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Shaun Hotchkiss

Publications and source records attributed to Shaun Hotchkiss.

At least 19 recordsLinked to original sources
arXiv2021

Inflation in a Gaussian Random Landscape

Random, multifield functions can set generic expectations for landscape-style cosmologies. We consider the inflationary implications of a landscape defined by a Gaussian random function, which is perhaps the simplest such scenario. Many key properties of this landscape, including the distribution of saddles as a function of height in the potential, depend only on its dimensionality, $N$, and a single parameter, $γ$, which is set by the power spectrum of the random function. We show that for saddles with a single downhill direction the negative mass term grows smaller, relative to the average mass, as $N$ increases, a result with potential implications for the $η$-problem in landscape scenarios. For some power spectra Planck-scale saddles have $η \sim 1$ and eternal, topological inflation would be common in these scenarios. Lower-lying saddles typically have large $η$, but the fraction of these saddles which would support inflation is computable, allowing us to identify which scenarios can deliver a universe that resembles ours. Finally, by drawing inferences about the relative viability of different multiverse proposals we also illustrate ways in which quantitative analyses of multiverse scenarios are feasible.

hep-th↗
arXiv2020

The Distribution of Vacua in Random Landscape Potentials

Landscape cosmology posits the existence of a convoluted, multidimensional, scalar potential -- the "landscape" -- with vast numbers of metastable minima. Random matrices and random functions in many dimensions provide toy models of the landscape, allowing the exploration of conceptual issues associated with these scenarios. We compute the relative number and slopes of minima as a function of the vacuum energy $Λ$ in an $N$-dimensional Gaussian random potential, quantifying the associated probability density, $p(Λ)$. After normalisations $p(Λ)$ depends only on the dimensionality $N$ and a single free parameter $γ$, which is related to the power spectrum of the random function. For a Gaussian landscape with a Gaussian power spectrum, the fraction of positive minima shrinks super-exponentially with $N$; at $N=100$, $p(Λ>0) \approx 10^{-1197}$. Likewise, typical eigenvalues of the Hessian matrices reveal that the flattest approaches to typical minima grow flatter with $N$, while the ratio of the slopes of the two flattest directions grows with $N$. We discuss the implications of these results for both swampland and conventional anthropic constraints on landscape cosmologies. In particular, for parameter values when positive minima are extremely rare, the flattest approaches to minima where $Λ\approx 0$ are much flatter than for typical minima, increasingly the viability of quintessence solutions.

hep-th↗
arXiv2019

Lighting the Dark: The Evolution of the Post-Inflationary Universe

In simple inflationary cosmological scenarios the near-exponential growth can be followed by a long period in which the Universe is dominated by the oscillating inflaton condensate. The condensate is initially almost homogeneous, but perturbations grow gravitationally, eventually fragmenting the condensate if it is not disrupted more quickly by resonance or prompt reheating. We show that the gravitational fragmentation of the condensate is well-described by the Schrödinger-Poisson equations and use numerical solutions to show that large overdensities form quickly after the onset of nonlinearity. This is the first exploration of this phase of nonlinear dynamics in the very early universe, which can affect the detailed form of the inflationary power spectrum and the dark matter fraction when the dark sector is directly coupled to the inflaton.

astro-ph.CO↗
arXiv2019

WIMPs and stellar-mass primordial black holes are incompatible

We recently showed that postulated ultracompact minihalos with a steep density profile do not form in realistic simulations with enhanced initial perturbations. In this paper we assume that a small fraction of the dark matter consists of primordial black holes (PBHs) and simulate the formation of structures around them. We find that in this scenario halos with steep density profiles do form, consistent with theoretical predictions. If the rest of the dark matter consists of weakly interacting massive particles (WIMPs), we also show that WIMPs in the dense innermost part of these halos would annihilate and produce a detectable gamma-ray signal. The non-detection of this signal implies that PBHs make up at most one billionth of the dark matter, provided that their mass is greater than one millionth of the mass of the Sun. Similarly, a detection of PBHs would imply that the remaining dark matter could not be WIMPs.

astro-ph.CO↗
arXiv2018

PyUltraLight: A Pseudo-Spectral Solver for Ultralight Dark Matter Dynamics

PyUltraLight simulates the dynamics of ultralight dark matter in a non-expanding background. PyUltraLight can describe the evolution of several interacting ultralight dark matter halos or one or more halos orbiting a central, fixed Newtonian potential, the latter scenario corresponding to dwarf galaxies orbiting a massive central galaxy. We verify PyUltraLight by showing that it reproduces qualitative dynamical features of previously published simulations and demonstrate that it has excellent energy-conservation properties. PyUltraLight is implemented in a Python-based Jupyter notebook, solving the Schrodinger-Poisson equation governing ultralight scalar field dark matter dynamics in the non-relativistic regime using a symmetrised split-step pseudospectral algorithm. The notebook interface makes it simple to specify simulation parameters and visualise the resulting output but performance-critical routines are managed via calls to computationally efficient compiled libraries. PyUltraLight runs on standard desktop hardware with support for shared memory mutlithreading and is available on GitHub.

astro-ph.CO↗
arXiv2018

3D simulations with boosted primordial power spectra and ultracompact minihalos

We perform three-dimensional simulations of structure formation in the early Universe, when boosting the primordial power spectrum on approximately kpc scales. We demonstrate that our simulations are capable of producing power-law profiles close to the steep $ρ\propto r^{-9/4}$ halo profiles that are commonly assumed to be a good approximation to ultracompact minihalos (UCMHs). However, we show that for more realistic initial conditions in which halos are neither perfectly symmetric nor isolated, the steep power-law profile is disrupted and we find that the Navarro-Frenk-White profile is a better fit to most halos. In the presence of background fluctuations even extreme, nearly spherical initial conditions do not remain exceptional. Nonetheless, boosting the amplitude of initial fluctuations causes all structures to form earlier and thus at larger densities. With sufficiently large amplitude of fluctuations we find that values for the concentration of typical halos in our simulations can become very large. However, despite the signal coming from dark matter annihilation inside the cores of these halos being enhanced, it is still orders-of-magnitude smaller compared to the usually assumed UCMH profile. The upper bound on the primordial power spectrum from the non-observation of UCMHs should therefore be re-evaluated.

astro-ph.CO↗
arXiv2017

The matter power spectrum in redshift space using effective field theory

The use of Eulerian 'standard perturbation theory' to describe mass assembly in the early universe has traditionally been limited to modes with k $\lesssim$ 0.1 h/Mpc at z = 0. At larger k the SPT power spectrum deviates from measurements made using N-body simulations. Recently, there has been progress in extending the reach of perturbation theory to larger k using ideas borrowed from effective field theory. We revisit the computation of the redshift-space matter power spectrum within this framework, including for the first time the full one-loop time dependence. We use a resummation scheme proposed by Vlah et al. to account for damping of baryonic acoustic oscillations due to large-scale random motions and show that this has a significant effect on the multipole power spectra. We renormalize by comparison to a suite of custom N-body simulations matching the MultiDark MDR1 cosmology. At z = 0 and for scales k $\lesssim$ 0.4 h/Mpc we find that the EFT furnishes a description of the real-space power spectrum up to $\sim$2%, for the $\ell$ = 0 mode up to $\sim$5%, and for the $\ell$ = 2, 4 modes up to $\sim$25%. We argue that, in the MDR1 cosmology, positivity of the $\ell$ = 0 mode gives a firm upper limit of k $\approx$ 0.75 h/Mpc for the validity of the one-loop EFT prediction in redshift space using only the lowest-order counterterm. We show that replacing the one-loop growth factors by their Einstein-de Sitter counterparts is a good approximation for the $\ell$ = 0 mode, but can induce deviations as large as 2% for the $\ell$ = 2, 4 modes. An accompanying software bundle, distributed under open source licenses, includes Mathematica notebooks describing the calculation, together with parallel pipelines capable of computing both the necessary one-loop SPT integrals and the effective field theory counterterms.

astro-ph.CO↗
arXiv2017

Tracing the gravitational potential using cosmic voids

The properties of large underdensities in the distribution of galaxies in the Universe, known as cosmic voids, are potentially sensitive probes of fundamental physics. We use data from the MultiDark suite of N-body simulations and multiple halo occupation distribution mocks to study the relationship between galaxy voids, identified using a watershed void-finding algorithm, and the gravitational potential $Φ$. We find that the majority of galaxy voids correspond to local density minima in larger-scale overdensities, and thus lie in potential wells. However, a subset of voids can be identified that closely trace maxima of the gravitational potential and thus stationary points of the velocity field. We identify a new void observable, $λ_v$, which depends on a combination of the void size and the average galaxy density contrast within the void, and show that it provides a good proxy indicator of the potential at the void location. A simple linear scaling of $Φ$ as a function of $λ_v$ is found to hold, independent of the redshift and properties of the galaxies used as tracers of voids. We provide an accurate fitting formula to describe the spherically averaged potential profile $Φ(r)$ about void centre locations. We discuss the importance of these results for the understanding of the evolution history of voids, and for their use in precision measurements of the integrated Sachs-Wolfe effect, gravitational lensing and peculiar velocity distortions in redshift space.

astro-ph.CO↗
arXiv2017

A Consistent Approach to Falsifying Lambda-CDM with Rare Galaxy Clusters

We consider methods with which to answer the question "is any observed galaxy cluster too unusual for Lambda-CDM?" After emphasising that many previous attempts to answer this question will overestimate the confidence level at which Lambda-CDM can be ruled out, we outline a consistent approach to these rare clusters, which allows the question to be answered. We define three statistical measures, each of which are sensitive to changes in cluster populations arising from different modifications to the cosmological model. We also use these properties to define the 'equivalent mass at redshift zero' for a cluster --- the mass of an equally unusual cluster today. This quantity is independent of the observational survey in which the cluster was found, which makes it an ideal proxy for ranking the relative unusualness of clusters detected by different surveys. These methods are then used on a comprehensive sample of observed galaxy clusters and we confirm that all are less than 2-sigma deviations from the Lambda-CDM expectation. Whereas we have only applied our method to galaxy clusters, it is applicable to any isolated, collapsed, halo. As motivation for future surveys, we also calculate where in the mass redshift plane the rarest halo is most likely to be found, giving information as to which objects might be the most fruitful in the search for new physics.

astro-ph.CO↗
arXiv2015

The nature of voids: I. Watershed void finders and their connection with theoretical models

The statistical study of voids in the matter distribution promises to be an important tool for precision cosmology, but there are known discrepancies between theoretical models of voids and the voids actually found in large simulations or galaxy surveys. The empirical properties of observed voids are also not well understood. In this paper, we study voids in an N-body simulation, using the ZOBOV watershed algorithm. As in other studies, we use sets of subsampled dark matter particles as tracers to identify voids, but we use the full-resolution simulation output to measure dark matter densities at the identified locations. Voids span a wide range of sizes and densities, but there is a clear trend towards larger voids containing deeper density minima, a trend which is expected for all watershed void finders. We also find that the tracer density at void locations is usually smaller than the true density, and that this relationship depends on the sampling density of tracers. We show that fits given in the literature fail to match the observed density profiles of voids. The average enclosed density contrast within watershed voids varies widely with both the size of the void and the minimum density within it, but is always far from the shell crossing threshold expected from theoretical models. Voids with deeper density minima also show much broader density profiles. We discuss the implications of these results for the excursion set approach to modelling such voids.

astro-ph.CO↗
arXiv2015

Spherically Symmetric N-body Simulations with General Relativistic Dynamics

Within a cosmological context, we study the behaviour of collisionless particles in the weak field approximation to General Relativity, allowing for large gradients of the fields and relativistic velocities for the particles. We consider a spherically symmetric setup such that high resolution simulations are possible with minimal computational resources. We test our formalism by comparing it to two exact solutions: the Schwarzschild solution and the Lemaître-Tolman-Bondi model. In order to make the comparison we consider redshifts and lensing angles of photons passing through the simulation. These are both observable quantities and hence are gauge independent. We demonstrate that our scheme is more accurate than a Newtonian scheme, correctly reproducing the leading-order post-Newtonian correction. In addition, our setup is able to handle shell-crossings, which is not possible within a fluid model. Furthermore, by introducing angular momentum, we find configurations corresponding to bound objects which may prove useful for numerical studies of the effects of modified gravity, dynamical dark energy models or even compact bound objects within General Relativity.

astro-ph.CO↗
arXiv2015

The nature of voids: II. Tracing underdensities with biased galaxies

We study how the properties of cosmic voids depend on those of the tracer galaxy populations in which they are identified. We use a suite of halo occupation distribution (HOD) mocks in a simulation, identify voids in these populations using the ZOBOV void finder and measure their abundances, sizes, tracer densities, and dark matter content. To separate the effects of bias from those of sampling density, we do the same for voids traced by randomly down-sampled subsets of the simulation dark matter particles. At the same sampling density, galaxy bias reduces the total number of voids by ~50% and can dramatically change their size distribution. The matter content of voids in biased and unbiased tracers also differs. Deducing void properties from simulation therefore requires the use of realistic galaxy mocks. We discuss how the void observables can be related to their matter content. In particular we consider the compensation of the total mass deficit in voids and find that the distinction between over- and under-compensated voids is not a function of void size alone, as has previously been suggested. However, we find a simple linear relationship between the average density of tracers in the void and the total mass compensation on much larger scales. The existence of this linear relationship holds independent of the bias and sampling density of the tracers. This provides a universal tool to classify void environments and will be important for the use of voids in observational cosmology.

astro-ph.CO↗
arXiv2014

Can a supervoid explain the Cold Spot?

The discovery of a void of size $\sim200\;h^{-1}$Mpc and average density contrast of $\sim-0.1$ aligned with the Cold Spot direction has been recently reported. It has been argued that, although the first-order integrated Sachs-Wolfe (ISW) effect of such a void on the CMB is small, the second-order Rees-Sciama (RS) contribution exceeds this by an order of magnitude and can entirely explain the observed Cold Spot temperature profile. In this paper we examine this surprising claim using both an exact calculation with the spherically symmetric Lemaître-Tolman-Bondi metric, and perturbation theory about a background Friedmann-Robertson-Walker (FRW) metric. We show that both approaches agree well with each other, and both show that the dominant temperature contribution of the postulated void is an unobservable dipole anisotropy. If this dipole is subtracted, we find that the remaining temperature anisotropy is dominated by the linear ISW signal, which is orders of magnitude larger than the second-order RS effect, and that the total magnitude is too small to explain the observed Cold Spot profile. We calculate the density and size of a void that would be required to explain the Cold Spot, and show that the probability of existence of such a void is essentially zero in $Λ$CDM. We identify the importance of \emph{a posteriori} selection effects in the identification of the Cold Spot, but argue that even after accounting for them, a supervoid explanation of the Cold Spot is always disfavoured relative to a random statistical fluctuation on the last scattering surface.

astro-ph.CO↗
arXiv2014

A robust public catalogue of voids and superclusters in the SDSS Data Release 7 galaxy surveys

The study of the interesting cosmological properties of voids in the Universe depends on the efficient and robust identification of such voids in galaxy redshift surveys. Recently, Sutter et al. (2012) have published a public catalogue of voids in the Sloan Digital Sky Survey Data Release 7 main galaxy and luminous red galaxy samples, using the void-finding algorithm ZOBOV, which is based on the watershed transform. We examine the properties of this catalogue and show that it suffers from several problems and inconsistencies, including the identification of some extremely overdense regions as voids. As a result, cosmological results obtained using this catalogue need to be reconsidered. We provide instead an alternative, self-consistent, public catalogue of voids in the same galaxy data, obtained from using an improved version of the same watershed transform algorithm. We provide a more robust method of dealing with survey boundaries and masks, as well as with a radially varying selection function, which means that our method can be applied to any other survey. We discuss some basic properties of the voids thus discovered, and describe how further information may be obtained from the catalogue. In addition, we apply an inversion of the algorithm to the same data to obtain a corresponding catalogue of large-scale overdense structures, or "superclusters". Our catalogues are available for public download at www.hip.fi/nadathur/download/dr7catalogue.

astro-ph.CO↗
arXiv2013

The small scale power asymmetry in the cosmic microwave background

We investigate the hemispherical power asymmetry in the cosmic microwave background on small angular scales. We find an anomalously high asymmetry in the multipole range l=601-2048, with a naive statistical significance of 6.5 sigma. However, we show that this extreme anomaly is simply a coincidence of three other effects, relativistic power modulation, edge effects from the mask applied, and inter-scale correlations. After correcting for all of these effects, the significance level drops to ~1 sigma, i.e., there is no anomalous intrinsic asymmetry in the small angular scales. Using this null result, we derive a constraint on a potential dipolar modulation amplitude, A(k)<0.0045 on the ~10 Mpc-scale, at 95% C.L. This new constraint must be satisfied by any theoretical model attempting to explain the hemispherical asymmetry at large angular scales.

astro-ph.CO↗
arXiv2013

The stacked ISW signal of rare superstructures in ΛCDM

A detection of the stacked integrated Sachs-Wolfe (ISW) signal in the CMB of rare superstructures identified in the SDSS Luminous Red Galaxy catalogue has been reported at very high statistical significance. The magnitude of the observed signal has previously been argued to be more than 3 standard deviations larger than the theoretical ΛCDM expectation. However, this calculation was made in the linear approximation, and relied on assumptions that may potentially have caused the ΛCDM expectation to be underestimated. Here we update the theoretical model calculation and compare it with an analysis of ISW maps obtained from N-body simulations of a ΛCDM universe. The differences between model predictions and the map analyses are found to be small and cannot explain the discrepancy with observation, which remains at >3 s.d. significance. We discuss the cosmological significance of this anomaly and speculate on the potential of alternative models to explain it.

astro-ph.CO↗
arXiv2012

The integrated Sachs-Wolfe imprints of cosmic superstructures: a problem for ΛCDM

A crucial diagnostic of the ΛCDM cosmological model is the integrated Sachs-Wolfe (ISW) effect of large-scale structure on the cosmic microwave background (CMB). The ISW imprint of superstructures of size \sim100\;h^{-1} Mpc at redshift $z\sim0.5$ has been detected with $>4σ$ significance, however it has been noted that the signal is much larger than expected. We revisit the calculation using linear theory predictions in ΛCDM cosmology for the number density of superstructures and their radial density profile, and take possible selection effects into account. While our expected signal is larger than previous estimates, it is still inconsistent by $>3σ$ with the observation. If the observed signal is indeed due to the ISW effect then huge, extremely underdense voids are far more common in the observed universe than predicted by ΛCDM.

astro-ph.CO↗