arXiv subjects

James B. Mertens

Publications and source records attributed to James B. Mertens.

At least 19 recordsLinked to original sources

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↗

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↗

arXiv2023

Constraining the quantum gravity polymer scale using LIGO data

We present the first empirical constraints on the polymer scale describing polymer quantized GWs propagating on a classical background. These constraints are determined from the polymer-induced deviation from the classically predicted propagation speed of GWs. We leverage posterior information on the propagation speed of GWs from two previously reported sources: 1) inter-detector arrival time delays for signals from the LIGO-Virgo Collaboration's first gravitational-wave transient catalog, GWTC1, and 2) from arrival time delays between GW signal GW170817 and its associated gamma-ray burst GRB170817A. For pure-GW constraints, we find relatively uninformative combined constraints of $ν= 0.96\substack{+0.15 \\ -0.21} \times 10^{-53} \, \rm{kg}^{1/2}$ and $μ= 0.94\substack{+0.75 \\ -0.20} \times 10^{-48} \, \rm{kg}^{1/2} \cdot s$ at the $90\%$ credible level for the two polymer quantization schemes, where $ν$ and $μ$ refer to polymer parameters associated to the polymer quantization schemes of propagating gravitational degrees of freedom. For constraints from GW170817/GRB170817A, we report much more stringent constraints of $ν_{\mathrm{low}} =2.66\substack{+0.60 \\ -0.10}\times 10^{-56}$, $ν_{\mathrm{high}} = 2.66\substack{+0.45 \\ -0.10}\times 10^{-56} $ and $μ_{\mathrm{low}} = 2.84\substack{+0.64 \\ -0.11}\times 10^{-52}$, $μ_{\mathrm{high}} = 2.76\substack{+0.46 \\ -0.11}\times 10^{-52}$ for both representations of polymer quantization and two choices of spin prior indicated by the subscript. Additionally, we explore the effect of varying the lag between emission of the GW and EM signals in the multimessenger case.

gr-qc↗

arXiv2022

What do gravitational wave detectors say about polymer quantum effects?

We compute the expected response of detector arms of gravitational wave observatories to polymerized gravitational waves. The mathematical and theoretical features of these waves were discussed in our previous work. In the present manuscript, we find both perturbative analytical, and full nonperturbative numerical solutions to the equations of motion of the detector arms using the method of geodesic deviations. These results show the modifications to both frequency and amplitude of the signal measured by the detector. Furthermore, we study the detectability of these signals in LISA by analyzing the modes in the frequency space.

gr-qc↗

arXiv2022

What is flat ΛCDM, and may we choose it?

The Universe is neither homogeneous nor isotropic, but it is close enough that we can reasonably approximate it as such on suitably large scales. The inflationary-$Λ$-Cold Dark Matter ($Λ$CDM) concordance cosmology builds on these assumptions to describe the origin and evolution of fluctuations. With standard assumptions about stress-energy sources, this system is specified by just seven phenomenological parameters, whose precise relations to underlying fundamental theories are complicated and may depend on details of those fields. Nevertheless, it is common practice to set the parameter that characterizes the spatial curvature, $Ω_K$, exactly to zero. This parameter-fixed $Λ$CDM is awarded distinguished status as separate model, "flat $Λ$CDM.'' Ipso facto this places the onus on proponents of "curved $Λ$CDM'' to present sufficient evidence that $Ω_K\neq0$, and is needed as a parameter. While certain inflationary model Lagrangians, with certain values of their parameters, and certain initial conditions, will lead to a present-day universe well-described as containing zero curvature, this does not justify distinguishing that subset of Lagrangians, parameters and initial conditions into a separate model. Absent any theoretical arguments, we cannot use observations that suggest small $Ω_K$ to enforce $Ω_K=0$. Our track record in picking inflationary models and their parameters a priori makes such a choice dubious, and concerns about tensions in cosmological parameters and large-angle cosmic-microwave-background anomalies strengthens arguments against this choice. We argue that $Ω_K$ must not be set to zero, and that $Λ$CDM remains a phenomenological model with at least 7 parameters.

astro-ph.CO↗

arXiv2022

Gravitational Waves from Fully General Relativistic Oscillon Preheating

As long-lived quasi-solitons from the fragmentation of a scalar condensate, oscillons may dominate the preheating era after inflation. During this period, stochastic gravitational waves can also be generated. We quantify the gravitational wave production in this period with simulations accounting for full general relativity to capture all possible non-perturbative effects. We compute the gravitational wave spectra across a range of choices of the oscillon preheating models and compare our results to a conventional perturbative approach on an FLRW background. We clarify the gauge ambiguities in computing induced gravitational waves from scenarios where dense non-perturbative objects such as oscillons are being formed. In particular, we find that the synchronous gauge tends to contain large artificial enhancements in the gravitational wave spectrum due to gauge modes if gravity plays an important role in the formation of the oscillons, while other gauge choices, such as the radiation gauge or a suitably chosen "1+log" gauge, can efficiently reduce the contributions of gauge modes. The full general relativistic simulations indicate that gravitational wave spectra obtained from the perturbative approach on the FLRW background are fairly accurate, except when oscillon formation induces strong gravitational effects, for which case there can be an order unity enhancement.

gr-qc↗

arXiv2022

A model of polymer gravitational waves: theory and some possible observational consequences

We propose a polymer quantization scheme to derive the effective propagation of gravitational waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. These waves, which may originate from a high energy source, are a consequence of the dynamics of the gravitational field in a linearized low-energy regime. A novel method of deriving the effective Hamiltonian of the system is applied to overcome the challenge of polymer quantizing a time-dependent Hamiltonian. Using such a Hamiltonian, we derive the effective equations of motion and show that (i) the form of the waves is modified, (ii) the speed of the waves depends on their frequencies, and (iii) quantum effects become more apparent as waves traverse longer distances.

gr-qc↗

arXiv2021

Accurate relativistic observables from post-processing light cone catalogues

We introduce and study a new scheme to construct relativistic observables from post-processing light cone data. This construction is based on a novel approach, LC-Metric, which takes general light cone or snapshot output generated by arbitrary N-body simulations or emulations and solves the linearized Einstein equations to determine the spacetime metric on the light cone. We find that this scheme is able to determine the metric to high precision, and subsequently generate accurate mock cosmological observations sensitive to effects such as post-Born lensing and nonlinear ISW contributions. By comparing to conventional methods in quantifying those general relativistic effects, we show that this scheme is able to accurately construct the lensing convergence signal. We also find the accuracy of this method in quantifying the ISW effects in the highly nonlinear regime outperforms conventional methods by an order of magnitude. This scheme opens a new path for exploring and modeling higher-order and nonlinear general relativistic contributions to cosmological observables, including mock observations of gravitational lensing and the moving lens and Rees-Sciama effects.

astro-ph.CO↗

arXiv2021

Propagation of quantum gravity-modified gravitational waves on a classical FLRW spacetime

The linearized Einstein field equations provide a low-energy wave equation for the propagation of gravitational fields which may originate from a high energy source. Motivated by loop quantum gravity, we propose the polymer quantization scheme to derive the effective propagation of such waves on a classical Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime. To overcome the challenge of polymer quantizing a time-dependent Hamiltonian, we rewrite such a Hamiltonian in a time-independent manner in the extended phase space, polymerize it, and then transform it back to the usual phase space. In this way we obtain a time-dependent polymer Hamiltonian for the gravitational waves. We then derive the effective equations of motion and show that (i) the form of the waves is modified, (ii) the speed of the waves depends on their frequencies, and (iii) quantum effects become more apparent as waves traverse longer distances.

gr-qc↗

arXiv2020

Numerical solutions to Einstein's equations in a shearing-dust Universe: a code comparison

A number of codes for general-relativistic simulations of cosmological structure formation have been developed in recent years. Here we demonstrate that a sample of these codes produce consistent results beyond the Newtonian regime. We simulate solutions to Einstein's equations dominated by gravitomagnetism -- a vector-type gravitational field that doesn't exist in Newtonian gravity and produces frame-dragging, the leading-order post-Newtonian effect. We calculate the coordinate-invariant effect on intersecting null geodesics by performing ray tracing in each independent code. With this observable quantity, we assess and compare each code's ability to compute relativistic effects.

astro-ph.CO↗

arXiv2019

Cosmic expansion from spinning black holes

We examine how cosmological expansion arises in a universe containing a lattice of spinning black holes. We study averaged expansion properties as a function of fundamental properties of the black holes, including the bare mass of the black holes and black hole spin. We then explore how closely the expansion properties correspond to properties of a corresponding matter-dominated FLRW universe. As residual radiation present in the initial data decays, we find good agreement with a matter-dominated FLRW solution, and the effective density in the volume is well-described by the horizon mass of the black hole.

gr-qc↗

arXiv2019

Probing correlated compensated isocurvature perturbations using scale-dependent galaxy bias

Compensated isocurvature perturbations (CIPs) are modulations of the relative baryon and dark matter density that leave the total matter density constant. The best current constraints from the primary cosmic microwave background (CMB) are consistent with CIPs some two orders of magnitude larger in amplitude than adiabatic perturbations, suggesting that there may be a huge gap in our knowledge of the early Universe. However, it was recently suggested by Barreira~et.~al. that CIPs which are correlated with the primordial curvature perturbation, as arises in some versions of the curvaton model, lead to a new observable: scale dependent galaxy bias. Combining a galaxy survey with an unbiased tracer of the density field facilitates a measurement of the amplitude of correlated CIPs that is free from cosmic variance, the main limitation on constraints from the primary CMB. Among the most promising tracers to use for this purpose is the remote dipole field, reconstructed using the technique of kinetic Sunyaev Zel'dovich (kSZ) tomography. In this paper, we evaluate the detection significance on the amplitude of correlated CIPs possible with next-generation CMB and galaxy surveys using kSZ tomography. Our analysis includes all relativistic contributions to the observed galaxy number counts and allows for both CIPs and primordial non-Gaussianity, which also gives rise to a scale dependent galaxy bias. We find that kSZ tomography can probe CIPs of comparable amplitude to the adiabatic fluctuations, representing an improvement of over two orders of magnitude upon current constraints, and an order of magnitude over what will be possible using future CMB or galaxy surveys alone.

astro-ph.CO↗

arXiv2019

Towards detection of relativistic effects in galaxy number counts using kSZ Tomography

High-resolution, low-noise observations of the cosmic microwave background (CMB) planned for the near-future will enable new cosmological probes based on re-scattered CMB photons -- the secondary CMB. At the same time, enormous galaxy surveys will map out huge volumes of the observable Universe. Using the technique of kinetic Sunyaev Zel'dovich (kSZ) tomography these new probes can be combined to reconstruct the remote dipole field, the CMB dipole as observed from different vantage points in our Universe. The volume accessible to future galaxy surveys is large enough that general relativistic corrections to the observed distribution of galaxies must be taken into account. These corrections are interesting probes of gravity in their own right, but can also obscure potential signatures of primordial non-Gaussianity. In this paper, we demonstrate that correlations between the reconstructed remote dipole field and the observed galaxy number counts can in principle be used to detect general relativistic corrections. We show that neglecting general relativistic corrections leads to an $\mathcal{O}(1)$ bias on the inferred amplitude of primordial non-Gaussianity, $f_{\rm NL}$. In addition, we demonstrate that the reconstructed remote dipole field can provide useful constraining power on various bias parameters appearing in the galaxy number counts, and can significantly mitigate the effects of alignment bias.

astro-ph.CO↗

arXiv2018

Transverse Velocities with the Moving Lens Effect

Gravitational potentials which change in time induce fluctuations in the observed cosmic microwave background (CMB) temperature. Cosmological structure moving transverse to our line of sight provides a specific example known as the moving lens effect. Here we explore how the observed CMB temperature fluctuations combined with the observed matter over-density can be used to infer the transverse velocity of cosmological structure on large scales. We show that near-future CMB surveys and galaxy surveys will have the statistical power to make a first detection of the moving lens effect, and we discuss applications for the reconstructed transverse velocity.

astro-ph.CO↗

arXiv2018

The Limited Accuracy of Linearized Gravity

Standard cosmological models rely on an approximate treatment of gravity, utilizing solutions of the linearized Einstein equations as well as physical approximations. In an era of precision cosmology, we should ask: are these approximate predictions sufficiently accurate for comparison to observations, and can we draw meaningful conclusions about properties of our Universe from them? In this work we examine the accuracy of linearized gravity in the presence of collisionless matter and a cosmological constant utilizing fully general relativistic simulations. We observe the gauge-dependence of corrections to linear theory, and note the amplitude of these corrections. For perturbations whose amplitudes are in line with expectations from the standard $Λ$CDM model, we find that the full, general relativistic metric is well-described by linear theory in Newtonian and harmonic gauges, while the metric in comoving-synchronous gauge is not. For the largest observed structures in our Universe, our results suggest that corrections to linear gravitational theory can reach or surpass the percent-level.

astro-ph.CO↗

arXiv2018

Simulated reconstruction of the remote dipole field using the kinetic Sunyaev Zel'dovich effect

The kinetic Sunyaev Zel'dovich (kSZ) effect, cosmic microwave background (CMB) anisotropies induced by scattering from free electrons in bulk motion, is a primary target of future CMB experiments. Measurements of the kSZ effect have the potential to address fundamental questions about the structure and evolution of our Universe on the largest scales and at the earliest times. This potential is unlocked by combining measurements of small-scale CMB anisotropies with large-scale structure surveys, a technique known as kSZ tomography. Previous work established a quadratic estimator for the remote dipole field, the CMB dipole observed at different locations in the Universe. This previous work did not include gravitational lensing, redshift space distortions, or non-linear evolution of structure. In this paper, we investigate how well the remote dipole field can be reconstructed in the presence of such effects by using mock data from a suite of simulations. To properly model both large and small scales, we develop a novel box-in-box simulation pipeline, where small-scale information is obtained from N-body simulations, and large-scale information obtained by evolving fields using linear theory and adding the resulting corrections to the N-body particle data. This pipeline allows us to create properly correlated maps of the primary CMB including lensing, as well as the kSZ effect and density maps on the past light cone of an observer. Analyzing an ensemble of mocks, we find that the dipole field can be reconstructed with high fidelity over a range of angular scales and redshift bins, although there is evidence of excess power from nonlinear structure. We also analyze correlations with the primary CMB, investigating the ability of kSZ tomography to reconstruct the intrinsic CMB dipole. Our results constitute a proof-of-principle that kSZ tomography is a promising technique for future datasets.

astro-ph.CO↗

arXiv2017

General Relativistic Corrections to the Weak Lensing Convergence Power Spectrum

We compute the weak lensing convergence power spectrum, $C^{κκ}(θ)$, in a dust-filled universe using fully non-linear general relativistic simulations. The spectrum is then compared to more standard, approximate calculations by computing the Bardeen (Newtonian) potentials in linearized gravity and utilizing the Born approximation. We find corrections to the angular power spectrum amplitude of order ten percent at very large angular scales, $\ell ~ 2-3$, and percent-level corrections at intermediate angular scales of $\ell ~ 20-30$.

astro-ph.CO↗