. However, current data do exclude some PBH mass distributions, and future data may be able to rule out the possibility that all observed BH mergers had a primordial origin.

astro-ph.CO↗