arXiv subjects

Glenn D. Starkman

Publications and source records attributed to Glenn D. Starkman.

At least 19 recordsLinked to original sources

arXiv2026

Breaking de Sitter Symmetry with Cosmic Topology: Cosmological Role of Infrared Vacuum Freedom

When spatial sections of spacetime are topologically nontrivial, the symmetry arguments usually used to choose the Bunch-Davies vacuum are no longer guaranteed to apply. We study this problem for a scalar field on de Sitter spacetime with toroidal spatial sections. The Hadamard conditions, which ensure the same short-distance structure as in flat space, are local and naturally insensitive to the compactification. By contrast, we find that the infrared sector is affected by the toroidal identifications that break global de Sitter invariance, thereby removing the usual argument for discarding zero-mode contributions. We treat the remaining zero-mode freedom as an effective topology-induced source and analyze its effects on an inflationary de Sitter expansion within a semiclassical setting. We show that, for a massless scalar, the zero-mode sector can contain a contribution to the stress-energy tensor with equation of state $P=-ρ$, behaving as a cosmological constant. Thus, the source driving an early-Universe de Sitter phase need not be determined solely by local terms in the action, but can also depend on the infrared structure of the quantum state. Nontrivial topology, as a concrete realization of de Sitter symmetry violation, turns the otherwise-unfixed infrared freedom in vacuum selection to a contribution directly relevant to the semiclassical expansion. This contribution could potentially be applicable to the current accelerated expansion of the Universe.

hep-th↗

arXiv2026

Quantum Signatures of Cosmic Topology: How Casimir Backreaction Transmits Isotropy Violation

A finite, scheme-independent Casimir contribution to the stress-energy tensor arises naturally for quantum fields in universes with non-trivial spatial topology. We compute this Casimir stress-energy tensor contribution for a conformally coupled scalar field and for a minimally coupled scalar field. We show that, for the conformally coupled case, the backreaction of this contribution to the Einstein equations during an expanding de Sitter phase drives anisotropic expansion even when the Universe begins in a locally homogeneous and isotropic state. We conclude that quantum imprints of the underlying non-trivial topology inevitably give rise to local departures from homogeneity and isotropy.

hep-th↗

arXiv2026

To CPL, or not to CPL? What we have not learned about the dark energy equation of state

We show that using a Taylor expansion for the dark energy equation-of-state parameter and limiting it to the zeroth and first-order terms, i.e., the so-called Chevallier-Polarski-Linder (CPL) parametrization in regimes where it has been shown to fail as a physics-based two-parameter model, instead of allowing for higher-order terms and then marginalizing over them, adds extra information not present in the data and leads to markedly different and potentially misleading conclusions. Fixing the higher-order terms to zero, one concludes that vacuum energy that is currently non-dynamical (e.g., the cosmological constant) is excluded at several $σ$ significance as the explanation of cosmic acceleration, even in Dark Energy Spectroscopic Survey (DESI) DR1 data. Meanwhile, instead marginalizing over the higher-order terms shows that we know neither the current dark energy equation of state nor its current rate of change well enough to make such a claim. The CPL parametrization also implies that dark energy exhibits phantom behavior at high redshifts, while we show that by allowing the higher-order terms---which is required in order to capture the behavior of the dark energy equation of state in regimes beyond the validity of the CPL parametrization---the evidence for this phantom-like dark energy significantly weakens. This is not an argument for the higher-order phenomenological parametrizations, but rather a caution regarding such parametrizations in general. This issue has become more prominent now with the recent release of high-quality Stage IV galaxy survey data. The results of analyses using simple parametrizations should be interpreted with great care.

astro-ph.CO↗

arXiv2026

Cosmic topology. Part Va. Information content of the observable Universe

If the Universe possesses a compact spatial topology with characteristic scale not much larger than the diameter of the observable Universe, then the associated symmetry transformations imprint specific statistical correlations on density perturbations. We derive the covariance between perturbation modes in the full topology volume and compute the induced covariance between modes in the observable subvolume. We then use this covariance to estimate the available information about topology contained in the full set of observable linear perturbations. For two sample Euclidean examples - the cubic three-torus ($E_1$) and a three-torus with a quarter turn ($E_3$) - the three-dimensional density field carries enough information to detect topology on scales up to 25 percent larger than those accessible from the two-dimensional cosmic microwave background anisotropies alone. Future probes of the cosmic density field using deep galaxy surveys or neutral-hydrogen 21-cm intensity mapping, combined with computationally intensive searches over the large parameter space of admissible topologies, thus offer a plausible avenue to extending the range of detectable cosmic topologies.

astro-ph.CO↗

arXiv2026

The Topology of the Universe

Is the Universe infinite in all directions? The only way to know is to look. A non-trivial cosmic topology would imprint subtle signatures on the cosmic microwave background (CMB) and on the three-dimensional distribution of matter, breaking statistical isotropy and, potentially, homogeneity at the largest scales. If the topology scale is small enough, these signatures would be observable. Over the past three decades, successive space missions, most notably WMAP and $\textit{Planck}$, have enabled sophisticated searches for these signatures, using methods ranging from looking for matched circle pairs to full Bayesian likelihood analysis based on topology-dependent covariance matrices. Although these searches have yielded no definitive evidence for non-trivial topology, current constraints exclude only some topologies, parameter ranges, and observer positions. Recent advances show that detectable signals may persist even when the topology scale exceeds the size of the visible Universe. Planned CMB experiments, including LiteBIRD and $\textit{Taurus}$, and high-precision galaxy and line intensity-mapping surveys, could expand the detectable parameter space by exploiting polarisation data, and by exploring topology-induced correlations at all accessible redshifts. Whether cosmic topology is observable remains uncertain, but current and future data offer an unprecedented opportunity to probe the global structure of the Universe.

astro-ph.CO↗

arXiv2026

Strong Evidence Against a Statistically Isotropic Universe

The standard cosmological model predicts statistically isotropic cosmic microwave background (CMB) fluctuations characterized by the CMB temperature coefficients $a_{\ell m}$ being independent Gaussian random variables with zero mean and with variance that depends only on $\ell$. However, several summary statistics of CMB isotropy have anomalous values, including: the low level of large-angle temperature correlations, $S_{1/2}$; the excess power in odd versus even low-$\ell$ multipoles, $R^{TT}$; the (low) variance of large-scale temperature anisotropies in the ecliptic north, but not the south, $σ^2_{16}$; and the alignment and planarity of the quadrupole and octopole of temperature, $S_{QO}$. Individually, their low $p$-values are weak evidence for violation of statistical isotropy. We study the tail values of these statistics and find very little correlation among them. We show that the joint probability of all four anomalies occurring by chance in $Λ$CDM is likely $\leq3\times10^{-8}$. We examine the balance in the impact of look-elsewhere effects and the existence of other anomalies on the significance of this result. We argue that non-Gaussianity alone is unlikely to account for the anomalies seen at the level of the angular power spectrum, $C_\ell$, and that they instead appear to require correlations between $a_{\ell m}$. Our results provide strong evidence for a violation of statistical isotropy, and we conclude that the anomalies should not be dismissed as flukes within $Λ$CDM.

astro-ph.CO↗

arXiv2026

Cosmic topology. Part IIc. Detectability with non-standard primordial power spectrum

Non-trivial spatial topology of the Universe can imprint potentially observable signatures on the cosmic microwave background (CMB). In this study, we investigate how deviations from the standard nearly-scale-free primordial power spectrum impact observables for the fully compact, orientable Euclidean topologies ($E_1$--$E_6$). We examine how such deviations modify the detectability of the underlying topology, depending on whether they are an intrinsic consequence of non-trivial topology or independent of it. We compute CMB temperature correlation matrices across a range of topologies, fundamental domain sizes, and observer locations for both standard and modified primordial power spectra. The impact of these modifications on the detectability of topology is quantified using the Kullback-Leibler divergence, providing an estimate of the distinguishability of non-trivial and simply-connected topologies based solely on CMB temperature observations. In addition, we employ the CatBoost machine learning algorithm to classify harmonic-space realizations of CMB temperature maps and thereby assess the observational prospects for topology detection. Signatures of non-trivial topology are encoded in the off-diagonal structure of the CMB temperature correlation matrices and are most prominent on the largest angular scales. Deviations from the simple power-law primordial spectrum at these scales can substantially alter the detectability of topology, either enhancing its characteristic CMB imprints or suppressing them below observational sensitivity. Our results demonstrate that uncertainties in the primordial power spectrum must be carefully accounted for in robust searches for cosmic topology using the CMB.

astro-ph.CO↗

arXiv2025

Cosmic topology. Part IIb. Eigenmodes, correlation matrices, and detectability of non-orientable Euclidean manifolds

If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. In this paper we consider the non-orientable Euclidean topologies \E{7}--\E{10}, \E{13}--\E{15}, and \E{17}, encompassing the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the CMB sky. We find that in manifolds where the distance to our nearest clone is less than about $1.2$ times the diameter of the last scattering surface of the CMB, we expect a correlation signal that is larger than cosmic variance noise in the CMB. Our limited selection of manifold parameters are exemplary of interesting behaviors, but not necessarily representative. Future searches for topology will require a thorough exploration of the parameter space to determine what values of the parameters predict statistical correlations that are convincingly attributable to topology.[Abridged]

astro-ph.CO↗

arXiv2025

Cosmic topology. Part IIIb. Eigenmodes and correlation matrices of spin-2 perturbations in orientable Euclidean manifolds

We study the eigenmodes of the spin-2 Laplacian in orientable Euclidean manifolds and their implications for the tensor-induced part of the cosmic microwave background (CMB) temperature and polarization anisotropies. We provide analytic expressions for the correlation matrices of Fourier-mode amplitudes and of spherical harmonic coefficients. We demonstrate that non-trivial spatial topology alters the statistical properties of CMB tensor anisotropies, inducing correlations between harmonic coefficients of differing $\ell$ and $m$ and across every possible pair of temperature and $E$- and $B$-modes of polarization. This includes normally forbidden $TB$ and $EB$ correlations. We compute the Kullback-Leibler (KL) divergence between the pure tensor-induced CMB fluctuations in the usual infinite covering space and those in each of the non-trivial manifolds under consideration, varying both the size of the manifolds and the location of the observer. We find that the amount of information about the topology of the Universe contained in tensor-induced anisotropies does not saturate as fast as its scalar counterpart; indeed, the KL divergence continues to grow with the inclusion of higher multipoles up to the largest $\ell$ we have computed. Our results suggest that CMB polarization measurements from upcoming experiments can provide new avenues for detecting signatures of cosmic topology, motivating a full analysis where scalar and tensor perturbations are combined and noise is included.

astro-ph.CO↗

arXiv2025

Cosmic topology. Part Ic. Limits on lens spaces from circle searches

Cosmic microwave background (CMB) temperature and polarization observations indicate that in the best-fit $Λ$ Cold Dark Matter model of the Universe, the local geometry is consistent with at most a small amount of positive or negative curvature, i.e., $\vertΩ_K\vert\ll1$. However, whether the geometry is flat ($E^3$), positively curved ($S^3$) or negatively curved ($H^3$), there are many possible topologies. Among the topologies of $S^3$ geometry, the lens spaces $L(p,q)$, where $p$ and $q$ ($p>1$ and $0<q<p$) are positive integers, are quotients of the covering space of $S^3$ (the three-sphere) by ${\mathbb{Z}}_p$, the cyclic group of order $p$. We use the absence of any pair of circles on the CMB sky with matching patterns of temperature fluctuations to establish constraints on $p$ and $q$ as a function of the curvature scale that are considerably stronger than those previously asserted for most values of $p$ and $q$. The smaller the value of $\vertΩ_K\vert$, i.e., the larger the curvature radius, the larger the maximum allowed value of $p$. For example, if $\vertΩ_K\vert\simeq 0.05$ then $p\leq 9 $, while if $\vertΩ_K\vert\simeq 0.02$, $p$ can be as high as 24. Future work will extend these constraints to a wider set of $S^{3}$ topologies.

astro-ph.CO↗

arXiv2025

Gravitational Wave Scattering From the Sun and Planets

General relativity predicts that massless waves should scatter from the Riemann curvature of their backgrounds. These scattered waves are sometimes called $\textit{tails}$ and have never been directly observed. Here we calculate the gravitational waves scattered in the backward direction (scattering angle $\vartheta=π$) from the weak-field curvature of an extended massive object, finding close agreement with previous results in the long-wavelength limit. These long-wavelength results are then applied to gravitational waves in the Laser Interferometer Space Antenna (LISA) sensitivity band scattering from the Sun and planets. We estimate that scattering from the Sun and the planets from Jupiter to Neptune could contribute a $10^{-3}$ amplitude modulation to LISA observations when these objects almost intersect the line of sight between LISA and the source, leading to forward scattering with $\vartheta\simeq0$. These conditions should be realized for the Sun during the lifetime of LISA if the detection rate of long-duration sources is not much smaller than a thousand per year.

gr-qc↗

arXiv2024

Cosmic topology. Part I. Limits on orientable Euclidean manifolds from circle searches

The Einstein field equations of general relativity constrain the local curvature at every point in spacetime, but say nothing about the global topology of the Universe. Cosmic microwave background anisotropies have proven to be the most powerful probe of non-trivial topology since, within $Λ$CDM, these anisotropies have well-characterized statistical properties, the signal is principally from a thin spherical shell centered on the observer (the last scattering surface), and space-based observations nearly cover the full sky. The most generic signature of cosmic topology in the microwave background is pairs of circles with matching temperature and polarization patterns. No such circle pairs have been seen above noise in the WMAP or Planck temperature data, implying that the shortest non-contractible loop around the Universe through our location is longer than 98.5% of the comoving diameter of the last scattering surface. We translate this generic constraint into limits on the parameters that characterize manifolds with each of the nine possible non-trivial orientable Euclidean topologies, and provide a code which computes these constraints. In all but the simplest cases, the shortest non-contractible loop in the space can avoid us, and be shorter than the diameter of the last scattering surface by a factor ranging from 2 to at least 6. This result implies that a broader range of manifolds is observationally allowed than widely appreciated. Probing these manifolds will require more subtle statistical signatures than matched circles, such as off-diagonal correlations of harmonic coefficients.

astro-ph.CO↗

arXiv2024

Cosmic topology. Part IIIa. Microwave background parity violation without parity-violating microphysics

The standard cosmological model, which assumes statistical isotropy and parity invariance, predicts the absence of correlations between even-parity and odd-parity observables of the cosmic microwave background (CMB). Contrary to these predictions, large-angle CMB temperature anomalies generically involve correlations between even-$\ell$ and odd-$\ell$ angular power spectrum $C_\ell$, while recent analyses of CMB polarization have revealed non-zero equal-$\ell$ $EB$ correlations. These findings challenge the conventional understanding, suggesting deviations from statistical isotropy, violations of parity, or both. Cosmic topology, which involves changing only the boundary conditions of space relative to standard cosmology, offers a compelling framework to potentially account for such parity-violating observations. Topology inherently breaks statistical isotropy, and can also break homogeneity and parity, providing a natural paradigm for explaining observations of parity-breaking observables without the need to add parity violation to the underlying microphysics. Our investigation delves into the harmonic space implications of topology for CMB correlations, using as an illustrative example $EB$ correlations generated by tensor perturbations under both parity-preserving and parity-violating scenarios. Consequently, these findings not only challenge the foundational assumptions of the standard cosmological model but also open new avenues for exploring the topological structure of the Universe through CMB observations.

astro-ph.CO↗

arXiv2024

Cosmological constraints on anisotropic Thurston geometries

Much of modern cosmology relies on the Cosmological Principle, the assumption that the Universe is isotropic and homogeneous on sufficiently large scales, but it remains worthwhile to examine cosmological models that violate this principle slightly. We examine a class of such spacetimes that maintain homogeneity but break isotropy through their underlying local spatial geometries. These spacetimes are endowed with one of five anisotropic model geometries of Thurston's geometrization theorem, and their evolution is sourced with perfect fluid dust and cosmological constant. We show that the background evolution of these spacetimes induces fluctuations in the observed cosmic microwave background (CMB) temperature with amplitudes coupled to the curvature parameter $Ω_K$. In order for these fluctuations to be compatible with the observed CMB angular power spectrum, we find $|Ω_K| \lesssim 10^{-5}$ is required in all five geometries. This strongly limits the cosmological consequences of these models.

astro-ph.CO↗

arXiv2024

Cosmic topology. Part IVa. Classification of manifolds using machine learning: a case study with small toroidal universes

Non-trivial spatial topology of the Universe may give rise to potentially measurable signatures in the cosmic microwave background. We explore different machine learning approaches to classify harmonic-space realizations of the microwave background in the test case of Euclidean $E_1$ topology (the 3-torus) with a cubic fundamental domain of a size scale significantly smaller than the diameter of the last scattering surface. This is the first step toward developing a machine learning approach to classification of cosmic topology and likelihood-free inference of topological parameters. Different machine learning approaches are capable of classifying the harmonic-space realizations with accuracy greater than 99% if the topology scale is half of the diameter of the last-scattering surface and orientation of the topology is known. For distinguishing random rotations of these sky realizations from realizations of the covering space, the extreme gradient boosting classifier algorithm performs best with an accuracy of 88%. Slightly lower accuracies of 83% to 87% are obtained with the random forest classifier along with one- and two-dimensional convolutional neural networks. The techniques presented here can also accurately classify non-rotated cubic $E_1$ topology realizations with a topology scale slightly larger than the diameter of the last-scattering surface, if enough training data are provided. While information compressing methods like most machine learning approaches cannot exceed the statistical power of a likelihood-based approach that captures all available information, they potentially offer a computationally cheaper alternative. A principle challenge appears to be accounting for arbitrary orientations of a given topology, although this is also a significant hurdle for likelihood-based approaches.

astro-ph.CO↗

arXiv2024

Cosmic topology. Part IIa. Eigenmodes, correlation matrices, and detectability of orientable Euclidean manifolds

If the Universe has non-trivial spatial topology, observables depend on both the parameters of the spatial manifold and the position and orientation of the observer. In infinite Euclidean space, most cosmological observables arise from the amplitudes of Fourier modes of primordial scalar curvature perturbations. Topological boundary conditions replace the full set of Fourier modes with specific linear combinations of selected Fourier modes as the eigenmodes of the scalar Laplacian. We present formulas for eigenmodes in orientable Euclidean manifolds with the topologies $E_{1}-E_{6}$, $E_{11}$, $E_{12}$, $E_{16}$, and $E_{18}$ that encompass the full range of manifold parameters and observer positions, generalizing previous treatments. Under the assumption that the amplitudes of primordial scalar curvature eigenmodes are independent random variables, for each topology we obtain the correlation matrices of Fourier-mode amplitudes (of scalar fields linearly related to the scalar curvature) and the correlation matrices of spherical-harmonic coefficients of such fields sampled on a sphere, such as the temperature of the cosmic microwave background (CMB). We evaluate the detectability of these correlations given the cosmic variance of the observed CMB sky. We find that topologies where the distance to our nearest clone is less than about 1.2 times the diameter of the last scattering surface of the CMB give a correlation signal that is larger than cosmic variance noise in the CMB. This implies that if cosmic topology is the explanation of large-angle anomalies in the CMB, then the distance to our nearest clone is not much larger than the diameter of the last scattering surface. We argue that the topological information is likely to be better preserved in three-dimensional data, such as will eventually be available from large-scale structure surveys.

astro-ph.CO↗

arXiv2024

Promise of Future Searches for Cosmic Topology

The shortest distance around the Universe through us is unlikely to be much larger than the horizon diameter if microwave background anomalies are due to cosmic topology. We show that observational constraints from the lack of matched temperature circles in the microwave background leave many possibilities for such topologies. We evaluate the detectability of microwave background multipole correlations for sample cases. Searches for topology signatures in observational data over the large space of possible topologies pose a formidable computational challenge.

astro-ph.CO↗

arXiv2024

Extremal Kerr Black Hole Dark Matter from Hawking Evaporation

The Hawking process results in a monotonic decrease of the black hole mass, but a biased random walk of the black hole angular momentum. We demonstrate that this stochastic process leads to a significant fraction of primordial black holes becoming extremal Kerr black holes (EKBHs) of one to a few Planck masses regardless of their initial mass. For these EKBHs, the probability of ever absorbing a photon or other particle from the cosmic environment is small, even in the cores of galaxies. Assuming that EKBHs are stable, they behave as cold dark matter, and can comprise all of the dark matter if they are formed with the correct initial abundance.

gr-qc↗