Search

It has been known that a non-perfect fluid that accounts for dissipative viscous effects can evade a highly anisotropic chaotic mixmaster approach to a singularity. Viscosity is often simply parameterised in this context, so it remains unclear whether isotropisation can really occur in physically motivated contexts. We present a few examples of microphysical manifestations of viscosity in fluids that interact either gravitationally or, for a scalar field for instance, through a self-coupling term in the potential. In each case, we derive the viscosity coefficient and comment on the applicability of the approximations involved when dealing with dissipative non-perfect fluids. Upon embedding the fluids in a cosmological context, we then show the extent to which these models allow for isotropisation of the universe in the approach to a singularity. We first do this in the context of expansion anisotropy only, i.e., in the case of a Bianchi type-I universe. We then include anisotropic 3-curvature modelled by the Bianchi type-IX metric. It is found that a self-interacting scalar field at finite temperature allows for efficient isotropisation, whether in a Bianchi type-I or type-IX spacetime, although the model is not tractable all the way to a singularity. Mixmaster chaotic behaviour, which is well known to arise in anisotropic models including anisotropic 3-curvature, is found to be suppressed in the latter case as well. We find that the only model permitting an isotropic singularity is that of a dense gas of black holes., Comment: 24 pages, 3 figures; v2: typos corrected, clarifications and references added; v3: more clarifications and references added, matches published version

We probe the cosmological consequences of a recently proposed class of solutions to the cosmological constant problem. In these models, the universe undergoes a long period of inflation followed by a contraction and a bounce that sets the stage for the hot big bang era. A requirement of any successful early universe model is that it must reproduce the observed scale-invariant density perturbations at cosmic microwave background (CMB) scales. While these class of models involve a long period of inflation, the inflationary Hubble scale during their observationally relevant stages is at or below the current Hubble scale, rendering the de Sitter fluctuations too weak to seed the CMB anisotropies. We show that sufficiently strong perturbations can still be sourced thermally if the relaxion field serving as the inflaton interacts with a thermal bath, which can be generated and maintained by the same interaction. We present a simple model where the relaxion field is derivatively (i.e., technically naturally) coupled to a non-Abelian gauge sector, which gets excited tachyonically and subsequently thermalizes due to its nonlinear self-interactions. This model explains both the smallness of the cosmological constant and the amplitude of CMB anisotropies.

Detection of a stochastic background of gravitational waves is likely to occur in the next few years. Beyond searches for the isotropic component of SGWBs, there have been various mapping methods proposed to target anisotropic backgrounds. Some of these methods have been applied to data taken by the Laser Interferometer Gravitational-wave Observatories (LIGO) and Virgo. Specifically, these directional searches have focused on mapping the intensity of the signal on the sky via maximum likelihood solutions. We compare this intensity mapping approach to a previously proposed, but never employed, amplitude-phase mapping method to understand whether this latter approach may be employed in future searches. We build up our understanding of the differences between these two approaches by analysing simple toy models of time-stream data, and run mock-data mapping tests for the two methods. We find that the amplitude-phase method is only applicable to the case of a background which is phase-coherent on large scales or, at the very least, has an intrinsic coherence scale that is larger than that of the detector. Otherwise, the amplitude-phase mapping method leads to a loss of overall information, with respect to both phase and amplitude. Since we do not expect these phase-coherent properties to hold for any of the gravitational-wave background signals we hope to detect in the near future, we conclude that intensity mapping is the preferred method for such backgrounds., 15 pages, 4 figures

Macroscopic dark matter is almost unconstrained over a wide "asteroid-like" mass range, where it could scatter on baryonic matter with geometric cross section. We show that when such an object travels through a star, it produces shock waves which reach the stellar surface, leading to a distinctive transient optical, UV and X-ray emission. This signature can be searched for on a variety of stellar types and locations. In a dense globular cluster, such events occur far more often than flare backgrounds, and an existing UV telescope could probe orders of magnitude in dark matter mass in one week of dedicated observation., 13 pages, 5 figures. v2: clarifications and references added, matches journal version

We introduce and validate a delensing framework for the Simons Observatory (SO), which will be used to improve constraints on inflationary gravitational waves (IGWs) by reducing the lensing noise in measurements of the $B$-modes in CMB polarization. SO will initially observe CMB by using three small aperture telescopes and one large-aperture telescope. While polarization maps from small-aperture telescopes will be used to constrain IGWs, the internal CMB lensing maps used to delens will be reconstructed from data from the large-aperture telescope. Since lensing maps obtained from the SO data will be noise-dominated on sub-degree scales, the SO lensing framework constructs a template for lensing-induced $B$-modes by combining internal CMB lensing maps with maps of the cosmic infrared background from Planck as well as galaxy density maps from the LSST survey. We construct a likelihood for constraining the tensor-to-scalar ratio $r$ that contains auto- and cross-spectra between observed $B$-modes and the lensing $B$-mode template. We test our delensing analysis pipeline on map-based simulations containing survey non-idealities, but that, for this initial exploration, does not include contamination from Galactic and extragalactic foregrounds. We find that the SO survey masking and inhomogeneous and atmospheric noise have very little impact on the delensing performance, and the $r$ constraint becomes $\sigma(r)\approx 0.0015$ which is close to that obtained from the idealized forecasts in the absence of the Galactic foreground and is nearly a factor of two tighter than without delensing. We also find that uncertainties in the external large-scale structure tracers used in our multi-tracer delensing pipeline lead to bias much smaller than the $1\,\sigma$ statistical uncertainties., Comment: 22 pages, 14 figures

It was recently shown that a powerful beam of radio/microwave radiation sent out to space can produce detectable back-scattering via the stimulated decay of ambient axion dark matter. This echo is a faint and narrow signal centered at an angular frequency close to half the axion mass. In this article, we provide a detailed analytical and numerical analysis of this signal, considering the effects of the axion velocity distribution as well as the outgoing beam shape. In agreement with the original proposal, we find that the divergence of the outgoing beam does not affect the echo signal, which is only constrained by the axion velocity distribution. Moreover, our findings are relevant for the optimization of the experimental parameters in order to attain maximal signal to noise or minimal energy consumption., Comment: Matches published version

Improved measurement of the Cosmic Microwave Background polarization from Planck allows a detailed study of reionization beyond the average optical depth. The lower value of the optical depth disfavours an early onset and an early completion of reionization in favour of a redsfhit range where different astrophysical probes provide sensible information on the sources of reionization and the status of the intergalactic medium. In this work we extend our previous study in which we constrained reionization by combining three different probes - CMB, UV luminosity density and neutral hydrogen fraction data - in both treatment and data: we first allow variation in the UV source term varying the product of the efficiency of conversion of UV luminosity into ionizing photons and the escape fraction together with the reionization and cosmological parameters, and then we investigate the impact of a less conservative cut for the UV luminosity function. We find that the estimate for the efficiency is consistent within 95% C.L. with the fixed value we considered in our previous results and is mostly constrained by the QHII data. We find that allowing the efficiency to vary does not affect significantly our results for the average optical depth for monotonic reionization histories, recovering $\tau=0.0519_{-0.0008}^{+0.0010}$ at 68% CL , consistent with our previous studies. Using a less conservative cut for the UV luminosity function, we find $\tau=0.0541_{-0.0016}^{+0.0013}$ at 68% CL, due to the faint end of the luminosity function in the data we use, that also prefers a larger contribution from higher redshifts., Comment: 18 pages, 20 figures, updated version to match the published one

Cosmic Microwave Background (CMB) observations are used to constrain reheating to Standard Model (SM) particles after a period of inflation. As a light spectator field, the SM Higgs boson acquires large field values from its quantum fluctuations during inflation, gives masses to SM particles that vary from one Hubble patch to another, and thereby produces large density fluctuations. We consider both perturbative and resonant decay of the inflaton to SM particles. For the case of perturbative decay from coherent oscillations of the inflaton after high scale inflation, we find strong constraints on the reheat temperature for the inflaton decay into heavy SM particles. For the case of resonant particle production (preheating) to (Higgsed) SM gauge bosons, we find temperature fluctuations larger than observed in the CMB for a range of gauge coupling that includes those found in the SM and conclude that such preheating cannot be the main source of reheating the Universe after inflation., Comment: 24 pages, 10 figures, references added, minor changes

We investigate the phenomenological consequences of axion-like particle (ALP) dark matter with an early matter domination triggered by primordial black holes (PBHs). We focus on light BHs with masses smaller than $\sim 10^9~$g which fully evaporate before Big Bang nucleosynthesis. We numerically solve the coupled Boltzmann equations, carefully taking the greybody factors and BH angular momentum into account. We find that the entropy injection from PBH evaporation dilutes the ALP relic abundance originally produced via the vacuum misalignment mechanism, opening the parameter space with larger scales $f_a$ or, equivalently, smaller ALP-photon couplings $g_{a\gamma}$, within the reach of future detectors as ABRACADABRA, KLASH, ADMX, and DM-Radio. Moreover, the ALP minicluster masses can be several orders of magnitude larger if the early Universe features an PBH dominated epoch. For the relativistic ALPs produced directly from Hawking radiation, we find that their contribution to the dark radiation is within the sensitivity of next generation CMB experiments. For the sake of completeness, we also revisit the particular case of the QCD axion., Comment: 23 pages, 6 figures; V2: references updated; version accepted for publication in PRD

Paleo-detectors are a proposed experimental technique to search for dark matter by reading out the damage tracks caused by nuclear recoils in small samples of natural minerals. Unlike a conventional real-time direct detection experiment, paleo-detectors have been accumulating these tracks for up to a billion years. These long integration times offer a unique possibility: by reading out paleo-detectors of different ages, one can explore the time-variation of signals on megayear to gigayear timescales. We investigate two examples of dark matter substructure that could give rise to such time-varying signals. First, a dark disk through which the Earth would pass every $\sim$45 Myr, and second, a dark matter subhalo that the Earth encountered during the past gigayear. We demonstrate that paleo-detectors are sensitive to these examples under a wide variety of experimental scenarios, even in the presence of substantial background uncertainties. This paper shows that paleo-detectors may hold the key to unraveling our Galactic history., 26 pages, 16 figures, 2 tables, code available at https://github.com/sbaum90/paleoSens and https://github.com/sbaum90/paleoSpec. Published version

The next generation of galaxy surveys like the Dark Energy Spectroscopic Instrument (DESI) and Euclid will provide datasets orders of magnitude larger than anything available to date. Our ability to model nonlinear effects in late time matter perturbations will be a key to unlock the full potential of these datasets, and the area of initial condition reconstruction is attracting growing attention. Iterative reconstruction developed in Ref. [1] is a technique designed to reconstruct the displacement field from the observed galaxy distribution. The nonlinear displacement field and initial linear density field are highly correlated. Therefore, reconstructing the nonlinear displacement field enables us to extract the primordial cosmological information better than from the late time density field at the level of the two-point statistics. This paper will test to what extent the iterative reconstruction can recover the true displacement field and construct a perturbation theory model for the postreconstructed field. We model the iterative reconstruction process with Lagrangian perturbation theory~(LPT) up to third order for dark matter in real space and compare it with $N$-body simulations. We find that the simulated iterative reconstruction does not converge to the nonlinear displacement field, and the discrepancy mainly appears in the shift term, i.e., the term correlated directly with the linear density field. On the contrary, our 3LPT model predicts that the iterative reconstruction should converge to the nonlinear displacement field. We discuss the sources of discrepancy, including numerical noise/artifacts on small scales, and present an ad hoc phenomenological model that improves the agreement., Comment: 19 pages, 11 figures, submitted to PRD

In our recent companion paper [arXiv:2106.00022], we pointed out a novel signature of ultralight kinetically mixed dark-photon dark matter. This signature is a quasi-monochromatic, time-oscillating terrestrial magnetic field that takes a particular pattern over the surface of the Earth. In this work, we present a search for this signal in existing, unshielded magnetometer data recorded by geographically dispersed, geomagnetic stations. The dataset comes from the SuperMAG Collaboration and consists of measurements taken with one-minute cadence since 1970, with $\mathcal{O}(500)$ stations contributing in all. We aggregate the magnetic field measurements from all stations by projecting them onto a small set of global vector spherical harmonics (VSH) that capture the expected vectorial pattern of the signal at each station. Within each dark-photon coherence time, we use a data-driven technique to estimate the broadband background noise in the data, and search for excess narrowband power in this set of VSH components; we stack the searches in distinct coherence times incoherently. Following a Bayesian analysis approach that allows us to account for the stochastic nature of the dark-photon dark-matter field, we set exclusion bounds on the kinetic mixing parameter in the dark-photon dark-matter mass range $2\times10^{-18}\,\text{eV} \lesssim m_{A'} \lesssim 7\times10^{-17}\,\text{eV}$ (corresponding to frequencies $6\times 10^{-4}\,\text{Hz}\lesssim f_{A'} \lesssim 2\times 10^{-2}\,\text{Hz}$). These limits are complementary to various existing astrophysical constraints. Although our main analysis also identifies a number of candidate signals in the SuperMAG dataset, these appear to either fail or be in tension with various additional robustness checks we apply to those candidates. We report no robust and significant evidence for a dark-photon dark-matter signal in the SuperMAG dataset., Comment: 41 pages, 11 figures. Published version

A problematic feature of low energy scale inflationary models, such as Starobinsky inflation, in a spatially closed universe is the occurrence of a recollapse and a big crunch singularity before inflation can even set in. In a recent work it was shown that this problem can be successfully resolved in loop quantum cosmology for a large class of initial conditions due to a non-singular cyclic evolution and a hysteresis-like phenomena. However, for certain highly unfavorable initial conditions the onset of inflation was still difficult to obtain. In this work, we explore the role of dissipative particle production, which is typical in warm inflation scenario, in the above setting. We find that entropy production sourced by such dissipative effects makes hysteresis-like phenomena stronger. As a result, the onset of inflation is quick in general including for highly unfavorable initial conditions where it fails or is significantly delayed in the absence of dissipative effects. We phenomenologically consider three warm inflation scenarios with distinct forms of dissipation coefficient, and from dynamical solutions and phase space portraits find that the phase space of favorable initial conditions turns out to be much larger than in cold inflation., 19 pages, 12 figures. Discussion revised. References added. To appear in Phys. Rev. D

Gravitational-wave cosmology began in 2017 with the observation of the gravitational waves emitted in the merger of two neutron stars, and the coincident observation of the electromagnetic emission that followed. Although only a $30\%$ measurement of the Hubble constant was achieved, future observations may yield more precise measurements either through other coincident events or through cross correlation of gravitational-wave events with galaxy catalogs. Here, we implement a new way to measure the Hubble constant without an electromagnetic counterpart and through the use of the binary Love relations. These relations govern the tidal deformabilities of neutron stars in an equation-of-state insensitive way. Importantly, the Love relations depend on the component masses of the binary in the source frame. Since the gravitational-wave phase and amplitude depend on the chirp mass in the observer (and hence redshifted) frame, one can in principle combine the binary Love relations with the gravitational-wave data to directly measure the redshift, and thereby infer the value of the Hubble constant. We implement this approach in both real and synthetic data through a Bayesian parameter estimation study in a range of observing scenarios. We find that for the LIGO/Virgo/KAGRA design sensitivity era, this method results in a similar measurement accuracy of the Hubble constant to those of current-day, dark-siren measurements. For third generation detectors, this accuracy improves to $\lesssim 10\%$ when combining measurements from binary neutron star events in the LIGO Voyager era, and to $\lesssim 2\%$ in the Cosmic Explorer era., accepted in PRD

Velocity fields can be reconstructed at cosmological scales from their influence on the correlation between the cosmic microwave background and large-scale structure. Effects that induce such correlations include the kinetic Sunyaev Zel'dovich (kSZ) effect and the moving-lens effect, both of which will be measured to high precision with upcoming cosmology experiments. Galaxy measurements also provide a window into measuring velocities from the effect of redshift-space distortions (RSDs). The information that can be accessed from the kSZ or RSDs, however, is limited by astrophysical uncertainties and systematic effects, which may significantly reduce our ability to constrain cosmological parameters such as $f\sigma_8$. In this paper, we show how the large-scale transverse-velocity field, which can be reconstructed from measurements of the moving-lens effect, can be used to measure $f\sigma_8$ to high precision., Comment: 7 pages, 5 figures, comments welcome

We consider searches for the inelastic scattering of low-mass dark matter at direct detection experiments, using the Migdal effect. We find that there are degeneracies between the dark matter mass and the mass splitting that are difficult to break. Using XENON1T data we set bounds on a previously unexplored region of the inelastic dark matter parameter space. For the case of exothermic scattering, we find that the Migdal effect allows xenon-based detectors to have sensitivity to dark matter with ${\cal O}(\mathrm{MeV})$ mass, far beyond what can be obtained with nuclear recoils alone., 6 pages, 4 figures (v2: 1 figure and additional discussion added)

It was recently found that, when linearised in the absence of matter, 58 cases of the general gravitational theory with quadratic curvature and torsion are (i) free from ghosts and tachyons and (ii) power-counting renormalisable. We inspect the nonlinear Hamiltonian structure of the eight cases whose primary constraints do not depend on the curvature tensor. We confirm the particle spectra and unitarity of all these theories in the linear regime. We uncover qualitative dynamical changes in the nonlinear regimes of all eight cases, suggesting at least a broken gauge symmetry, and possibly the activation of negative kinetic energy spin-parity sectors and acausal behaviour. Two of the cases propagate a pair of massless modes at the linear level, and were interesting as candidate theories of gravity. However, we identify these modes with vector excitations, rather than the tensor polarisations of the graviton. Moreover, we show that these theories do not support a viable cosmological background., Comment: 20 pages, 0 figures

Electroweak baryogenesis (EWBG) is sourced by nonstandard $CP$-violating interactions of the Higgs boson with fermions, usually taken to be the top quark, enhanced by its large Yukawa coupling. Numerous papers have studied EWBG sourced by lighter fermions, including the tau lepton and off-diagonal quark mass terms. We critically reassess the viability of EWBG in these scenarios, comparing the predictions based on the semiclassical (WKB) formalism for the source term to those from the VEV insertion approximation (VIA), using updated values for the collision terms, and clarifying discrepancies in the definition of the weak sphaleron rate. The VIA systematically predicts a baryon asymmetry that is orders of magnitude larger than the WKB formalism. We trace this to the differing shapes of the $CP$-violating source terms in the two formalisms, showing that the additional spatial derivative in the WKB source term causes large cancellations when it is integrated over the bubble wall profile. An important exception is a source term from $c$-$t$ quark mixing, where the WKB prediction also allows for a realistically large baryon asymmetry. In contrast, the analogous $b$-$s$ mixing source is found to be orders of magnitude too small., Comment: 13 pages, 4 figures

Ultralight axion-like particles are well-motivated dark matter candidates that are the target of numerous direct detection efforts. In the vicinity of the Solar System, such particles can be treated as oscillating scalar fields. The velocity dispersion of the Milky Way determines a coherence time of about 10^6 oscillations, beyond which the amplitude of the axion field fluctuates stochastically. Any analysis of data from an axion direct detection experiment must carefully account for this stochastic behavior to properly interpret the results. This is especially true for experiments sensitive to the gradient of the axion field that are unable to collect data for many coherence times. Indeed, the direction, in addition to the amplitude, of the axion field gradient fluctuates stochastically. We present the first complete stochastic treatment for the gradient of the axion field, including multiple computationally efficient methods for performing likelihood-based data analysis, which can be applied to any axion signal, regardless of coherence time. Additionally, we demonstrate that ignoring the stochastic behavior of the gradient of the axion field can potentially result in failure to discover a true axion signal., Comment: 16 pages, figures

An excess of 511 keV photons has been detected from the central region of the Milky Way. It has been suggested that the positrons responsible for this signal could be produced through the Hawking evaporation of primordial black holes. After evaluating the constraints from INTEGRAL, COMPTEL, and Voyager 1, we find that black holes in mass range of $\sim(1-4)\times10^{16}$ g could potentially produce this signal if they make up a small fraction of the total dark matter density. Proposed MeV-scale gamma-ray telescopes such as AMEGO or e-ASTROGAM should be able to test this class of scenarios by measuring the diffuse gamma ray emission from the Milky Way's inner halo., Comment: 8 pages, 5 figures

Exotic electromagnetic energy injection in the early Universe may alter cosmological recombination, and ultimately cosmic microwave background (CMB) anisotropies. Moreover, if energy injection is inhomogeneous, it may induce a spatially-varying ionization fraction, and non-Gaussianity in the CMB. The observability of these signals, however, is contingent upon how far the injected particles propagate and deposit their energy into the primordial plasma, relative to the characteristic scale of energy injection fluctuations. In this study we inspect the spatial properties of energy deposition and perturbed recombination resulting from an inhomogeneous energy injection of sub-10 MeV photons, relevant to accreting primordial black holes (PBHs). We develop a novel Monte-Carlo radiation transport code accounting for all relevant photon interactions in this energy range, and including secondary electron energy deposition efficiency through a new analytic approximation. For a specified injected photon spectrum, the code outputs an injection-to-deposition Green's function depending on time and distance from the injection point. Combining this output with a linearized solution of the perturbed recombination problem, we derive time- and scale-dependent deposition-to-ionization Green's functions. We apply this general framework to accreting PBHs, whose luminosity is strongly spatially modulated by supersonic relative velocities between cold dark matter and baryons. We find that the resulting spatial fluctuations of the free-electron fraction are of the same magnitude as its mean deviation from standard recombination, from which current CMB power spectra constraints are derived. This work suggests that the sensitivity to accreting PBHs might be substantially improved by propagating these inhomogeneities to CMB anisotropy power spectra and non-Gaussian statistics, which we study in subsequent papers., Comment: Version accepted in PRD

Dark matter (DM) could be a relic of freeze-in through a light mediator, where the DM is produced by extremely feeble, IR-dominated processes in the thermal Standard Model plasma. In the simplest viable models with the DM mass below the MeV scale, the DM has a small effective electric charge and is born with a nonthermal phase-space distribution. This DM candidate would cause observable departures from standard cosmological evolution. In this work, we combine data from the cosmic microwave background (CMB), Lyman-$\alpha$ forest, quasar lensing, stellar streams, and Milky Way satellite abundances to set a lower limit on freeze-in DM masses up to $\sim 20\,$keV, with the exact constraint depending on whether the DM thermalizes in its own sector. We perform forecasts for the CMB-S4 experiment, the Hydrogen Epoch of Reionization Array, and the Vera Rubin Observatory, finding that freeze-in DM masses up to $\sim 80\,$keV can be explored. These cosmological probes are highly complementary with proposed direct-detection efforts to search for this DM candidate., Comment: 5+17 pages, 3+9 figures

We identify potential sources of decoherence for $U(1)$ gauge bosons from a cosmological standpoint. Besides interactions with different species in the cosmological medium, we also consider effects due to the expansion of the Universe, which can produce particles (especially scalars) than can potentially interact with the photon in a quantum state. We look in particular at the case of axion-like particles and their predicted decay channels in our analysis. These interactions are shown to have a negligible effect as far as decoherence goes. Interaction rates with CMB radiation or through Thomson scattering are small, so that the interstellar medium remains the biggest decoherence factor. Thus, quantum teleportation experiments with photon energies in the range $1$-$10$ keV should be feasible at cosmological distances up to the galaxy formation epoch or beyond ($z \sim 100$)., Comment: 11 pages

We propose a new reionization probe that uses cosmic microwave background (CMB) observations; the cross-correlation between fluctuations in the CMB optical depth which probes the integrated electron density, $\delta\tau$, and the Compton $y$-map which probes the integrated electron pressure. This cross-correlation is much less contaminated than the $y$-map power spectrum by late-time cluster contributions. In addition, this cross-correlation can constrain the temperature of ionized bubbles while the optical-depth fluctuations and kinetic SZ effect can not. We measure this new observable using a Planck $y$-map as well as a map of optical-depth fluctuations that we reconstruct from Planck CMB temperature data. We use our measurements to derive a first CMB-only upper limit on the temperature inside ionized bubbles, $T_{\rm b}\lesssim 7.0\times10^5\,$K ($2\,\sigma$). We also present future forecasts, assuming a fiducial model with characteristic reionization bubble size $R_{\rm b}=5\,$Mpc and $T_{\rm b}=5\times10^4\,$K. The signal-to-noise ratio of the fiducial cross-correlation using a signal dominated PICO-like $y$-map becomes $\simeq7$ with CMB-S4 $\delta\tau$ and $\simeq13$ with CMB-HD $\delta\tau$. For the fiducial model, we predict that the CMB-HD $-$ PICO cross-correlation should achieve an accurate measurement of the reionization parameters; $T_{\rm b}\simeq 49800^{+4500}_{-5100}\,$K and $R_{\rm b}\simeq 5.09^{+0.66}_{-0.79}\,$Mpc. Since the power spectrum of the electron density fluctuations is constrained by the $\delta\tau$ auto spectrum, the temperature constraints should be only weakly model-dependent on the details of the electron distributions and should be statistically representative of the temperature in ionized bubbles during reionization. This cross-correlation could, therefore, become an important observable for future CMB experiments., Comment: 13 pages, 9 figures, Accepted for publication in PRD

We propose a novel probe of fundamental physics that involves the exploration of temporal correlations between the multi-frequency electromagnetic (EM) signal and the sub-threshold GW signal or stochastic gravitational wave background (SGWB) originating from coalescing binaries. This method will be useful for the detection of EM counterparts associated with the sub-threshold/SGWB signal. Exploiting the time delay between concomitant emission of the gravitational wave and EM signals enables inference of the redshifts of the contributing sources by studying the time delay dilation due to cosmological expansion, provided that the time-lag between the emission of gravitational wave signal and the EM signal acts like a standard clock. Measurement of the inevitable time-domain correlations between different frequencies of gravitational and EM waves, most notably in gamma-rays, will test several aspects of fundamental physics and gravitation theory, and enable a new pathway for current and future gravitational wave telescopes to study the universal nature of binary compact objects to high redshifts., Comment: 12 pages, 3 figures, 1 table. Accepted for publication in Phys. Rev. D

We consider k-essence, a scalar-tensor theory with first-order derivative self-interactions that can screen local scales from scalar fifth forces, while allowing for sizeable deviations from general relativity on cosmological scales. We construct fully nonlinear static stellar solutions that show the presence of this screening mechanism, and we use them as initial data for simulations of stellar oscillations and gravitational collapse in spherical symmetry. We find that for k-essence theories of relevance for cosmology, the screening mechanism works in the case of stellar oscillation and suppresses the monopole scalar emission to undetectable levels. In collapsing stars, we find that the Cauchy problem, although locally well posed, can lead to diverging characteristic speeds for the scalar field. By introducing a "fixing equation"in the spirit of J. Cayuso et al. [Phys. Rev. D 96, 084043 (2017)PRVDAQ2470-001010.1103/PhysRevD.96.084043], inspired in turn by dissipative relativistic hydrodynamics, we manage to evolve collapsing neutron stars past the divergence of the characteristic speeds. We show that, in these systems, the screening mechanism is less efficient than for oscillating and static stars, because the collapsing star must shed away all of its scalar hair before forming a black hole. For k-essence theories of relevance for cosmology, the characteristic frequency of the resulting scalar monopole signal is too low for terrestrial detectors, but we conjecture that space-borne interferometers such as the Laser Interferometer Space Antenna might detect it if a supernova explodes in the Galaxy., We thank L. Lehner for enlightening conversations on the well-posedness of the Cauchy problem. M. B., L. t. H., M. C., and E. B. acknowledge support from the European Union’s H2020 ERC Consolidator Grant “Gravity from Astrophysical to Microscopic Scales” (Grant No. GRAMS-815673). C. P. acknowledges support from the Spanish Ministry of Economy and Competitiveness Grants No. AYA2016-80289-P and No. PID2019–110301 GB-I00 (AEI/FEDER, UE). M. B. acknowledges the support of the PHAROS COST Action (CA16214).

We investigate scenarios with $\mathcal{O}(1\mathrm{\,TeV})$ scalar leptoquarks that act as portals between the Standard Model and Dark Matter. We assume that Dark Matter is a scalar singlet $S$ which couples to a scalar leptoquark $\Delta$ and the Higgs boson via the terms in the scalar potential. In addition, the leptoquark is endowed with Yukawa couplings to quarks and leptons that may address the anomalies in $B$ meson decays. We consider the $SS$ annihilation cross sections to estimate the Dark Matter relic abundance and explore the interplay between astrophysical, collider and flavour physics bounds on such models. In the heavy Dark Matter window, $m_S > m_\Delta$, the leptoquark portal becomes the dominant mechanism to explain the Dark Matter abundance. We find that the leptoquark Yukawa couplings, relevant for quark and lepton flavour physics, are decoupled from the dark matter phenomenology. By focussing on a scenario with a single leptoquark state, we find that relic density can only be explained when both $\Delta$ and $S$ masses are lighter than $\mathcal{O}(10\mathrm{\,TeV})$., Comment: Version as published

It is shown that the equalization of temperatures between our and mirror sectors occurs during one Hubble time due to microscopic black hole production and evaporation in particle collisions if the temperature of the Universe is near the multidimensional Plank mass. This effect excludes the multidimensional Planck masses smaller than the reheating temperature of the Universe ($\sim10^{13}$ GeV) in the mirror matter models, because the primordial nucleosynthesis theory requires that the temperature of the mirror world should be lower than ours. In particular, the birth of microscopic black holes in the LHC is impossible if the dark matter of our Universe is represented by baryons of mirror matter. It excludes some of the possible coexisting options in particle physics and cosmology. Multidimensional models with flat additional dimensions are already strongly constrained in maximum temperature due to the effect of Kaluza-Klein mode (KK-mode) overproduction. In these models, the reheating temperature should be significantly less than the multidimensional Planck mass, so our restrictions in this case are not paramount. The new constraints play a role in multidimensional models in which the spectrum of KK-modes does not lead to their overproduction in the early Universe, for example, in theories with hyperbolic additional space., Comment: 8 pages, 1 figure, accepted for publication in Phys. Rev. D, replaced by the accepted version

Dwarf spheroidal galaxies are dark matter dominated systems, and as such, ideal for indirect dark matter searches. If dark matter decays into high-energy photons in the dwarf galaxies, they will be a good target for current and future generations of X-ray and gamma-ray telescopes. By adopting the latest estimates of density profiles of dwarf galaxies in the Milky Way, we revise the estimates dark matter decay rates in dwarf galaxies; our results are more robust, but weaker than previous estimates. Applying these results, we study the detectability of dark matter decays with X-ray and very-high-energy gamma-ray telescopes, such as eROSITA, XRISM, Athena, HAWC, and CTA. Our projection shows that all of these X-ray telescopes will be able to critically assess the claim of the 7 keV sterile neutrino decays from stacked galaxy clusters and nearby galaxies. For TeV decaying dark matter, we can constrain its lifetime to be longer than $\sim$10$^{27}$-10$^{28}$ s. We also make projections for future dwarf galaxies that would be newly discovered with the Vera Rubin Observatory Legacy Survey of Space and Time, which will further improve the expected sensitivity to dark matter decays both in the keV and PeV mass ranges., Comment: 18 pages, 15 figures; comments welcome

The vacuum expectation value $v_s$ of a Higgs triplet field $\Delta$ carrying two units of lepton number $L$ induces neutrino masses $\propto v_s$. The neutral component of $\Delta$ gives rise to two Higgs particles, a pseudoscalar $A$ and a scalar $S$. The most general renormalizable Higgs potential $V$ for $\Delta $ and the Standard-Model Higgs doublet $\Phi$ does not permit the possibility that the mass of either $A$ or $S$ is small, of order $v_s$, while the other mass is heavy enough to forbid the decay $Z\to A S$ to comply with LEP 1 data. We present a model with additional dimension-6 terms in $V$, in which this feature is absent and either $A$ or $S$ can be chosen light. Subsequently we propose the model as a remedy to cosmological anomalies, namely the tension between observed and predicted tensor-to-scalar mode ratios in the cosmic microwave background and the different values of the Hubble constant measured at different cosmological scales. Furthermore, if $\Delta$ dominantly couples to the third-generation doublet $L_\tau=(\nu_\tau,\tau)$, the deficit of $\nu_\tau$ events at IceCube can be explained. The singly and doubly charged triplet Higgs bosons are lighter than 280 GeV and 400 GeV respectively, and could be found at the LHC., Comment: 5 pages, 2 figures. More pedagogical explanation of model and UV completion (with extra figure), typos fixed

We study the gravitational field sourced by localized scalar fields (lumps) in higher-derivative theories of gravity. By working in a static and spherically symmetric configuration, we find the linearized spacetime metrics generated by scalar lumps for several Lagrangians: the vanishing potential, i.e. free massive scalar field, a polynomial potential, and the tachyon potential in open string field theory. We perform the analysis for different theories of gravity: Einstein's general relativity, four-derivative gravity, and ghost-free nonlocal gravity. We discuss the limit of validity of our analysis and comment on possible future applications in the context of astrophysical compact objects., 21 pages, 6 figures. V2: version accepted for publication in PRD

A cosmological model with an energy transfer between dark matter (DM) and dark energy (DE) can give rise to comparable energy densities at the present epoch. The present work deals with the perturbation analysis, parameter estimation and Bayesian evidence calculation of interacting models with dynamical coupling parameter that determines the strength of the interaction. We have considered two cases, where the interaction is a more recent phenomenon and where the interaction is a phenomenon in the distant past. Moreover, we have considered the quintessence DE equation of state with Chevallier-Polarski-Linder (CPL) parametrisation and energy flow from DM to DE. Using the current observational datasets like the cosmic microwave background (CMB), baryon acoustic oscillation (BAO), Type Ia Supernovae (SNe Ia) and redshift-space distortions (RSD), we have estimated the mean values of the parameters. Using the perturbation analysis and Bayesian evidence calculation, we have shown that interaction present as a brief early phenomenon is preferred over a recent interaction., Version published in Phys. Rev. D

The Planck mass and the cosmological constant determine the minimum and the maximum distances in the physical universe. A relativistic theory that takes into account a fundamental distance limit $\ell$ on par with the fundamental speed limit $c$, is based on the de Sitter extension of the Lorentz symmetry. This article proposes a new de Sitter gauge theory of gravity which allows the consistent cosmological evolution of the $\ell$. The theory is locally equivalent to Dirac's scale-invariant version of general relativity, and suggests a novel non-singular extension of cosmology., 9 pages, 0 figures

Dark sector particles with small electric charge, or millicharge, (mCPs) may lead to a variety of diverse phenomena in particle physics, astrophysics and cosmology. Assuming their possible existence, we investigate the accumulation and propagation of mCPs in matter, specifically inside the Earth. Even small values of millicharge lead to sizeable scattering cross sections on atoms, resulting in complete thermalization, and as a consequence, considerable build-up of number densities of mCPs, especially for the values of masses of GeV and higher when the evaporation becomes inhibited. Enhancement of mCP densities compared to their galactic abundance, that can be as big as $10^{14}$, leads to the possibility of new experimental probes for this model. The annihilation of pairs of mCPs will result in new signatures for the large volume detectors (such as Super-Kamiokande). Formation of bound states of negatively charged mCPs with nuclei can be observed by direct dark matter detection experiments. A unique probe of mCP can be developed using underground electrostatic accelerators that can directly accelerate mCPs above the experimental thresholds of direct dark matter detection experiments., Comment: 15 pages, 8 figures

We investigate the inflationary consequences of the oscillating dark energy model proposed by Ti��n [\href{https://doi.org/10.1103/PhysRevD.101.063531}{Phys. Rev. D {\bf 101}, 063531 (2020)}], which aims to solve the cosmological coincidence problem with multi-accelerating Universe (MAU). We point out that the inflationary dynamics belong to slow-roll inflation. The spectral index of scalar perturbations and the tensor-to-scalar ratio $r$ are shown to be consistent with current \textit{Planck} measurements. Especially, this model predicts $r\sim10^{-7}$, which is far below the observation limits. This result motivates us to explore the smallness of $r$ in the general MAU. We propose a quintessential generalization of the original model and prove $r, 8 pages, 3 figures, published in Phys. Rev. D

A new dynamic is identified between dark matter and nuclei. Nuclei accelerated to MeV energies by the internal potential of composite dark matter can undergo nuclear fusion. This effect arises in simple models of composite dark matter made of heavy fermions bound by a light scalar field. Cosmologies and detection prospects are explored for composites that catalyze nuclear reactions in underground detectors and stars, including bremsstrahlung radiation from nuclei scattering against electrons in hot plasma formed in the composite interior. If discovered and collected, this kind of composite dark matter could in principle serve as a ready-made, compact nuclear fusion generator., Comment: 8 pages, 2 figures, PRD version

Germanium is the detector material of choice in many rare-event searches looking for low-energy nuclear recoils induced by dark matter particles or neutrinos. We perform a systematic exploration of its quenching factor for sub-keV nuclear recoils, using multiple techniques: photo-neutron sources, recoils from gamma-emission following thermal neutron capture, and a monochromatic filtered neutron beam. Our results point to a marked deviation from the predictions of the Lindhard model in this mostly unexplored energy range. We comment on the compatibility of our data with low-energy processes such as the Migdal effect, and on the impact of our measurements on upcoming searches., Comment: 10 pages, 10 figures

Physical review letters 126(24), 241801 (2021). doi:10.1103/PhysRevLett.126.241801, We show that the commonly adopted hot dark matter bound on the axion mass ma≲1 eV is not reliable, since it is obtained by extrapolating the chiral expansion in a region where the effective field theory breaks down. This is explicitly shown via the calculation of the axion-pion thermalization rate at the next-to-leading order in chiral perturbation theory. We finally advocate a strategy for a sound extraction of the axion hot dark matter bound via lattice QCD techniques., Published by APS, College Park, Md.

The possibility of a non-gravitational interaction between the dark matter and the dark energy has been reconstructed using some recent datasets. The crucial aspect is that the interaction is not parametrized at the outset, but rather reconstructed directly from the data in a non-parametric way. The Cosmic Chronometer Hubble data, the Pantheon Supernova compilation of CANDELS and CLASH Multy-Cycle Treasury programs obtained by the HST, and the Baryon Acoustic Oscillation Hubble data have been considered in this work. The widely accepted Gaussian Process is used for the reconstruction. The results clearly indicate that a no interaction scenario is quite a possibility. Also, the interaction, if any, is not really significant at the present epoch. The direction of the flow of energy is clearly from the dark energy to the dark matter which is consistent with the thermodynamic requirement., Comment: 19 pages, 12 sets of figures, Accepted for publication in Phys. Rev. D

We provide evidence that gravitational radiation in a 4D radiation-dominated universe, with equation-of-state $w=1/3$, consists of two components: helicity-2 gravitons and massless scalar acoustic waves. On physical grounds, we would expect the homogeneous solution of the Weyl tensor components to be a good approximation to its inhomogeneous counterparts, whenever the observer is located well in the far zone of an isolated astrophysical source of cosmological gravitational radiation. We show explicitly that these homogeneous and inhomogeneous solutions both receive contributions from the gauge-invariant tensor {\it and} the two Bardeen (acoustic) scalars. Comparison of these Weyl tensor computations thus allows us to not only identify, in the high frequency limit, the corresponding gravitational tensor and scalar radiation; but also their oscillatory polarization patterns., 30 pages, version accepted by PRD

We have studied the merger rate of primordial black holes (PBHs) in the ellipsoidal-collapse model of halo to explain the dark matter abundance by the PBH merger estimated from the gravitational waves detections via the Advanced LIGO (aLIGO) detectors. We have indicated that the PBH merger rate within each halo for the ellipsoidal models is more significant than for the spherical models. We have specified that the PBH merger rate per unit time and per unit volume for the ellipsoidal-collapse halo models is about one order of magnitude higher than the corresponding spherical models. Moreover, we have calculated the evolution of the PBH total merger rate as a function of redshift. The results indicate that the evolution for the ellipsoidal halo models is more sensitive than spherical halo models, as expected from the models. Finally, we have presented a constraint on the PBH abundance within the context of ellipsoidal and spherical models. By comparing the results with the aLIGO mergers during the third observing run (O3), we have shown that the merger rate in the ellipsoidal-collapse halo models falls within the aLIGO window, while the same result is not valid for the spherical-collapse ones. Furthermore, we have compared the total merger rate of PBHs in terms of their fraction in the ellipsoidal-collapse halo models for several masses of PBHs. The results suggest that the total merger rate of PBHs changes inversely with their masses. We have also estimated the relation between the fraction of PBHs and their masses in the ellipsoidal-collapse halo model and have shown it for a narrow mass distribution of PBHs. The outcome shows that the constraint inferred from the PBH merger rate for the ellipsoidal-collapse halo models can be potentially stronger than the corresponding result obtained for the spherical-collapse ones., Comment: 13 pages, 6 figures, refs. added

The advent of Stage IV weak lensing surveys will open up a new era in precision cosmology. These experiments will offer more than an order-of-magnitude leap in precision over existing surveys, and we must ensure that the accuracy of our theory matches this. Accordingly, it is necessary to explicitly evaluate the impact of the theoretical assumptions made in current analyses on upcoming surveys. One effect typically neglected in present analyses is the Doppler-shift of the measured source comoving distances. Using Fisher matrices, we calculate the biases on the cosmological parameter values inferred from a Euclid-like survey, if the correction for this Doppler-shift is omitted. We find that this Doppler-shift can be safely neglected for Stage IV surveys. The code used in this investigation is made publicly available., 8 pages, 1 figure. Accepted to Phys. Rev. D. Matches published version. Code available at https://github.com/desh1701/k-cut_reduced_shear

We determine the upper limit on the mass of the lightest neutrino from the most robust recent cosmological and terrestrial data. Marginalizing over possible effective relativistic degrees of freedom at early times ($N_\mathrm{eff}$) and assuming normal mass ordering, the mass of the lightest neutrino is less than 0.037 eV at 95% confidence; with inverted ordering, the bound is 0.042 eV. These results improve upon the strength and robustness of other recent limits and constrain the mass of the lightest neutrino to be barely larger than the largest mass splitting. We show the impacts of realistic mass models, and different sources of $N_\mathrm{eff}$., 5 pages, 2 figures + Appendix. Full dataset available at https://doi.org/10.5281/zenodo.4005381 (v3: Matches version published in PRD)

Although the idea that there is a maximum force in nature seems untenable, we explore whether this concept can make sense in the restricted context of black holes. We discuss uniformly accelerated and cosmological black holes and we find that, although a maximum force acting on these black holes can in principle be introduced, this concept is rather tautological., Comment: 7 pages, no figures, to appear in Phys. Rev. D

We propose a novel method to detect cosmic magnification signals by cross-correlating foreground convergence fields constructed from galaxy shear measurements with background galaxy positional distributions, namely shear-number density correlation. We apply it to the Hyper Suprime-Cam Subaru Strategic Program (HSC-SSP) survey data. With 27 non-independent data points and their full covariance, $\chi_0^2\approx 34.1$ and $\chi_T^2\approx 24.0$ with respect to the null and the cosmological model with the parameters from HSC shear correlation analyses in Hamana et al. 2020 (arXiv:1906.06041), respectively. The Bayes factor of the two is $\log_{10}B_{T0}\approx 2.2$ assuming equal model probabilities of null and HSC cosmology, showing a clear detection of the magnification signals. Theoretically, the ratio of the shear-number density and shear-shear correlations can provide a constraint on the effective multiplicative shear bias $\bar m$ using internal data themselves. We demonstrate the idea with the signals from our HSC-SSP mock simulations and rescaling the statistical uncertainties to a survey of $15000\deg^2$. For two-bin analyses with background galaxies brighter than $m_{lim}=23$, the combined analyses lead to a forecasted constraint of $\sigma(\bar m) \sim 0.032$, $2.3$ times tighter than that of using the shear-shear correlation alone. Correspondingly, $\sigma(S_8)$ with $S_8=\sigma_8(\Omega_\mathrm{m}/0.3)^{0.5}$ is tightened by $\sim 2.1$ times. Importantly, the joint constraint on $\bar m$ is nearly independent of cosmological parameters. Our studies therefore point to the importance of including the shear-number density correlation in weak lensing analyses, which can provide valuable consistency tests of observational data, and thus to solidify the derived cosmological constraints., Comment: 9 pages, 4 figures; Accepted for publication in PRD

We examine the cosmological and astrophysical signatures of a "dark baryon," a neutral fermion that mixes with the neutron. As the mixing is through a higher-dimensional operator at the quark level, production of the dark baryon at high energies is enhanced so that its abundance in the early universe may be significant. Treating its initial abundance as a free parameter, we derive new, powerful limits on the properties of the dark baryon. Primordial nucleosynthesis and the cosmic microwave background provide strong constraints due to the inter-conversion of neutrons to dark baryons through their induced transition dipole, and due to late decays of the dark baryon. Additionally, neutrons in a neutron star could decay slowly to dark baryons, providing a novel source of heat that is constrained by measurements of pulsar temperatures. Taking all the constraints into account, we identify parameter space where the dark baryon can be a viable dark matter candidate and discuss promising avenues for probing it., Comment: 10 pages + refs revtex4, 4 figures

Galactic scale tests have proven to be powerful tools in constraining fundamental physics in previously under-explored regions of parameter space. The astrophysical regime which they probe is inherently complicated, and the inference methods used to make these constraints should be robust to baryonic effects. Previous analyses have assumed simple empirical models for astrophysical noise without detailed calibration or justification. We outline a framework for assessing the reliability of such methods by constructing and testing more advanced baryonic models using cosmological hydrodynamical simulations. As a case study, we use the Horizon-AGN simulation to investigate warping of stellar disks and offsets between gas and stars within galaxies, which are powerful probes of screened fifth forces. We show that the degree of `U'-shaped warping of galaxies is well modelled by Gaussian random noise, but that the magnitude of the gas-star offset is correlated with the virial radius of the host halo. By incorporating this correlation we confirm recent results ruling out astrophysically relevant Hu-Sawicki $f(R)$ gravity, and identify a $\sim 30\%$ systematic uncertainty due to baryonic physics. Such an analysis must be performed case-by-case for future galactic tests of fundamental physics., 17 pages, 11 figures, 2 tables, accepted for publication in Physical Review D

We study the phenomenon of gravitational particle production as applied to a scalar spectator field in the context of $\alpha$-attractor inflation. Assuming that the scalar has a minimal coupling to gravity, we calculate the abundance of gravitationally-produced particles as a function of the spectator's mass $m_\chi$ and the inflaton's $\alpha$ parameter. If the spectator is stable and sufficiently weakly coupled, such that it does not thermalize after reheating, then a population of spin-0 particles is predicted to survive in the universe today, providing a candidate for dark matter. Inhomogeneities in the spatial distribution of dark matter correspond to an isocurvature component, which can be probed by measurements of the cosmic microwave background anisotropies. We calculate the dark matter-photon isocurvature power spectrum and by comparing with upper limits from Planck, we infer constraints on $m_\chi$ and $\alpha$. If the scalar spectator makes up all of the dark matter today, then for $\alpha = 10$ and $T_\text{RH} = 10^4 \ \mathrm{GeV}$ we obtain $m_\chi > 1.8 \times 10^{13} \ \mathrm{GeV} \approx 1.2 \, m_\phi$, where $m_\phi$ is the inflaton's mass., Comment: 21 pages + references, 8 figures; added references, matches PRD

We propose a self-interacting inelastic dark matter (DM) scenario as a possible origin of the recently reported excess of electron recoil events by the XENON1T experiment. Two quasi-degenerate Majorana fermion DM interact within themselves via a light hidden sector massive gauge boson and with the standard model particles via gauge kinetic mixing. We also consider an additional long-lived singlet scalar which helps in realising correct dark matter relic abundance via a hybrid setup comprising of both freeze-in and freeze-out mechanisms. While being consistent with the required DM phenomenology along with sufficient self-interactions to address the small scale issues of cold dark matter, the model with GeV scale DM can explain the XENON1T excess via inelastic down scattering of heavier DM component into the lighter one. All these requirements leave a very tiny parameter space keeping the model very predictive for near future experiments., Comment: 34 pages, 14 figures, version accepted for publication in PRD

We study cross correlations between line intensity and weak lensing maps to search for axion-like particles (ALPs). Radiative decay of eV-mass ALPs can contribute to cosmic background emissions at optical and infrared wavelengths. Line intensity mapping is a unique means of measuring the background emission at a given photon frequency. If ALPs constitute the abundance of cosmic dark matter, line intensity maps can correlate with large-scale structures probed by weak gravitational lensing effects in galaxy imaging surveys. We develop a theoretical framework to predict the cross correlation. We then explore potentiality of probing ALPs with the cross correlation in upcoming galaxy-imaging and spectral surveys. Assuming SPHEREx and the Vera Rubin Observatory's Legacy Survey of Space and Time (LSST), we find that the cross correlation by the ALP decay can be greater than the astrophysical-line counterparts at wavelength of $\sim3000\, {\rm nm}$ for ALPs with a particle mass of $m_a\sim1\, \mathrm{eV}$ and a particle-to-two-photons coupling of $g_{a\gamma\gamma}\sim1\times10^{-11}\, \mathrm{GeV}^{-1}$. We also predict that a null detection of the cross correlation can place a $2\sigma$-level upper bound of $g_{a\gamma\gamma} \lower.5ex\hbox{$\; \buildrel < \over \sim \;$} 10^{-11}\, \mathrm{GeV}^{-1}$ for eV-mass ALPs, improving the current constraint by a factor of $\sim10$. We then make a forecast of expected constraints on ALP parameters in SPHEREx and LSST by Fisher analysis, providing a guideline of searching for the ALP decay with the large-scale structure data., Comment: 18 pages, 9 figures, 2 tables. Accepted for publication in Phys. Rev. D