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We numerically simulate the motion of a black hole as it plunges radially through an ultralight dark matter soliton. We investigate the timescale in which dynamical friction reduces the kinetic energy of the black hole to a minimum, and consider the sensitivity of this timescale to changes in the ULDM particle mass, the total soliton mass, and the mass of the black hole. We contrast our numerical results with a semi-analytic treatment of dynamical friction, and find that the latter is poorly suited to this scenario. In particular, we find that the back-reaction of the soliton to the presence of the black hole is significant, resulting in oscillations in the coefficient of dynamical friction which cannot be described in the simple semi-analytical framework. Furthermore, we observe a late-time reheating effect, in which a significant amount of kinetic energy is transferred back to the black hole after an initial damping phase. This complicates the discussion of ULDM dynamical friction on the scales relevant to the final parsec problem., Comment: 15 pages

The post-inflationary Universe can pass through a long epoch of effective matter-dominated expansion. This era may allow for both the parametric amplification of initial fluctuations and the gravitational collapse of inflaton perturbations. We perform first-of-their-kind high-resolution simulations that span the resonant phase and the subsequent gravitational collapse of the inflaton field by seguing from a full Klein-Gordon treatment of resonance to a computationally efficient Schr\"odinger-Poisson description that accurately captures the gravitational dynamics when most quanta are nonrelativistic. We consider a representative example in which resonance generates $\mathcal{O}(10^{-1})$ overdensities and gravitational collapse follows promptly as resonance ends. We observe the formation of solitonic cores inside inflaton halos and complex gravitational dynamics on scales of $10^{-27}\,\mathrm{m}$, greatly extending the possible scope of nonlinear post-inflationary gravitational dynamics., Comment: 11 pages, 8 figures, matches version accepted in Phys Rev D

We quantify the differences between stellar accelerations in disk galaxies formed in a MONDian universe relative to galaxies with the identical baryonic matter distributions and a fitted cold dark matter halo. In a Milky Way-like galaxy the maximal transverse acceleration is ${\cal {O}}(10^{-9})$ arcseconds per year per decade, well beyond even the most optimistic extrapolations of current capabilities. Conversely, the maximum difference in the line-of-sight acceleration is ${\cal {O}}(1)$ centimetre per second per decade at solar distances from the galactic centre. This level of precision is within reach of plausible future instruments., Comment: 13 pages v2 typos fixed, ref added

It was recently suggested that "cosmologically coupled" black holes with masses that increase in proportion to the volume of the Universe might constitute the physical basis of dark energy. We take this claim at face value and discuss its potential astrophysical implications. We show that the gravitational wave emission in binary systems would be significantly enhanced so that the number of black hole mergers would exceed the observed rate by orders of magnitude, with typical masses much larger than those seen by the LIGO-Virgo-KAGRA network. Separately, if the mass growth happens at fixed angular momentum, the supermassive black holes in matter-deficient elliptical galaxies should be slowly rotating. Finally, cosmological coupling would stabilize small black holes against Hawking radiation-induced evaporation., Comment: 11 Pages, 5 Figures, Matches Accepted version

Ultralight dark matter (ULDM) is an interesting alternative to the cold dark matter (CDM) paradigm. Due to the extremely low mass of the constituent particle ($\sim 10^{-22}$ eV), ULDM can exhibit quantum effects up to kiloparsec scales. In particular, runaway collapse in the centres of ULDM halos is prevented by quantum pressure, providing a possible resolution to the 'core-cusp problem' of CDM. However, the the detailed relationship between the ULDM core mass and that of the overall halo is poorly understood. We simulate the collapse of both spherical and aspherical isolated ULDM overdensities using AxioNyx, finding that the central cores of collapsed halos undergo sustained oscillatory behaviour which affects both their peak density and overall morphology. The variability in core morphology increases with the asphericity of the initial overdensity and remnants of initial asphericity persist long after collapse. Furthermore, the peak central densities are higher in spherical configurations. Consequently, astrophysically realistic halos may exhibit substantial departures from theoretical core-halo profiles and we would expect a significant variance of the properties of halos with the same mass., Comment: 11 pages, 11 figures

In this Working Paper we analyse computational strategies for using aggregated spatio-temporal population data acquired from telecommunications networks to infer travel and movement patterns between geographical regions. Specifically, we focus on hour-by-hour cellphone counts for the SA-2 geographical regions covering the whole of New Zealand. This Working Paper describes the implementation of the inference algorithms, their ability to produce models of travel patterns during the day, and lays out opportunities for future development., Comment: Submitted to Covid-19 Modelling Aotearoa

Ultralight dark matter (ULDM) is usually taken to be a single scalar field. Here we explore the possibility that ULDM consists of $N$ light scalar fields with only gravitational interactions. This configuration is more consistent with the underlying particle physics motivations for these scenarios than a single ultralight field. ULDM halos have a characteristic granular structure that increases stellar velocity dispersion and can be used as observational constraints on ULDM models. In multifield simulations, we find that inside a halo the amplitude of the total density fluctuations decreases as $1/\sqrt{N}$ and that the fields do not become significantly correlated over cosmological timescales. Smoother halos heat stellar orbits less efficiently, reducing the velocity dispersion relative to the single field case and thus weakening the observational constraints on the field mass. Analytically, we show that for $N$ equal-mass fields with mass $m$ the ULDM contribution to the stellar velocity dispersion scales as $1/(N m^3)$. Lighter fields heat the most efficiently and if the smallest mass $m_L$ is significantly below the other field masses the dispersion scales as $1/(N^2 m_L^3)$., Comment: 11 pages, 7 figures, to be submitted to PRD

UltraLight Dark Matter (ULDM) is an axion-like dark matter candidate with an extremely small particle mass. ULDM halos consist of a spherically symmetric solitonic core and an NFW-like skirt. We simulate halo creation via soliton mergers and use these results to explore the core-halo mass relation. We calculate the eigenstates of the merged halos and use these to isolate the solitonic core and calculate its relative contribution to the halo mass. We compare this approach to using a fitting function to isolate the core and find a difference in masses up to 30%. We analyze three families of simulations: equal-mass mergers, unequal-mass mergers, and halos with a two-step merger history. Setting the halo mass to the initial mass in the simulation does not yield a consistent core-halo relationship. Excluding material "ejected" by the collision yields a core-halo relationship with a slope of 1/3 for simultaneous mergers and roughly 0.4 for two-step mergers. Our findings suggest there is no universal core-halo mass relationship for ULDM and shed light on the differing results for the core-halo relationship previously reported in the literature., Comment: 10 pages, 8 figures; published in PRD, updated with referee changes

The ability to test and constrain theories of cosmic inflation will advance substantially over the next decade. Key data sources include cosmic microwave background (CMB) measurements and observations of the distribution of matter at low-redshift from optical, near-infrared, and 21cm intensity surveys. A positive detection of a CMB B-mode consistent with a primordial stochastic gravitational wave background (SGWB) is widely viewed as a smoking gun for an inflationary phase. Still, a null result does not exclude inflation. However, in a significant class of inflationary scenarios, a low SGWB amplitude is correlated with a more significant running, $\alpha_s$, in the primordial density perturbations than is seen with the simplest inflationary potentials. With this motivation, we forecast the precision with which the spectral index $n_{\rm{s}}$ and $\alpha_{\rm{s}}$ can be constrained by currently envisaged observations, including CMB (Simons Observatory, CMB-S4 and LiteBIRD), optical/near infra-red (DESI and SPHEREx), and 21cm intensity mapping (Tianlai and CHIME) surveys. We identify optimal combinations of datasets for constraining the running and show that they may yield additional and informative constraints on the overall inflationary parameter space if the SGWB remains undetected., Comment: 12 pages, 8 figures. Version matches the one accepted by MNRAS

Following inflation, the Universe may pass through an early matter-dominated phase supported by the oscillating inflaton condensate. Initially small fluctuations in the condensate grow gravitationally on subhorizon scales and can collapse to form nonlinear ``inflaton halos''. Their formation and subsequent tidal interactions will source gravitational waves, resulting in a stochastic background in the present Universe. We extend N-body simulations that model the growth and interaction of collapsed structures to compute the resulting gravitational wave emission. The spectrum of this radiation is well-matched by semi-analytical estimates based on the collapse of inflaton halos and their tidal evolution. We use this semi-analytic formalism to infer the spectrum for scenarios where the early matter-dominated phase gives way to a thermalized universe at temperatures as low as $100\,\mathrm{MeV}$ and we discuss the possible experimental opportunities created by this signal in inflationary models in which thermalization takes place long after inflation has completed., Comment: 9 pages, 4 figures. Published version, Editors' suggestion

The Laser Interferometer Space Antenna (LISA) has the potential to reveal wonders about the fundamental theory of nature at play in the extreme gravity regime, where the gravitational interaction is both strong and dynamical. In this white paper, the Fundamental Physics Working Group of the LISA Consortium summarizes the current topics in fundamental physics where LISA observations of GWs can be expected to provide key input. We provide the briefest of reviews to then delineate avenues for future research directions and to discuss connections between this working group, other working groups and the consortium work package teams. These connections must be developed for LISA to live up to its science potential in these areas., Comment: Accepted in: Living Reviews in Relativity

The Laser Interferometer Space Antenna (LISA) has two scientific objectives of cosmological focus: to probe the expansion rate of the universe, and to understand stochastic gravitational-wave backgrounds and their implications for early universe and particle physics, from the MeV to the Planck scale. However, the range of potential cosmological applications of gravitational wave observations extends well beyond these two objectives. This publication presents a summary of the state of the art in LISA cosmology, theory and methods, and identifies new opportunities to use gravitational wave observations by LISA to probe the universe.

Inflationary cosmology proposes that the early Universe undergoes accelerated expansion, driven, in simple scenarios, by a single scalar field, or inflaton. The form of the inflaton potential determines the initial spectra of density perturbations and gravitational waves. We show that constraints on the duration of inflation together with the BICEP3/Keck bounds on the gravitational wave background imply that higher derivatives of the potential are nontrivial with a confidence of 99%. Such terms contribute to the scale-dependence, or running, of the density perturbation spectrum. We clarify the ``universality classes'' of inflation in this limit showing that a very small gravitational wave background can be correlated with a larger running. If pending experiments do not observe a gravitational wave background the running will be at the threshold of detectability if inflation is well-described at third-order in the slow roll expansion., Comment: 5 pages; 5 figures; as published in PRD -- change of title, minor clarifications

The Universe may pass through an effectively matter-dominated epoch between inflation and Big Bang Nucleosynthesis during which gravitationally bound structures can form on subhorizon scales. In particular, the inflaton field can collapse into inflaton halos, forming "large scale" structure in the very early universe. We combine N-body simulations with high-resolution zoom-in regions in which the non-relativistic Schr\"odinger-Poisson equations are used to resolve the detailed, wave-like structure of inflaton halos. Solitonic cores form inside them, matching structure formation simulations with axion-like particles in the late-time universe. We denote these objects \textit{inflaton stars}, by analogy with boson stars. Based on a semi-analytic formalism we compute their overall mass distribution which shows that some regions will reach overdensities of $10^{15}$ if the early matter-dominated epoch lasts for 20 $e$-folds. The radii of the most massive inflaton stars can shrink below the Schwarzschild radius, suggesting that they could form primordial black holes prior to thermalization., Comment: 9 pages, 6 figures, accepted by PRD

We simulate the gravitational dynamics of a massive object interacting with Ultralight / Fuzzy Dark Matter (ULDM/FDM), non-relativistic quantum matter described by the Schrodinger-Poisson equation. We first consider a point mass moving in a uniform background, and then a supermassive black hole (SMBH) moving within a ULDM soliton. After replicating simple dynamical friction scenarios to verify our numerical strategies, we demonstrate that the wake induced by a moving mass in a uniform medium may undergo gravitational collapse that dramatically increases the drag force, albeit in a scenario unlikely to be encountered astrophysically. We broadly confirm simple estimates of dynamical friction timescales for a black hole at the center of a halo but see that a large moving point mass excites coherent "breathing modes" in a ULDM soliton. These can lead to "stone skipping" trajectories for point masses which do not sink uniformly toward the center of the soliton, as well as stochastic motion near the center itself. These effects will add complexity to SMBH-ULDM interactions and to SMBH mergers in a ULDM universe., Comment: 14 pages, 19 figures

Self-gravitating quantum matter may exist in a wide range of cosmological and astrophysical settings from the very early universe through to present-day boson stars. Such quantum matter arises in a number of different theories, including the Peccei-Quinn axion and UltraLight (ULDM) or Fuzzy (FDM) dark matter scenarios. We consider the dynamical evolution of perturbations to the spherically symmetric soliton, the ground state solution to the Schr\"{o}dinger-Poisson system common to all these scenarios. We construct the eigenstates of the Schr\"{o}dinger equation, holding the gravitational potential fixed to its ground state value. We see that the eigenstates qualitatively capture the properties seen in full ULDM simulations, including the soliton "breathing" mode, the random walk of the soliton center, and quadrupolar distortions of the soliton. We then show that the time-evolution of the gravitational potential and its impact on the perturbations can be well described within the framework of time-dependent perturbation theory. Applying our formalism to a synthetic ULDM halo reveals considerable mixing of eigenstates, even though the overall density profile is relatively stable. Our results provide a new analytic approach to understanding the evolution of these systems as well as possibilities for faster approximate simulations., Comment: 12 pages, 11 figures; accepted to PRD The content and conclusions of Sec IV changed in the review process. Fig 9 was changed and Fig 10 added to illustrate our averaging procedure. Fig 11 changed significantly due to a tweak in the analysis pipeline. We added more discussion on the utility of our approach, more information on our numerical solver, and made small editorial changes

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, ${\gamma}$, 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 ${\eta}$-problem in landscape scenarios. For some power spectra Planck-scale saddles have ${\eta} \sim 1$ and eternal, topological inflation would be common in these scenarios. Lower-lying saddles typically have large ${\eta}$, 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., Comment: 21 pages, 13 figures; v2 fixed typo in metadata

The early Universe may have passed through an extended period of matter-dominated expansion following inflation and prior to the onset of radiation domination. Sub-horizon density perturbations grow gravitationally during such an epoch, collapsing into bound structures if it lasts long enough. The strong analogy between this phase and structure formation in the present-day universe allows the use of N-body simulations and approximate methods for halo formation to model the fragmentation of the inflaton condensate into inflaton halos. For a simple model we find these halos have masses of up to $20\,\mathrm{kg}$ and radii of the order of $10^{-20}\,\mathrm{m}$, roughly $10^{-24}$ seconds after the Big Bang. We find that the N-body halo mass function matches predictions of the mass-Peak Patch method and the Press-Schechter formalism within the expected range of scales. A long matter-dominated phase would imply that reheating and thermalization occurs in a universe with large variations in density, potentially modifying the dynamics of this process. In addition, large overdensities can source gravitational waves and may lead to the formation of primordial black holes., Comment: 12 pages, 8 figures, accepted by PRD

The distinctive effects of fuzzy dark matter are most visible at non-linear galactic scales. We present the first simulations of mixed fuzzy and cold dark matter, obtained with an extended version of the Nyx code. Fuzzy (or ultralight, or axion-like) dark matter dynamics are governed by the comoving Schr\"odinger-Poisson equation. This is evolved with a pseudospectral algorithm on the root grid, and with finite differencing at up to six levels of adaptive refinement. Cold dark matter is evolved with the existing N-body implementation in Nyx. We present the first investigations of spherical collapse in mixed dark matter models, focusing on radial density profiles, velocity spectra and soliton formation in collapsed halos. We find that the effective granule masses decrease in proportion to the fraction of fuzzy dark matter which quadratically suppresses soliton growth, and that a central soliton only forms if the fuzzy dark matter fraction is greater than 10\%. The Nyx framework supports baryonic physics and key astrophysical processes such as star formation. Consequently, AxioNyx will enable increasingly realistic studies of fuzzy dark matter astrophysics.

Scientific analyses often rely on slow, but accurate forward models for observable data conditioned on known model parameters. While various emulation schemes exist to approximate these slow calculations, these approaches are only safe if the approximations are well understood and controlled. This workshop submission reviews and updates a previously published method, which has been used in cosmological simulations, to (1) train an emulator while simultaneously estimating posterior probabilities with MCMC and (2) explicitly propagate the emulation error into errors on the posterior probabilities for model parameters. We demonstrate how these techniques can be applied to quickly estimate posterior distributions for parameters of the $\Lambda$CDM cosmology model, while also gauging the robustness of the emulator approximation., Comment: code available from https://doi.org/10.5281/zenodo.3764460 or https://github.com/auckland-cosmo/LearnAsYouGoEmulator

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 $\Lambda$ in an $N$-dimensional Gaussian random potential, quantifying the associated probability density, $p(\Lambda)$. After normalisations $p(\Lambda)$ depends only on the dimensionality $N$ and a single free parameter $\gamma$, 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 $N=100$, $p(\Lambda>0) \approx 10^{-1197}$. 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 $\Lambda \approx 0$ are much flatter than for typical minima, increasingly the viability of quintessence solutions., Comment: 22 pages, 11 figures. $P(\Lambda > 0$ at $N=100$ updated from $10^{-780}$ to $10^{-1197}$; the original error was due to an incorrect value of $\gamma$

In a broad class of scenarios, inflation is followed by an extended era of matter-dominated expansion during which the inflaton condensate is nonrelativistic on subhorizon scales. During this phase density perturbations grow to the point of nonlinearity and collapse into bound structures. This epoch strongly resembles structure formation with ultra-light axion-like particles. This parallel permits us to adapt results from studies of cosmological structure formation to describe the nonlinear dynamics of this post-inflationary epoch. We show that the inflaton condensate fragments into "inflaton clusters", analogues of axion dark matter halos in present-day cosmology. Moreover, solitonic objects or "inflaton stars" can form inside these clusters, leading to density contrasts as large as $10^6$ in the post-inflationary universe., Comment: 11 pages; 3 figures; reformatted, references added, minor changes

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 Schr\"odinger-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., Comment: 4 pages, 3 figures (v2 added refs)

The core-cusp problem is a widely cited motivation for the exploration of dark matter models beyond standard CDM. One such alternative is ULDM; extremely light scalar particles exhibiting wavelike properties on kiloparsec scales. Astrophysically realistic ULDM halos are expected to consist of inner solitonic cores embedded in NFW-like outer halos. The presence of the solitonic core suggests that ULDM may resolve the core-cusp discrepancy associated with pure NFW halos without recourse to baryonic physics. However, it has been demonstrated that the density of ULDM halos can exceed those of comparable NFW configurations at some radii and halo masses, apparently exacerbating the problem rather than solving it. This situation arises because, although solitonic cores are flat at their centres, they obey an inverse mass-radius scaling relationship. Meanwhile, the mass of the inner soliton increases with the total halo mass, and therefore the inner core becomes more peaked at large halo masses. We describe a parameterisation of the radial density profiles of ULDM halos that allows for environmental variability of the core-halo mass relation in order to investigate this issue in more detail. For halos up to 10^12 solar masses we find feasible ULDM profiles for which the central density is lower than their NFW counterparts at astrophysically accessible radii. However, comparisons to observed profiles do not strongly favour either option; both give reasonable fits to subsets of the data for some parameter choices. Consequently, we find that robust tests of the core-cusp problem in ULDM will require more comprehensive observational data and simulations that include baryonic feedback., Comment: 15 pages, accepted for publication in PASA

Direct measurement of acceleration is a key scientific goal for both cosmology and exoplanets. For cosmology, the concept of redshift drift (more than 60 years old by the 2020s) could directly establish the Friedmann-Lema{\^\i}tre-Robertson-Walker model. It would increase the dark energy figure of merit by a factor of 3 beyond Stage 4 experiments, in combination with cosmic microwave background measurements. For exoplanets, the same technology required provides unprecedented radial velocity accuracy, enabling detection of Earth mass planets in the habitable zone. Other science cases include mapping the Milky Way gravitational potential and testing its dark matter distribution., Comment: Science White Paper for the Astro2020 Decadal Survey

Tight constraints on the abundance of primordial black holes can be deduced across a vast range of masses, with the exception of those light enough to fully evaporate before nucleosynthesis. This hypothetical population is almost entirely unconstrained, to the point where the early Universe could pass through a matter-dominated phase with primordial black holes as the primary component. The only obvious relic of this phase would be Hawking radiated gravitons which would constitute a stochastic gravitational wave background in the present-day Universe, albeit at frequencies far beyond the scope of any planned detector technology. This paper explores the effects of classical mergers in such a matter dominated phase. For certain ranges of parameters, a significant fraction of the black holes merge, providing an additional, classical source of primordial gravitational waves. The resulting stochastic background typically has a lower amplitude than the Hawking background and lies at less extreme frequencies, but is unlikely to be easily detectable, with a maximal present day density of $\Omega_{GW} \sim 10^{-12}$ and frequencies between $10^{15} - 10^{19}$ Hz. We also asses the impact of radiation accretion on the lifetimes of such primordial black holes and find that it increases the black hole mass by $\sim 14 \%$ and the lifetimes by about $50 \%$. However, this does not qualitatively change any of our conclusions., Comment: 17 pages, 5 figures; added references, comments on uniform mass distribution and spatial clustering assumptions

The next generation of instruments designed to measure the polarization of the cosmic microwave background (CMB) will provide a historic opportunity to open the gravitational wave window to the primordial Universe. Through high sensitivity searches for primordial gravitational waves, and tighter limits on the energy released in processes like phase transitions, the CMB polarization data of the next decade has the potential to transform our understanding of the laws of physics underlying the formation of the Universe., Comment: 5 pages + references; Submitted to the Astro2020 call for science white papers

Typical stars in the Milky Way galaxy have velocities of hundreds of kilometres per second and experience gravitational accelerations of $\sim 10^{-10}$ m s$^{-2}$, resulting in velocity changes of a few centimetres per second over a decade. Measurements of these accelerations would permit direct tests of the applicability of Newtonian dynamics on kiloparsec length scales and could reveal significant small scale inhomogeneities within the galaxy, as well increasing the sensitivity of measurements of the overall mass distribution of the galaxy. Noting that a reasonable extrapolation of progress in exoplanet hunting spectrographs suggests that centimetre per second level precision will be attainable in the coming decade(s), we explore the possibilities such measurements would create. We consider possible confounding effects, including apparent accelerations induced by stellar motion and reflex velocities from planetary systems, along with possible strategies for their mitigation. If these issues can be satisfactorily addressed it will be possible to use high precision measurements of changing stellar velocities to perform a "blind search" for dark matter, make direct tests of theories of non-Newtonian gravitational dynamics, detect local inhomogeneities in the dark matter density, and greatly improve measurements of the overall properties of the galaxy., Comment: 15 pages, 6 figures, submitted to PASA

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., Comment: available at: https://github.com/auckland-cosmo/PyUltraLight

We describe the general inflationary dynamics that can arise with a single, canonically coupled field where the inflaton potential is a 4-th order polynomial. This scenario yields a wide range of combinations of the empirical spectral observables, $n_s$, $r$ and $\alpha_s$. However, not all combinations are possible and next-generation cosmological experiments have the ability to rule out all inflationary scenarios based on this potential. Further, we construct inflationary priors for this potential based on physically motivated choices for its free parameters. These can be used to determine the degree of tuning associated with different combinations of $n_s$, $r$ and $\alpha_s$ and will facilitate treatments of the inflationary model selection problem. Finally, we comment on the implications of these results for the naturalness of the overall inflationary paradigm. We argue that ruling out all simple potentials would not necessarily imply that the inflationary paradigm itself was unnatural, but that this eventuality would increase the importance of building inflationary scenarios in the context of broader paradigms of ultra-high energy physics., Comment: 28 pages, 12 figures; references added

Oscillons are spatially stationary, quasi-periodic solutions of nonlinear field theories seen in settings ranging from granular systems, low temperature condensates and early universe cosmology. We describe a new class of oscillon in which the spatial envelope can have "off centre" maxima and pulsate on timescales much longer than the fundamental frequency. These are exact solutions of the 1-D sine-Gordon equation and we demonstrate numerically that similar solutions exist in up to three dimensions for a range of potentials. The dynamics of these solutions match key properties of oscillons that may form after cosmological inflation in string-motivated monodromy scenarios., Comment: 4 pages, figues; animations and further background at http://cosmology.blogs.auckland.ac.nz/2016/11/08/two-scale-oscillons/ v2: minor fixes

It is speculated that the correct theory of fundamental physics includes a large landscape of states, which can be described as a potential which is a function of N scalar fields and some number of discrete variables. The properties of such a landscape are crucial in determining key cosmological parameters including the dark energy density, the stability of the vacuum, the naturalness of inflation and the properties of the resulting perturbations, and the likelihood of bubble nucleation events. We codify an approach to landscape cosmology based on specifications of the overall form of the landscape potential and illustrate this approach with a detailed analysis of the properties of N-dimensional Gaussian random landscapes. We clarify the correlations between the different matrix elements of the Hessian at the stationary points of the potential. We show that these potentials generically contain a large number of minima. More generally, these results elucidate how random function theory is of central importance to this approach to landscape cosmology, yielding results that differ substantially from those obtained by treating the matrix elements of the Hessian as independent random variables., Comment: 27 pages, 5 figures and 4 tables

We test the sensitivity of neutrino parameter constraints from combinations of CMB and LSS data sets to the assumed form of the primordial power spectrum (PPS) using Bayesian model selection. Significantly, none of the tested combinations, including recent high-precision local measurements of $\mathrm{H}_0$ and cluster abundances, indicate a signal for massive neutrinos or extra relativistic degrees of freedom. For PPS models with a large, but fixed number of degrees of freedom, neutrino parameter constraints do not change significantly if the location of any features in the PPS are allowed to vary, although neutrino constraints are more sensitive to PPS features if they are known a priori to exist at fixed intervals in $\log k$. Although there is no support for a non-standard neutrino sector from constraints on both neutrino mass and relativistic energy density, we see surprisingly strong evidence for features in the PPS when it is constrained with data from Planck 2015, SZ cluster counts, and recent high-precision local measurements of $\mathrm{H}_0$. Conversely combining Planck with matter power spectrum and BAO measurements yields a much weaker constraint. Given that this result is sensitive to the choice of data this tension between SZ cluster counts, Planck and $\mathrm{H}_0$ measurements is likely an indication of unmodeled systematic bias that mimics PPS features, rather than new physics in the PPS or neutrino sector., Comment: 23 pages, 9 figures, 8 tables; matches version published in JCAP

Cosmological inflation generates primordial density perturbations on all scales, including those far too small to contribute to the cosmic microwave background. At these scales, isolated ultracompact minihalos of dark matter can form well before standard structure formation, if the perturbations have sufficient amplitude. Minihalos affect pulsar timing data and are potentially bright sources of gamma rays. The resulting constraints significantly extend the observable window of inflation in the presence of cold dark matter, coupling two of the key problems in modern cosmology., Comment: 6 pages, 2 figures, 2 tables; matches published version

Even simple inflationary scenarios have many free parameters. Beyond the variables appearing in the inflationary action, these include dynamical initial conditions, the number of fields, and couplings to other sectors. These quantities are often ignored but cosmological observables can depend on the unknown parameters. We use Bayesian networks to account for a large set of inflationary parameters, deriving generative models for the primordial spectra that are conditioned on a hierarchical set of prior probabilities describing the initial conditions, reheating physics, and other free parameters. We use $N_f$--quadratic inflation as an illustrative example, finding that the number of $e$-folds $N_*$ between horizon exit for the pivot scale and the end of inflation is typically the most important parameter, even when the number of fields, their masses and initial conditions are unknown, along with possible conditional dependencies between these parameters., Comment: 24 pages, 9 figures, 1 table; discussion updated

Cosmological analyses can be accelerated by approximating slow calculations using a training set, which is either precomputed or generated dynamically. However, this approach is only safe if the approximations are well understood and controlled. This paper surveys issues associated with the use of machine-learning based emulation strategies for accelerating cosmological parameter estimation. We describe a learn-as-you-go algorithm that is implemented in the Cosmo++ code and (1) trains the emulator while simultaneously estimating posterior probabilities; (2) identifies unreliable estimates, computing the exact numerical likelihoods if necessary; and (3) progressively learns and updates the error model as the calculation progresses. We explicitly describe and model the emulation error and show how this can be propagated into the posterior probabilities. We apply these techniques to the Planck likelihood and the calculation of $\Lambda$CDM posterior probabilities. The computation is significantly accelerated without a pre-defined training set and uncertainties in the posterior probabilities are subdominant to statistical fluctuations. We have obtained a speedup factor of $6.5$ for Metropolis-Hastings and $3.5$ for nested sampling. Finally, we discuss the general requirements for a credible error model and show how to update them on-the-fly., Comment: 20 pages excluding Appendices, 5 figures. Code publicly available at http://cosmopp.com; matches published version

A short inflationary phase may not erase all traces of the primordial universe. Associated observables include both spatial curvature and "anomalies" in the microwave background or large scale structure. The present curvature $\Omega_{K,0}$ reflects the initial curvature, $\Omega_{K,\mathrm{start}}$, and the angular size of anomalies depends on $k_\mathrm{start}$, the comoving horizon size at the onset of inflation. We estimate posteriors for $\Omega_{K,\mathrm{start}}$ and $k_\mathrm{start}$ using current data and simulations, and show that if either quantity is measured to have a non-zero value, both are likely to be observable. Mappings from $\Omega_{K,\mathrm{start}}$ and $k_\mathrm{start}$ to present-day observables depend strongly on the primordial equation of state; $\Omega_{K,0}$ spans ten orders of magnitude for a given $\Omega_{K,\mathrm{start}}$ while a simple and general relationship connects $\Omega_{K,0}$ and $k_\mathrm{start}$. We show that current bounds on $\Omega_{K,0}$ imply that if $k_\mathrm{start}$ is measurable, the curvature was already small when inflation began. Finally, since the energy density changes slowly during inflation, primordial gravitational wave constraints require that a short inflationary phase is preceded by a nontrivial pre-inflationary phase with critical implications for the expected value of $\Omega_{K,\mathrm{start}}$., Comment: Small updates. Matches the published version

We present MultiModeCode, a Fortran 95/2000 package for the numerical exploration of multifield inflation models. This program facilitates efficient Monte Carlo sampling of prior probabilities for inflationary model parameters and initial conditions and is the first publicly available code that can efficiently generate large sample-sets for inflation models with $\mathcal O(100)$ fields. The code numerically solves the equations of motion for the background and first-order perturbations of multi-field inflation models with canonical kinetic terms and arbitrary potentials, providing the adiabatic, isocurvature, and tensor power spectra at the end of inflation. For models with sum-separable potentials MultiModeCode also computes the slow-roll prediction via the $\delta N$ formalism for easy model exploration and validation. We pay particular attention to the isocurvature perturbations as the system approaches the adiabatic limit, showing how to avoid numerical instabilities that affect some other approaches to this problem. We demonstrate the use of MultiModeCode by exploring a few toy models. Finally, we give a concise review of multifield perturbation theory and a user's manual for the program., Comment: 20 pages excluding Appendices, 3 figures. Code publicly available at www.modecode.org

We study the tensor spectral index $n_t$ and the tensor-to-scalar ratio $r$ in the simplest multifield extension to single-field, slow-roll inflation models. We show that multifield models with potentials $V \sim \sum_i \lambda_i |\phi_i|^p$ have different predictions for $n_t/r$ than single-field models, even when all the couplings are equal $\lambda_i=\lambda_j$, due to the probabilistic nature of the fields' initial values. We analyze well-motivated prior probabilities for the $\lambda_i$ and initial conditions to make detailed predictions for the marginalized probability distribution of $n_t/r$. With $\mathcal O(100)$ fields and $p>3/4$, we find that $n_t/r$ differs from the single-field result of $n_t/r=-1/8$ at the 5$\sigma$ level. This gives a novel and testable prediction for the simplest multifield inflation models., Comment: 6 pages, 3 figures; v2: discussion updated, matches version accepted by Phys. Rev. Letters

While cosmological inflation can erase primordial inhomogeneities, it is possible that inflation may not begin in a significantly inhomogeneous universe. This issue is particularly pressing in multifield scenarios, where even the homogeneous dynamics may depend sensitively on the initial configuration. This paper presents an initial survey of the onset of inflation in multifield models, via qualitative lattice-based simulations that do not include local gravitational backreaction. Using hybrid inflation as a test model, our results suggest that small subhorizon inhomogeneities do play a key role in determining whether inflation begins in multifield scenarios. Interestingly, some configurations which do not inflate in the homogeneous limit "succeed" after inhomogeneity is included, while other initial configurations which inflate in the homogeneous limit "fail" when inhomogeneity is added., Comment: 15 pages, 8 figures, 1 table; v2: references added; v3: matches published version

An inflationary gravitational wave background consistent with BICEP2 is difficult to reconcile with a simple power-law spectrum of primordial scalar perturbations. Tensor modes contribute to the temperature anisotropies at multipoles with $l\lesssim 100$, and this effect --- together with a prior on the form of the scalar perturbations --- was the source of previous bounds on the tensor-to-scalar ratio. We compute Bayesian evidence for combined fits to BICEP2 and Planck for three nontrivial primordial spectra: a) a running spectral index, b) a cutoff at fixed wavenumber, and c) a spectrum described by a linear spline with a single internal knot. We find no evidence for a cutoff, weak evidence for a running index, and significant evidence for a "broken" spectrum. Taken at face-value, the BICEP2 results require two new inflationary parameters in order to describe both the broken scale invariance in the perturbation spectrum and the observed tensor-to-scalar ratio. Alternatively, this tension may be resolved by additional data and more detailed analyses., Comment: 14 pages, 5 figures, 4 tables; v2: references added, discussion updated, matches published version

Using the temperature data from Planck we search for departures from a power-law primordial power spectrum, employing Bayesian model-selection and posterior probabilities. We parametrize the spectrum with $n$ knots located at arbitrary values of $\log{k}$, with both linear and cubic splines. This formulation recovers both slow modulations and sharp transitions in the primordial spectrum. The power spectrum is well-fit by a featureless, power-law at wavenumbers $k>10^{-3} \, \mathrm{Mpc}^{-1}$. A modulated primordial spectrum yields a better fit relative to $\Lambda$CDM at large scales, but there is no strong evidence for a departure from a power-law spectrum. Moreover, using simulated maps we show that a local feature at $k \sim 10^{-3} \, \mathrm{Mpc}^{-1}$ can mimic the suppression of large-scale power. With multi-knot spectra we see only small changes in the posterior distributions for the other free parameters in the standard $\Lambda$CDM universe. Lastly, we investigate whether the hemispherical power asymmetry is explained by independent features in the primordial power spectrum in each ecliptic hemisphere, but find no significant differences between them., Comment: 24 pages, 9 figures, 4 tables, 1 appendix; v2: references added, discussion updated, matches published version

We explore whether multifield inflationary models make unambiguous predictions for fundamental cosmological observables. Focusing on $N$-quadratic inflation, we numerically evaluate the full perturbation equations for models with 2, 3, and $\mathcal{O}(100)$ fields, using several distinct methods for specifying the initial values of the background fields. All scenarios are highly predictive, with the probability distribution functions of the cosmological observables becoming more sharply peaked as $N$ increases. For $N=100$ fields, 95% of our Monte Carlo samples fall in the ranges $n_s \in (0.9455,0.9534)$; $\alpha \in (-9.741,-7.047)\times 10^{-4}$; $r\in(0.1445,0.1449)$; and $r_\mathrm{iso} \in (0.02137,3.510)\times 10^{-3}$ for the spectral index, running, tensor-to-scalar ratio, and isocurvature-to-adiabatic ratio, respectively. The expected amplitude of isocurvature perturbations grows with $N$, raising the possibility that many-field models may be sensitive to post-inflationary physics and suggesting new avenues for testing these scenarios., Comment: 5 pages, 4 figure; v2: minor clarifications and references added; version accepted by Phys. Rev. Letters; v3: minor typo corrected

Most treatments of large scale anomalies in the microwave sky are a posteriori, with unquantified look-elsewhere effects. We contrast these with physical models of specific inhomogeneities in the early universe which then generate apparent anomalies. Physical models predict correlations between candidate anomalies, as well as the corresponding signals in polarization and large scale structure, reducing the impact of cosmic variance. We compute the apparent spatial curvature associated with large-scale inhomogeneities and show that it is typically small, allowing for a self-consistent analysis. Focussing on a single large plane wave inhomogeneity, we show this can contribute to low-l mode alignment and odd-even asymmetry in the power spectra and the best fit inhomogeneity accounts for a significant part of the claimed odd-even asymmetry. We argue that this approach can be generalized to provide a more quantitative assessment of potential large scale anomalies in the universe., Comment: Updated to match the published version

We use data from the nominal Planck mission to constrain modulations in the primordial power spectrum associated with monodromy inflation. The largest improvement in fit relative to the unmodulated model has \Delta\chi^2~10 and we find no evidence for a primordial signal, in contrast to a previous analysis of the WMAP9 dataset, for which \Delta\chi^2~20. The Planck and WMAP9 results are broadly consistent on angular scales where they are expected to agree as far as best-fit values are concerned. However, even on these scales the significance of the signal is reduced in Planck relative to WMAP, and is consistent with a fit to the noise associated with cosmic variance. Our results motivate both a detailed comparison between the two experiments and a more careful study of the theoretical predictions of monodromy inflation., Comment: 9 pages + 6 figures

Within the Minimal Supersymmetric Standard Model (MSSM), LHC bounds suggest that scalar superpartner masses are far above the electroweak scale. Given a high superpartner mass, nonthermal dark matter is a viable alternative to WIMP dark matter generated via freezeout. In the presence of moduli fields nonthermal dark matter production is associated with a long matter dominated phase, modifying the spectral index and primordial tensor amplitude relative to those in a thermalized primordial universe. Nonthermal dark matter can have a higher self-interaction cross-section than its thermal counterpart, enhancing astrophysical bounds on its annihilation signals. We constrain the contributions to the neutralino mass from the bino, wino and higgsino using existing astrophysical bounds and direct detection experiments for models with nonthermal neutralino dark matter. Using these constraints we quantify the expected change to inflationary observables resulting from the nonthermal phase., Comment: 19 pages, 5 figures

Oscillons are long-lived, localized excitations of nonlinear scalar fields which may be copiously produced during preheating after inflation, leading to a possible oscillon-dominated phase in the early Universe. For example, this can happen after axion monodromy inflation, on which we run our simulations. We investigate the stochastic gravitational wave background associated with an oscillon-dominated phase. An isolated oscillon is spherically symmetric and does not radiate gravitational waves, and we show that the flux of gravitational radiation generated between oscillons is also small. However, a significant stochastic gravitational wave background may be generated during preheating itself (i.e, when oscillons are forming), and in this case the characteristic size of the oscillons is imprinted on the gravitational wave power spectrum, which has multiple, distinct peaks., Comment: 19 pages, 5 figures, JHEP version

We investigate the initial conditions problem for multifield inflation. In these scenarios the pre-inflationary dynamics can be chaotic, increasing the sensitivity of the onset of inflation to the initial data even in the homogeneous limit. To analyze physically equivalent scenarios we compare initial conditions at fixed energy. This ensures that each trajectory is counted once and only once, since the energy density decreases monotonically. We present a full analysis of hybrid inflation that reveals a greater degree of long range order in the set of "successful" initial conditions than was previously apparent. We explore the effective smoothing scale for the fractal set of successful initial conditions induced by the finite duration of the pre-inflationary phase. The role of the prior information used to specify the initial data is discussed in terms of Bayesian sampling., Comment: 18 pages, 8 figures, 3 tables; matches published version

We use cosmic microwave background (CMB) data from the 9-year WMAP release to derive constraints on monodromy inflation, which is characterized by a linear inflaton potential with a periodic modulation. We identify two possible periodic modulations that significantly improve the fit, but it is unclear whether this improvement is associated with a "signal" or with the scatter in the measured angular power spectrum. The unmodulated potential is mildly favored by standard model selection criteria. A modulated inflationary potential can generate substantial primordial non-Gaussianity, of a specific and characteristic form. For the best-fit parameters to the WMAP angular power spectrum, the corresponding non-Gaussianity might be detectable in upcoming CMB data, allowing nontrivial consistency checks on the predictions of a modulated inflationary potential., Comment: Version 3 -- minor editorial corrections. Version 2 -- significant revision from v1 (Overall amplitude of the potential added as a free parameter; still see two localized peaks in modulation frequency, but the best fit has significantly improved, to -2 \Delta log(L) ~ -20 with respect to reference model)