Search

Astrometric measurements provide a unique avenue for constraining the stochastic gravitational wave background (SGWB). In this work, we investigate the application of two neural network architectures, a fully connected network and a graph neural network, for analyzing astrometric data to detect the SGWB. Specifically, we generate mock Gaia astrometric measurements of the proper motions of sources and train two networks to predict the energy density of the SGWB, $\Omega_\text{GW}$. We evaluate the performance of both models under varying input datasets to assess their robustness across different configurations. Our results demonstrate that neural networks can effectively measure the SGWB, showing promise as tools for addressing systematic uncertainties and modeling limitations that pose challenges for traditional likelihood-based methods., Comment: 10 pages, 8 figures, comments welcome

Gravitational Wave (GW) sources are standard sirens that provide an independent way to map the cosmic expansion history by combining with an independent redshift measurement either from an electromagnetic counterpart for a bright siren or using different statistical techniques for dark sirens. In this analysis, we perform the first Blinded Mock Data Challenge (Blinded-MDC) to test the robustness in inferring the value of Hubble constant $H_0$ for a dark siren technique which depends on astrophysical mass distribution of Binary Black Holes (BBHs). We have considered different analysis setups for the Blinded-MDC to test both statistical and systematic uncertainties and demonstrate the capabilities in inferring $H_0$ with detector sensitivity as per the fourth observation run of LIGO-Virgo-KAGRA. We find that when the astrophysical population of BBHs matches with the underlying assumption of the model, a cosmological pipeline can recover the injected parameters using the observed mass distribution. However, when the mock mass distribution of the astrophysical population depends slightly on redshift and one is ignorant about it in analyzing the data, it can cause a systematic discrepancy in the inferred value of $H_0$ by about $1.5\sigma$, above the statistical fluctuations due to noise and a limited number of events. The discrepancy in $H_0$ is arising due to astrophysical mis-modeling, and in the future, elaborate studies will be required to mitigate systematic uncertainties due to unknown astrophysical populations of BBHs. This MDC framework sets the road map for inspecting the precision and accuracy of standard siren cosmology and provides the first insight into the robustness of the population-dependent cosmology inference in a blinded analysis setup., Comment: 19 pages (+ 9 pages appendices) and 20 figures (+ 9 figures in appendices). Prepared for submission to The Astrophysical Journal

In this paper, we use numerical relativity to study the spin induction effect within close hyperbolic encounters of initially spinning black holes. We review the initially non-spinning case and explore the cases of initially aligned, anti-aligned and orthogonal spins with respect to the orbital angular momentum $\vec L$. We find that, for a given initial effective spin, the black hole with a smaller initial spin acquires a greater spin-up than the other black hole after the interaction. We study three different scenarios regarding initial effective spin ($\chi_{\rm eff}=-0.1, \ 0.0, \ 0.1$), using three different scattering angles in order to obtain maximally spin-inducing scenarios. We also find that the final effective spin-ups with respect to the initial spins are well-fitted by a parabola. For spins orthogonal to $\vec L$, we observe that the black hole spins precess, and that the induced spin in the $z$-direction depends quadratically on the value of the initial spins. These phenomena suggest that dense black hole clusters present a rich spin dynamics, where black hole spins may acquire non-trivial distributions., Comment: 11 pages, 10 figures, 3 tables. Changes match published version

Gravitational lensing magnification of Type Ia supernovae (SNe Ia) allows information to be obtained about the distribution of matter on small scales. In this paper, we derive limits on the fraction $\alpha$ of the total matter density in compact objects (which comprise stars, stellar remnants, small stellar groupings and primordial black holes) of mass $M > 0.03 M_{\odot}$ over cosmological distances. Using 1,532 SNe Ia from the Dark Energy Survey Year 5 sample (DES-SN5YR) combined with a Bayesian prior for the absolute magnitude $M$, we obtain $\alpha < 0.12$ at the 95\% confidence level after marginalisation over cosmological parameters, lensing due to large-scale structure, and intrinsic non-Gaussianity. Similar results are obtained using priors from the cosmic microwave background, baryon acoustic oscillations and galaxy weak lensing, indicating our results do not depend on the background cosmology. We argue our constraints are likely to be conservative (in the sense of the values we quote being higher than the truth), but discuss scenarios in which they could be weakened by systematics of the order of $\Delta \alpha \sim 0.04$, Comment: Accepted by MNRAS

We present a surrogate numerical-relativity model for close hyperbolic black-hole encounters with equal masses and spins aligned with the orbital momentum. Our model, generated in terms of the Newman-Penrose scalar $\psi_4$, spans impact parameters $b/M\in [11, 15]$ and spin components $\chi_{i} \in [-0.5,0.5]$, modeling the $(\ell,m)=(2,0)$, $(2, \pm 2)$, $(3,\pm 2)$ and $(4,\pm 4)$ emission multipoles. The model is faithful to numerical relativity simulations, yielding mismatches lower than $10^{-3}$. We test the ability of our model to recover the parameters of numerically simulated signals. We find that, despite the high accuracy of the model, parameter inference struggles to correctly capture the parameters of the source even for SNRs as large as 50 due to the strong degeneracies present in the parameter space. This indicates that correctly identifying these systems will require of extremely large signal loudness, only typical of third generation detectors. Nevertheless, we also find that, if one attempts to infer certain combinations of such degenerated parameters, there might be a chance to prove the existence of this type of events, even with the current ground-based detectors, as long as these combinations make sense astrophysically and cosmologically., Comment: 18 pages, 15 figures

ANNZ is a fast and simple algorithm which utilises artificial neural networks (ANNs), it was known as one of the pioneers of machine learning approaches to photometric redshift estimation decades ago. We enhanced the algorithm by introducing new activation functions like tanh, softplus, SiLU, Mish and ReLU variants; its new performance is then vigorously tested on legacy samples like the Luminous Red Galaxy (LRG) and Stripe-82 samples from SDSS, as well as modern galaxy samples like the Physics of the Accelerating Universe Survey (PAUS). This work focuses on testing the robustness of activation functions with respect to the choice of ANN architectures, particularly on its depth and width, in the context of galaxy photometric redshift estimation. Our upgraded algorithm, which we named ANNZ+, shows that the tanh and Leaky ReLU activation functions provide more consistent and stable results across deeper and wider architectures with > 1 per cent improvement in root-mean-square error ($\sigma_{\textrm{RMS}}$) and 68th percentile error ($\sigma_{68}$) when tested on SDSS data sets. While assessing its capabilities in handling high dimensional inputs, we achieved an improvement of 11 per cent in $\sigma_{\textrm{RMS}}$ and 6 per cent in $\sigma_{68}$ with the tanh activation function when tested on the 40-narrowband PAUS dataset; it even outperformed ANNZ2, its supposed successor, by 44 per cent in $\sigma_{\textrm{RMS}}$. This justifies the effort to upgrade the 20-year-old ANNZ, allowing it to remain viable and competitive within the photo-z community today. The updated algorithm ANNZ+ is publicly available at https://github.com/imdadmpt/ANNzPlus., Comment: 38 pages, 9 figures, revised version submitted to JCAP

We present the Lyman-$\alpha$ (Ly$\alpha$) and ultraviolet (UV) luminosity function (LF), in bins of redshift, of quasars selected in the Physics of the Accelerating Universe Survey (PAUS). A sample of 915 objects was selected at $2.710^{44}$ ${\rm erg\,s}$$^{-1}$. In order to obtain corrections for the LF estimation, and assess the accuracy of our selection method, we produced mock catalogs of $0

The local universe is highly inhomogeneous and anisotropic. We live in a relatively sparse region of the Laniakea supercluster at the edge of a large 80 Mpc-wide void. We study the effect of these inhomogeneities on the measured gravitational wave event rates. In particular, we estimate how the measured merger rate of compact binaries is biased by the local matter distribution. The effect of the inhomogeneities on the merger rate is suppressed by the low angular resolution of gravitational wave detectors coupled with their smoothly decreasing population-averaged sensitivity with distance. We estimate the effect on the compact binary coalescence event rate to be at most 6% depending of the chirp mass of the target binary system and the sensitivity and orientation of the detectors., Comment: 8 pages, 5 figures

Narrowband galaxy surveys have recently gained interest as a promising method to achieve the necessary accuracy on the photometric redshift estimate of individual galaxies for stage-IV cosmological surveys. One key advantage is the ability to provide higher spectral resolution information about galaxies that should allow a more accurate and precise estimation of galaxy stellar population properties. However, the impact of adding narrow-band photometry on the stellar population properties estimate is largely unexplored. The scope of this work is two-fold: on one side, leveraging the predictive power of broad-band and narrow-band data to infer galaxy physical properties such as stellar masses, ages, star formation rates and metallicities. On the other hand, evaluating the improvement of performance in estimating galaxy properties when we use narrow-band data instead of broad-band. In this work we measure the stellar population properties of a sample of galaxies in the COSMOS field for which both narrowband and broadband data are available. In particular, we employ narrowband data from PAUS and broad-band data from CFHTLS. We use two different spectral energy distribution fitting codes to measure galaxy properties, namely CIGALE and Prospector. We find that the increased spectral resolution of narrow-band photometry does not yield a substantial improvement on constraining galaxy properties using spectral energy distribution fitting. Still we find that we obtain a more diverse distribution of metallicities and dust optical depths with cigale when employing the narrowband data. The effect is not as prominent as expected, which we relate this to the low narrowband SNR of a majority of the galaxies, the respective drawbacks of both codes as well as the coverage only in the optical regime. The measured properties are afterwards compared to the COSMOS2020 catalogue, showing good agreement., Comment: Published in A&A. 18 pages, 16 figures, 2 tables

GW230529 is the first compact binary coalescence detected by the LIGO-Virgo-KAGRA collaboration with at least one component mass confidently in the lower mass-gap, corresponding to the range 3-5$M_{\odot}$. If interpreted as a neutron star-black hole merger, this event has the most symmetric mass ratio detected so far and therefore has a relatively high probability of producing electromagnetic (EM) emission. However, no EM counterpart has been reported. At the merger time $t_0$, Swift-BAT and Fermi-GBM together covered 100$\%$ of the sky. Performing a targeted search in a time window $[t_0-20 \text{s},t_0+20 \text{s}]$, we report no detection by the Swift-BAT and the Fermi-GBM instruments. Combining the position-dependent $\gamma-$ray flux upper limits and the gravitational-wave posterior distribution of luminosity distance, sky localization and inclination angle of the binary, we derive constraints on the characteristic luminosity and structure of the jet possibly launched during the merger. Assuming a top-hat jet structure, we exclude at 90$\%$ credibility the presence of a jet which has at the same time an on-axis isotropic luminosity $\gtrsim 10^{48}$ erg s$^{-1}$, in the bolometric band 1 keV-10 MeV, and a jet opening angle $\gtrsim 15$ deg. Similar constraints are derived testing other assumptions about the jet structure profile. Excluding GRB 170817A, the luminosity upper limits derived here are below the luminosity of any GRB observed so far., Comment: 18 pages, 1 table, 11 figures

General Relativistic Entropic Acceleration (GREA) theory provides a covariant formalism for out-of-equilibrium phenomena in GR, extending the Einstein equations with an entropic force that behaves like bulk viscosity with a negative effective pressure. In particular, the growth of entropy associated with the homogeneous causal horizon can explain the present acceleration of the Universe, without introducing a cosmological constant. The dynamics of the accelerated Universe is characterized by a single parameter $\alpha$, the ratio of the causal horizon to the curvature scale, which provides a unique history of the Universe distinguishable from that of LCDM. In particular, we explain the coincidence problem and the Hubble tension by shifting the coasting point to higher redshifts. All background observables are correlated among themselves due to their common dependence on $\alpha$. This scenario gives a specific evolution for the effective equation of state parameter, $w(a)$. Furthermore, we study the linear growth of matter perturbations in the context of a homogeneous expanding background driven by the entropy of the causal horizon. We find that the rate of growth of matter fluctuations in GREA slows down due to the accelerated expansion and alleviates the $\sigma_8$ tension of LCDM. We compute the growth function of matter fluctuations, the redshift space distortions in the galaxy correlation function, as well as the redshift evolution of the BAO scale, and find that the ISW effect is significantly larger than in LCDM. It is interesting to note that many of the tensions and anomalies of the standard model of cosmology are alleviated by the inclusion of this transient period of acceleration of the Universe based on known fundamental physics. In the near future we will be able to constrain this theory with present data from deep galaxy surveys., Comment: 9 pages, 9 figures, minor changes, matches the published version in PDU

In this brief note, we pursue the systematic investigation of possible gravitational wave sources in the gigahertz band. We focus on hyperbolic encounters of light black holes and evaluate precisely the expected signal when accounting for the detailed characteristics of haloscope experiments. Considering the GraHal setup as a benchmark, we insist on the correct signal-to-noise ratio expression taking into account the appropriate timescales. The associated maximum distance - of the order of a few hundreds of astronomical units - at which an event can be detected is calculated for optimal, sub-optimal, and general trajectories.

The recent astrometric data of hundreds of millions of stars from Gaia DR3 has allowed a precise determination of the Milky Way rotation curve up to $28$~kpc. The data suggests a rapid decline in the density of dark matter beyond $19$~kpc. We fit the whole rotation curve with four components (gas, disk, bulge and halo) and compute the microlensing optical depth to the Large Magellanic Cloud. With this model of the galaxy we reanalyse the microlensing events of the MACHO and EROS-2 Collaborations. Using the published MACHO efficiency function for the duration of their survey, together with the rate of expected events according to the new density profile, we find that the Dark Matter halo could be composed up to $100\%$ of massive compact halo objects for any mass between $10^{-4}$ to $100~M_\odot$, except a broad range around $0.01~M_\odot$, where it cannot be larger than $\sim20~\%$. For the EROS-2 survey, using a modified efficiency curve for consistency with the MACHO analysis, we also find compatibility with a 100\% MACHO halo, but with a tighter constraint around $0.001~M_\odot$ where the halo fraction cannot be larger than $\sim12~\%$. This result assumes that MACHOs all have the same mass. If these were distributed in an extended mass function like that of the Thermal History Model, the constraints are weakened, allowing $100\%$ of all DM in the form of Primordial Black Holes., Comment: 15 pages, 5 figures

The search for subsolar mass primordial black holes (PBHs) poses a challenging problem due to the low signal-to-noise ratio, extended signal duration, and computational cost demands, compared to solar mass binary black hole events. In this paper, we explore the possibility of investigating the mass range between subsolar and planetary masses, which is not accessible using standard matched filtering and continuous wave searches. We propose a systematic approach employing the Viterbi algorithm, a dynamic programming algorithm that identifies the most likely sequence of hidden Markov states given a sequence of observations, to detect signals from small mass PBH binaries. We formulate the methodology, provide the optimal length for short-time Fourier transforms, and estimate sensitivity. Subsequently, we demonstrate the effectiveness of the Viterbi algorithm in identifying signals within mock data containing Gaussian noise. Our approach offers the primary advantage of being agnostic and computationally efficient., Comment: 15 pages, 9 figures. Version published in Physical Review D. Typos corrected and a new figure added

We present the largest full N-body simulation to date with local primordial non-Gaussianities (L-PNG), the \textsc{PNG-UNITsim}. It tracks the evolution of $4096^3$ particles within a periodic box with $L_{\rm box} = 1 \; h^{-1}\,{\rm Gpc}$, leading to a mass resolution of $m_{p} = 1.24\times 10^{9}\; h^{-1}\,M_\odot$. This is enough to resolve galaxies targeted by stage-IV spectroscopic surveys. The \textsc{PNG-UNIT} has \textit{Fixed} initial conditions whose phases are also \textit{Matched} to the pre-existing \textsc{UNIT} simulation. These two features in the simulations reduce our uncertainty significantly so we use 100 \textsc{FastPM} mocks to estimate this reduction. The amplitude of the non-Gaussianities used to set the initial conditions of this new simulation is $f_{\rm NL}^{\rm local} = 100$. In this first study, we use mass selected dark matter haloes from the \textsc{PNG-UNIT} simulation to constrain the local PNG parameters. PNG induce a scale dependent bias, parameterised through \bp or $p$, which might depend on the type of cosmological tracer. Those cases when $p=1$ are referred to as the {\it universality relation}. We measure $p$ as a function of the halo mass. Haloes with masses between $1\times 10^{12}$ and $2\times 10^{13} \, h^{-1} M_\odot$ are well described by the {\it universality relation}. For haloes with masses between $2\times 10^{10}$ and $1\times 10^{12} \, h^{-1} M_\odot$ we find that $p<1$ at $3\sigma$. Combining all the mass bins, we find $p$ consistent with a value of $0.955\pm0.013$, which is $3\sigma$ away from \textit{universality}, as low mass haloes are more numerous. We also study the effect of using priors on $p$ when constraining $f_{\rm NL}$. Using the values we obtain for $b_\phi$ as priors, we forecast that a DESI-like (stage-IV) survey will be able to constrain $f_{\rm NL}$ better than if the universality relation is assumed., Comment: 19 pages, 11 figures. Accepted for publication in A&A

A follow-up of a subsolar black hole candidate identified in the second part of the third observing run of the LIGO-Virgo-KAGRA collaboration is carried out. With a search signal-to-noise ratio of $8.90$ and a false-alarm rate of 1 per 5 years, close to the usual thresholds for claiming a gravitational-wave event, we cannot exclude a noise origin. A complete Bayesian parameter estimation of this candidate, denoted SSM200308, reveals that if the signal originates from a compact binary coalescence, the component masses are $m_1= 0.62^{+0.46}_{-0.20} M_{\odot}$ and $m_2 = 0.27^{+0.12}_{-0.10} M_{\odot}$ (90% credible intervals) with at least one component being firmly subsolar, below the minimum mass of a neutron star. This discards the hypothesis that the signal comes from a standard binary neutron star. The signal coherence test between the two LIGO detectors brings support to a compact object coalescence origin., Comment: 7 pages, 4 figures, comments welcome

LISA, the Laser Interferometer Space Antenna, will usher in a new era in gravitational-wave astronomy. As the first anticipated space-based gravitational-wave detector, it will expand our view to the millihertz gravitational-wave sky, where a spectacular variety of interesting new sources abound: from millions of ultra-compact binaries in our Galaxy, to mergers of massive black holes at cosmological distances; from the beginnings of inspirals that will venture into the ground-based detectors' view to the death spiral of compact objects into massive black holes, and many sources in between. Central to realising LISA's discovery potential are waveform models, the theoretical and phenomenological predictions of the pattern of gravitational waves that these sources emit. This white paper is presented on behalf of the Waveform Working Group for the LISA Consortium. It provides a review of the current state of waveform models for LISA sources, and describes the significant challenges that must yet be overcome., Comment: 239 pages, 11 figures, white paper from the LISA Consortium Waveform Working Group, invited for submission to Living Reviews in Relativity, updated with comments from community

In the recent years, primordial black holes (PBHs) have emerged as one of the most interesting and hotly debated topics in cosmology. Among other possibilities, PBHs could explain both some of the signals from binary black hole mergers observed in gravitational wave detectors and an important component of the dark matter in the Universe. Significant progress has been achieved both on the theory side and from the point of view of observations, including new models and more accurate calculations of PBH formation, evolution, clustering, merger rates, as well as new astrophysical and cosmological probes. In this work, we review, analyse and combine the latest developments in order to perform end-to-end calculations of the various gravitational wave signatures of PBHs. Different ways to distinguish PBHs from stellar black holes are emphasized. Finally, we discuss their detectability with LISA, the first planned gravitational-wave observatory in space., Comment: 161 pages, 47 figures, comments welcome

Reduced Order Quadrature (ROQ) methods can greatly reduce the computational cost of Gravitational Wave (GW) likelihood evaluations, and therefore greatly speed up parameter estimation analyses, which is a vital part to maximize the science output of advanced GW detectors. In this paper, we do an in-depth study of ROQ techniques applied to GW data analysis and present novel algorithms to enhance different aspects of the ROQ bases construction. We improve upon previous ROQ construction algorithms allowing for more efficient bases in regions of parameter space that were previously challenging. In particular, we use singular value decomposition (SVD) methods to characterize the waveform space and choose a reduced order basis close to optimal and also propose improved methods for empirical interpolation node selection, greatly reducing the error added by the empirical interpolation model. To demonstrate the effectiveness of our algorithms, we construct multiple ROQ bases ranging in duration from 4s to 256s for compact binary coalescence (CBC) waveforms including precession and higher order modes. We validate these bases by performing likelihood error tests and P-P tests and explore the speed up they induce both theoretically and empirically with positive results. Furthermore, we conduct end-to-end parameter estimation analyses on several confirmed GW events, showing the validity of our approach in real GW data., Comment: 21 pages, 9 figures

The hyperbolic encounters of two massive objects are characterized by the emission of a gravitational wave burst, with most of the energy released during the closest approach (near the periastron). The detection of such events, different from the well-known inspiral emission, would be an interesting discovery and provide complementary information to observations of binary mergers of black holes and neutron stars in the observable Universe, shedding light, for instance, on the clustering properties of black holes and providing valuable hints on their formation scenario. Here, we analyze the dynamics of such phenomena in the simplest case where two compact objects follow unbound/hyperbolic orbits. Moreover, we explore the effects of orbital precession on the gravitational wave emission, since the precession encodes certain general relativistic effects between two bodies. We also provide templates for the strain of gravitational waves and the power spectrum for the emission, and analytical expressions for the memory effect associated with such signals., Comment: 12 pages, 9 figures, changes match published version

General Relativistic Entropic Acceleration (GREA) gives a general framework in which to study multiple out-of-equilibrium phenomena in the context of general relativity, like the late accelerated expansion of the universe or the formation of galaxies and the large scale structure of the universe. Here we study the consequences of mass accretion onto massive Black Holes. We find that a population of Super Massive Black Holes (SMBH) whose mass grows significantly due to accretion can act as a source of entropic acceleration and constitute a significant part of the present acceleration of the Universe., Comment: 4 pages

We review numerous arguments for primordial black holes (PBHs) based on observational evidence from a variety of lensing, dynamical, accretion and gravitational-wave effects. This represents a shift from the usual emphasis on PBH constraints and provides what we term a positivist perspective. Microlensing observations of stars and quasars suggest that PBHs of around $1\,M_{\odot}$ could provide much of the dark matter in galactic halos, this being allowed by the Large Magellanic Cloud microlensing observations if the PBHs have an extended mass function. More generally, providing the mass and dark matter fraction of the PBHs is large enough, the associated Poisson fluctuations could generate the first bound objects at a much earlier epoch than in the standard cosmological scenario. This simultaneously explains the recent detection of high-redshift dwarf galaxies, puzzling correlations of the source-subtracted infrared and X-ray cosmic backgrounds, the size and the mass-to-light ratios of ultra-faint-dwarf galaxies, the dynamical heating of the Galactic disk, and the binary coalescences observed by LIGO/Virgo/KAGRA in a mass range not usually associated with stellar remnants. Even if PBHs provide only a small fraction of the dark matter, they could explain various other observational conundra, and sufficiently large ones could seed the supermassive black holes in galactic nuclei or even early galaxies themselves. We argue that PBHs would naturally have formed around the electroweak, quantum chromodynamics and electron-positron annihilation epochs, when the sound-speed inevitably dips. This leads to an extended PBH mass function with a number of distinct bumps, the most prominent one being at around $1\,M_{\odot}$, and this would allow PBHs to explain many of the observations in a unified way., Comment: 117 pages, 40 figures, 2 tables, 451 references; invited review for Physics Reports; replacement to match published version

Along their path from source to observer, gravitational waves may be gravitationally lensed by massive objects. This results in distortions of the observed signal which can be used to extract new information about fundamental physics, astrophysics, and cosmology. Searches for these distortions amongst the observed signals from the current detector network have already been carried out, though there have as yet been no confident detections. However, predictions of the observation rate of lensing suggest detection in the future is a realistic possibility. Therefore, preparations need to be made to thoroughly investigate the candidate lensed signals. In this work, we present some of the follow-up analyses and strategies that could be applied to assess the significance of such events and ascertain what information may be extracted about the lens-source system from such candidate signals by applying them to a number of O3 candidate events, even if these signals did not yield a high significance for any of the lensing hypotheses. For strongly-lensed candidates, we verify their significance using a background of simulated unlensed events and statistics computed from lensing catalogs. We also look for potential electromagnetic counterparts. In addition, we analyse in detail a candidate for a strongly-lensed sub-threshold counterpart that is identified by a new method. For microlensing candidates, we perform model selection using a number of lens models to investigate our ability to determine the mass density profile of the lens and constrain the lens parameters. We also look for millilensing signatures in one of the lensed candidates. Applying these additional analyses does not lead to any additional evidence for lensing in the candidates that have been examined. However, it does provide important insight into potential avenues to deal with high-significance candidates in future observations., Comment: 29 pages, 27 figures

We present findings of the detection of Magnesium II (Mg II, {\lambda} = 2796, 2803 {\AA}) absorbers from the early data release of the Dark Energy Spectroscopic Instrument (DESI). DESI is projected to obtain spectroscopy of approximately 3 million quasars (QSOs), of which over 99% are anticipated to be at redshifts greater than z > 0.3, such that DESI would be able to observe an associated or intervening Mg II absorber illuminated by the background QSO. We have developed an autonomous supplementary spectral pipeline that detects these systems through an initial line-fitting process and then confirms the line properties using a Markov Chain Monte Carlo sampler. Based upon a visual inspection of the resulting systems, we estimate that this sample has a purity greater than 99%. We have also investigated the completeness of our sample in regard to both the signal-to-noise properties of the input spectra and the rest-frame equivalent width (W0) of the absorber systems. From a parent catalog containing 83,207 quasars, we detect a total of 23,921 Mg II absorption systems following a series of quality cuts. Extrapolating from this occurrence rate of 28.8% implies a catalog at the completion of the five-year DESI survey that will contain over eight hundred thousand Mg II absorbers. The cataloging of these systems will enable significant further research because they carry information regarding circumgalactic medium environments, the distribution of intervening galaxies, and the growth of metallicity across the redshift range 0.3 < z < 2.5., Comment: 17 pages, 8 figures

We present the results from a search for gravitational-wave transients associated with core-collapse supernovae observed optically within 30 Mpc during the third observing run of Advanced LIGO and Advanced Virgo. No gravitational wave associated with a core-collapse supernova has been identified. We then report the detection efficiency for a variety of possible gravitational-wave emissions. For neutrino-driven explosions, the distance at which we reach 50% detection efficiency is up to 8.9 kpc, while more energetic magnetorotationally-driven explosions are detectable at larger distances. The distance reaches for selected models of the black hole formation, and quantum chromodynamics phase transition are also provided. We then constrain the core-collapse supernova engine across a wide frequency range from 50 Hz to 2 kHz. The upper limits on gravitational-wave energy and luminosity emission are at low frequencies down to $10^{-4}\,M_\odot c^2$ and $6 \times 10^{-4}\,M_\odot c^2$/s, respectively. The upper limits on the proto-neutron star ellipticity are down to 3 at high frequencies. Finally, by combining the results obtained with the data from the first and second observing runs of LIGO and Virgo, we improve the constraints of the parameter spaces of the extreme emission models. Specifically, the proto-neutron star ellipticities for the long-lasting bar mode model are down to 1 for long emission (1 s) at high frequency., Comment: 20 pages, 11 figures; https://dcc.ligo.org/LIGO-P2200361

Astrometric surveys can be used to constrain the stochastic gravitational wave background (SGWB) at very low frequencies. We use proper motion data provided by Gaia DR3 to fit a generic dipole+quadrupole field. We analyse several quasar-based datasets and discuss their purity and idoneity to set constraints on gravitational waves. For the cleanest dataset, we derive an upper bound on the (frequency-integrated) energy density of the SGWB $h_{70}^2\Omega_{\rm GW}\lesssim 0.087$ for $4.2\times 10^{-18}~\mathrm{Hz}\lesssim f\lesssim 1.1\times 10^{-8}~\mathrm{Hz}$. We also reanalyse previous VLBI-based data to set the constraint $h_{70}^2\Omega_{\rm GW}\lesssim 0.024$ for $5.8\times 10^{-18}~\mathrm{Hz}\lesssim f\lesssim 1.4\times 10^{-9}~\mathrm{Hz}$ under the same formalism, standing as the best astrometric constraint on GWs. Based on our results, we discuss the potential of future Gaia data releases to impose tighter constraints., Comment: 14 pages, 8 figures. Changes match published version

The coupling between a pseudo-scalar inflaton and a gauge field leads to an amount of additional density perturbations and gravitational waves (GWs) that is strongly sensitive to the inflaton speed. This naturally results in enhanced GWs at (relatively) small scales that exited the horizon well after the CMB ones, and that can be probed by a variety of GW observatories (from pulsar timing arrays, to astrometry, to space-borne and ground-based interferometers). This production occurs in a regime in which the gauge field significantly backreacts on the inflaton motion. Contrary to earlier assumptions, it has been recently shown that this regime is characterized by an oscillatory behavior of the inflaton speed, with a period of~${\rm O } \left( 5 \right)$ e-folds. Bursts of GWs are produced at the maxima of the speed, imprinting nearly periodic bumps in the frequency-dependent spectrum of GWs produced during inflation. This can potentially generate correlated peaks appearing in the same or in different GWs experiments., Comment: 32 pages, 6 figures, link to an animation of the results: https://www.youtube.com/watch?v=xRmiEhZEiRA

This article aims at clarifying the situation about astrophysical sources that might be observed with haloscope experiments sensitive to gravitational waves in the 1-10 GHz band. The GrAHal setup is taken as a benchmark. We follow a very pedagogical path so that the full analysis can easily be used by the entire community who might not be familiar with the theoretical framework. Different relevant physical regimes are considered in details and some formulas encountered in the literature are revised. In particular, we carefully take into account the fast drift of the gravitational wave frequency and the relevant experimental timescales. We also relax the usual assumption that only the merging phase should be considered. The distances that can be probed and expected event rates are carefully evaluated, taking into account degeneracies between physical parameters. We show where experimental efforts should be focused to improve the sensitivity and we conclude that any detection in the near future is extremely unlikely.

General Relativistic Entropic Acceleration (GREA) gives a general framework in which to study multiple out-of-equilibrium phenomena in the context of general relativity, like the late accelerated expansion of the universe or the formation of galaxies and the large scale structure of the universe. Here we analyze the conditions for collapse of a star of degenerate neutrons in the presence of entropy production due to the gravitational collapse itself. We find that the final mass and radius of the neutron star differs from that obtained with the adiabatic Tolman-Oppenheimer-Volkoff equation by a factor of order 15\%. We also find that the minimum mass of a neutron star is $\sim 1.1\,M_\odot$ and the maximum mass around $2.4\,M_\odot$. We discuss the possible implications for the search and interpretation of binary coalescing systems like neutron stars and neutron star-black holes detectable via their multimessenger (gravitational and electromagnetic wave) emission upon merging., Comment: 5 pages, 2 figures

The Bayesian evidence is a key tool in model selection, allowing a comparison of models with different numbers of parameters. Its use in analysis of cosmological models has been limited by difficulties in calculating it, with current numerical algorithms requiring supercomputers. In this paper we give exact formulae for the Bayesian evidence in the case of Gaussian likelihoods with arbitrary correlations and top-hat priors, and approximate formulae for the case of likelihood distributions with leading non-Gaussianities (skewness and kurtosis). We apply these formulae to cosmological models with and without isocurvature components, and compare with results we previously obtained using numerical thermodynamic integration. We find that the results are of lower precision than the thermodynamic integration, while still being good enough to be useful., Comment: Useful mathematical expressions for the computation of Bayesian evidence which I now think may be worth making them public

We perform an exhaustive follow-up analysis of a subsolar-mass (SSM) gravitational wave (GW) candidate reported by Phukon et al. from the second observing run of Advanced LIGO. This candidate has a reported signal-to-noise ratio (SNR) of $8.6$ and false alarm rate of $0.41$ yr which are too low to claim a clear gravitational-wave origin. When improving on the search by using more accurate waveforms, extending the frequency range from 45 Hz down to 20 Hz, and removing a prominent blip glitch, we find that the posterior distribution of the network SNR lies mostly below the search value, with the $90\%$ confidence interval being $7.94^{+0.70}_{-1.05}$. Assuming that the origin of the signal is a compact binary coalescence (CBC), the secondary component is $m_2 = \text{$0.76^{+0.50}_{-0.14}$} M_\odot$, with $m_2 < 1 M_\odot$ at $84\%$ confidence level, suggesting an unexpectedly light neutron star or a black hole of primordial or exotic origin. The primary mass would be $m_1 = \text{$4.71^{+1.57}_{-2.18}$} M_\odot$, likely in the hypothesized lower mass gap and the luminosity distance is measured to be $D_{\rm L}=124^{+82}_{-48}$Mpc. We then probe the CBC origin hypothesis by performing the signal coherence tests, obtaining a log Bayes factor of $4.96 \pm 0.13$ for the coherent vs. incoherent hypothesis. We demonstrate the capability of performing a parameter estimation follow-up on real data for an SSM candidate with moderate SNR. The improved sensitivity of O4 and subsequent LIGO-Virgo-KAGRA observing runs could make it possible to observe similar signals, if present, with a higher SNR and a more precise measurement of the parameters of the binary., Comment: 10 pages, 6 figures

We outline the ``dark siren'' galaxy catalog method for cosmological inference using gravitational wave (GW) standard sirens, clarifying some common misconceptions in the implementation of this method. When a confident transient electromagnetic counterpart to a GW event is unavailable, the identification of a unique host galaxy is in general challenging. Instead, as originally proposed by Schutz (1986), one can consult a galaxy catalog and implement a dark siren statistical approach incorporating all potential host galaxies within the localization volume. Trott & Hunterer 2021 recently claimed that this approach results in a biased estimate of the Hubble constant, $H_0$, when implemented on mock data, even if optimistic assumptions are made. We demonstrate explicitly that, as previously shown by multiple independent groups, the dark siren statistical method leads to an unbiased posterior when the method is applied to the data correctly. We highlight common sources of error possible to make in the generation of mock data and implementation of the statistical framework, including the mismodeling of selection effects and inconsistent implementations of the Bayesian framework, which can lead to a spurious bias., Comment: 19 pages, 11 figures. Submitted to ApJ

Cosmic Probes of Fundamental Physics take two primary forms: Very high energy particles (cosmic rays, neutrinos, and gamma rays) and gravitational waves. Already today, these probes give access to fundamental physics not available by any other means, helping elucidate the underlying theory that completes the Standard Model. The last decade has witnessed a revolution of exciting discoveries such as the detection of high-energy neutrinos and gravitational waves. The scope for major developments in the next decades is dramatic, as we detail in this report., Comment: Report of theTopical Group on Cosmic Probes of Fundamental Physics, for the U.S. decadal Particle Physics Planning Exercise (Snowmass 2021)

Local primordial non-Gaussianity (PNG) is a promising observable of the underlying physics of inflation, characterised by $f_{\rm NL}^{\rm loc}$. We present the methodology to measure $f_{\rm NL}^{\rm loc}$ from the Dark Energy Survey (DES) data using the 2-point angular correlation function (ACF) with scale-dependent bias. One of the focuses of the work is the integral constraint. This condition appears when estimating the mean number density of galaxies from the data and is key in obtaining unbiased $f_{\rm NL}^{\rm loc}$ constraints. The methods are analysed for two types of simulations: $\sim 246$ GOLIAT-PNG N-body small area simulations with $f_{\rm NL}$ equal to -100 and 100, and 1952 Gaussian ICE-COLA mocks with $f_{\rm NL}=0$ that follow the DES angular and redshift distribution. We use the ensemble of GOLIAT-PNG mocks to show the importance of the integral constraint when measuring PNG, where we recover the fiducial values of $f_{\rm NL}$ within the $1\sigma$ when including the integral constraint. In contrast, we found a bias of $\Delta f_{\rm NL}\sim 100$ when not including it. For a DES-like scenario, we forecast a bias of $\Delta f_{\rm NL} \sim 23$, equivalent to $1.8\sigma$, when not using the IC for a fiducial value of $f_{\rm NL}=100$. We use the ICE-COLA mocks to validate our analysis in a realistic DES-like setup finding it robust to different analysis choices: best-fit estimator, the effect of IC, BAO damping, covariance, and scale choices. We forecast a measurement of $f_{\rm NL}$ within $\sigma(f_{\rm NL})=31$ when using the DES-Y3 BAO sample, with the ACF in the $1\ {\rm deg}<\theta<20\ {\rm deg}$ range., Comment: Version after MNRAS reviewer comments. Improved discussion in Section 7. 16 pages, 11 figures

Gaussian noise is an irreducible component of the background in gravitational wave (GW) detectors. Although stationary Gaussian noise is uncorrelated in frequencies, we show that there is an important correlation in time when looking at the matched filter signal to noise ratio (SNR) of a template, with a typical autocorrelation time that depends on the template and the shape of the noise power spectral density (PSD). Taking this correlation into account, we compute from first principles the false alarm rate (FAR) of a template in Gaussian noise, defined as the number of occurrences per unit time that the template's matched filter SNR goes over a threshold $\rho$. We find that the Gaussian FAR can be well approximated by the usual expression for uncorrelated noise, if we replace the sampling rate by an effective sampling rate that depends on the parameters of the template, the noise PSD and the threshold $\rho$. This results in a minimum SNR threshold that has to be demanded to a given GW trigger, if we want to keep events generated from Gaussian noise below a certain FAR. We extend the formalism to multiple detectors and to the analysis of GW events. We apply our method to the GW candidates added in the GWTC-3 catalog, and discuss the possibility that GW200308\_173609 and GW200322\_091133 could be generated by Gaussian noise fluctuations., Comment: 22 pages, 11 figures

We present DESI observations of the inner halo of M31, which reveal the kinematics of a recent merger - a galactic immigration event - in exquisite detail. Of the 11,416 sources studied in 3.75 hour of on-sky exposure time, 7,438 are M31 sources with well measured radial velocities. The observations reveal intricate coherent kinematic structure in the positions and velocities of individual stars: streams, wedges, and chevrons. While hints of coherent structures have been previously detected in M31, this is the first time they have been seen with such detail and clarity in a galaxy beyond the Milky Way. We find clear kinematic evidence for shell structures in the Giant Stellar Stream, the Northeast Shelf and Western Shelf regions. The kinematics are remarkably similar to the predictions of dynamical models constructed to explain the spatial morphology of the inner halo. The results are consistent with the interpretation that much of the substructure in the inner halo of M31 is produced by a single galactic immigration event 1 - 2 Gyr ago. Significant numbers of metal-rich stars ([Fe/H]$>-0.5$) are present in all of the detected substructures, suggesting that the immigrating galaxy had an extended star formation history. We also investigate the ability of the shells and Giant Stellar Stream to constrain the gravitational potential of M31, and estimate the mass within a projected radius of 125 kpc to be ${\rm log_{10}}\, M_{\rm NFW}(<125\,{\rm kpc})/M_\odot = 11.80_{-0.10}^{+0.12}$. The results herald a new era in our ability to study stars on a galactic scale and the immigration histories of galaxies., Comment: 45 pages, 22 figures, 8 tables; Astrophysical Journal in press; Data at https://zenodo.org/record/6977494

It is generally assumed within the standard cosmological model that initial density perturbations are Gaussian at all scales. However, primordial quantum diffusion unavoidably generates non-Gaussian, exponential tails in the distribution of inflationary perturbations. These exponential tails have direct consequences for the formation of collapsed structures in the universe, as has been studied in the context of primordial black holes. We show that these tails also affect the very-large-scale structures, making heavy clusters like "El Gordo", or large voids like the one associated with the cosmic microwave background cold spot, more probable. We compute the halo mass function and cluster abundance as a function of redshift in the presence of exponential tails. We find that quantum diffusion generically enlarges the number of heavy clusters and depletes subhalos, an effect that cannot be captured by the famed $f_{\mathrm{NL}}$ corrections. These late-universe signatures could thus be fingerprints of quantum dynamics during inflation that should be incorporated in $N$-body simulations and checked against astrophysical data., Comment: 5 pages without appendices (total 8 pages), 3 figures, matches published version in Phys. Rev. Letters

Cosmological analyses with type Ia supernovae (SNe Ia) often assume a single empirical relation between color and luminosity ($\beta$) and do not account for varying host-galaxy dust properties. However, from studies of dust in large samples of galaxies, it is known that dust attenuation can vary significantly. Here we take advantage of state-of-the-art modeling of galaxy properties to characterize dust parameters (dust attenuation $A_V$, and a parameter describing the dust law slope $R_V$) for the Dark Energy Survey (DES) SN Ia host galaxies using the publicly available \texttt{BAGPIPES} code. Utilizing optical and infrared data of the hosts alone, we find three key aspects of host dust that impact SN Ia cosmology: 1) there exists a large range ($\sim1-6$) of host $R_V$ 2) high stellar mass hosts have $R_V$ on average $\sim0.7$ lower than that of low-mass hosts 3) there is a significant ($>3\sigma$) correlation between the Hubble diagram residuals of red SNe Ia that when corrected for reduces scatter by $\sim13\%$ and the significance of the ``mass step'' to $\sim1\sigma$. These represent independent confirmations of recent predictions based on dust that attempted to explain the puzzling ``mass step'' and intrinsic scatter ($\sigma_{\rm int}$) in SN Ia analyses. We also find that red-sequence galaxies have both lower and more peaked dust law slope distributions on average in comparison to non red-sequence galaxies. We find that the SN Ia $\beta$ and $\sigma_{\rm int}$ both differ by $>3\sigma$ when determined separately for red-sequence galaxy and all other galaxy hosts. The agreement between fitted host-$R_V$ and SN Ia $\beta$ \& $\sigma_{\rm int}$ suggests that host dust properties play a major role in SN Ia color-luminosity standardization and supports the claim that SN Ia intrinsic scatter is driven by $R_V$ variation., Comment: 22 pages. Submitted to MNRAS

A system of 5,020 robotic fiber positioners was installed in 2019 on the Mayall Telescope, at Kitt Peak National Observatory. The robots automatically re-target their optical fibers every 10 - 20 minutes, each to a precision of several microns, with a reconfiguration time less than 2 minutes. Over the next five years, they will enable the newly-constructed Dark Energy Spectroscopic Instrument (DESI) to measure the spectra of 35 million galaxies and quasars. DESI will produce the largest 3D map of the universe to date and measure the expansion history of the cosmos. In addition to the 5,020 robotic positioners and optical fibers, DESI's Focal Plane System includes 6 guide cameras, 4 wavefront cameras, 123 fiducial point sources, and a metrology camera mounted at the primary mirror. The system also includes associated structural, thermal, and electrical systems. In all, it contains over 675,000 individual parts. We discuss the design, construction, quality control, and integration of all these components. We include a summary of the key requirements, the review and acceptance process, on-sky validations of requirements, and lessons learned for future multi-object, fiber-fed spectrographs., Comment: 51 pages, 41 figures

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

Microlensing of extragalactic sources, in particular the probability of significant amplifications, is a potentially powerful probe of the abundance of compact objects outside the halo of the Milky Way. Accurate experimental constraints require an equally accurate theoretical model for the amplification statistics produced by such a population. In this article, we argue that the simplest (strongest-lens) model does not meet this demanding requirement. We thus propose an elaborate practical modelling scheme for extragalactic microlensing. We derive from first principles an expression for the amplification probability that consistently allows for: (i) the coupling between microlenses; (ii) realistic perturbations from the cosmic large-scale structure; (iii) extended-source corrections. An important conclusion is that the external shear applied on the dominant microlens, both by the other lenses and by the large-scale structure, is practically negligible. Yet, the predictions of our approach can still differ by a factor of a few with respect to existing models of the literature. Updated constraints on the abundance of compact objects accounting for such discrepancies may be required., Comment: 28 + 11 pages, 18 figures; v2: minor typos corrected, fig. 12 updated for more clarity, matches published version; v3: typo corrected in eq. (A.6)

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

The current understanding of dark matter comes largely from measurements of the total matter content in the universe, from the distribution of gravitating matter on very large scales, and from rotation curves and velocity dispersions on sub-galactic scales. However, small-scale structure may well hold the key to unlocking the particle physics of the still-mysterious 85% of matter in the universe. Novel small-scale astrophysical probes of new particles and dark matter will become possible with a large data volume of high-precision measurements enabled by next-generation gravitational-wave detectors and advanced astrometry instruments. Cosmic microwave background and large-scale structure surveys will provide complementary constraints on dark matter models with unique small-scale signatures. We lay out the studies of small-scale structures and compact objects as dark matter probes, and summarize the requirements to achieve the goals., Comment: 43 pages, 7 figures

Unresolved sources of gravitational waves (GWs) produced by the merger of a binary of black holes at cosmological distances combine into a stochastic background. Such a background is in the continuous or popcorn regime, depending on whether the GW rate is high enough so that two or more events overlap in the same frequency band. These two regimes respectively correspond to large and small values of the so-called {\it duty cycle}. We study the detection regime of the background in models of Primordial Black Holes (PBHs) and compare it to the one produced by black holes of stellar origin. Focusing on ground-based detectors, we show that the duty cycle of the PBH-origin background is larger than that of astrophysical black holes because of differences in their mass function and the merger rate. Our study opens up the possibility to learn about the primordial or astrophysical nature of black hole populations by examining the statistical properties of the stochastic background., Comment: 13 pages, 7 figures; v2 matches version published in MNRAS

The D4000 spectral break index is one of the most important features in the visible spectrum, as it is a proxy for stellar ages and is also used in galaxy classification. However, its direct measurement has always been reserved to spectroscopy. Here, we present a general method to directly measure the D4000 with narrow-band (NB) photometry; it has been validated using realistic simulations, and then evaluated with PAUS NBs, cross-matched with VIPERS spectra ($i_{\rm AB} < 22.5$, $0.562 < z < 0.967$). We also reconstruct the D4000 with the SED-fitting code CIGALE; the use of PAUS NBs instead of broad bands significantly improves the SED fitting results. For D4000$_{\rm n}$, the direct measurement has $\rm \langle SNR \rangle \sim 4$, but we find that for $i_{\rm AB}<21$ all direct D4000 measurements have $\rm SNR>3$. The CIGALE D4000$_{\rm n}$ has $\rm \langle SNR \rangle \sim 20$, but underestimates the error by $>$50\%. Furthermore, the direct method recreates well the D4000-SFR relation, as well as the D4000-mass relation for blue galaxies (for red galaxies, selection effects impact the results). On the other hand, CIGALE accurately classifies galaxies into red and blue populations. We conclude that the direct measurement of D4000 with narrow-band photometry is a promising tool to determine average properties of galaxy samples, with results compatible with spectroscopy., Comment: 21 pages, 18 figures. Accepted in MNRAS

Recently, a covariant formulation of non-equilibrium phenomena in the context of General Relativity was proposed in order to explain from first principles the observed accelerated expansion of the Universe, without the need for a cosmological constant, leading to the GREA theory. Here, we confront the GREA theory against the latest cosmological data, including type Ia supernovae, baryon acoustic oscillations, the cosmic microwave background (CMB) radiation, Hubble rate data from the cosmic chronometers and the recent $H_0$ measurements. We perform Markov Chain Monte Carlo analyses and a Bayesian model comparison, by estimating the evidence via thermodynamic integration, and find that when all the aforementioned data are included, but no prior on $H_0$, the difference in the log-evidence is $\sim -9$ in favor of GREA, thus resulting in overwhelming support for the latter over the cosmological constant and cold dark matter model ($\Lambda$CDM). When we also include priors on $H_0$, either from Cepheids or the Tip of the Red Giant Branch measurements, then due to the tensions with CMB data the GREA theory is found to be statistically equivalent with $\Lambda$CDM., Comment: 11 pages, 4 figures, 6 tables. Changes match published version

We use luminous red galaxies selected from the imaging surveys that are being used for targeting by the Dark Energy Spectroscopic Instrument (DESI) in combination with CMB lensing maps from the Planck collaboration to probe the amplitude of large-scale structure over $0.4\le z\le 1$. Our galaxy sample, with an angular number density of approximately $500\,\mathrm{deg}^{-2}$ over 18,000 sq.deg., is divided into 4 tomographic bins by photometric redshift and the redshift distributions are calibrated using spectroscopy from DESI. We fit the galaxy autospectra and galaxy-convergence cross-spectra using models based on cosmological perturbation theory, restricting to large scales that are expected to be well described by such models. Within the context of $\Lambda$CDM, combining all 4 samples and using priors on the background cosmology from supernova and baryon acoustic oscillation measurements, we find $S_8=\sigma_8(\Omega_m/0.3)^{0.5}=0.73\pm 0.03$. This result is lower than the prediction of the $\Lambda$CDM model conditioned on the Planck data. Our data prefer a slower growth of structure at low redshift than the model predictions, though at only modest significance., Comment: 44 pages, 16 figures. Matches version accepted by journal: more details on analysis, updated references, link to data added