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The Hubble function characterizes a given Friedmann-Robertson-Walker spacetime and can be related to the densities of the cosmological fluids and their equations of state. We show how physics-informed neural networks (PINNs) emulate this dynamical system and provide fast predictions of the luminosity distance for a given choice of densities and equations of state, as needed for the analysis of supernova data. We use this emulator to perform a model-independent and parameter-free reconstruction of the Hubble function on the basis of supernova data. As part of this study, we develop and validate an uncertainty treatment for PINNs using a heteroscedastic loss and repulsive ensembles., Comment: 21 pages, 12 figures

Non-Gaussian distributions in cosmology are commonly evaluated with Monte Carlo Markov-chain methods, as the Fisher-matrix formalism is restricted to the Gaussian case. The Metropolis-Hastings algorithm will provide samples from the posterior distribution after a burn-in period, and the corresponding convergence is usually quantified with the Gelman-Rubin criterion. In this paper, we investigate the convergence of the Metropolis-Hastings algorithm by drawing analogies to statistical Hamiltonian systems in thermal equilibrium for which a canonical partition sum exists. Specifically, we quantify virialisation, equipartition and thermalisation of Hamiltonian Monte Carlo Markov-chains for a toy-model and for the likelihood evaluation for a simple dark energy model constructed from supernova data. We follow the convergence of these criteria to the values expected in thermal equilibrium, in comparison to the Gelman-Rubin criterion. We find that there is a much larger class of physically motivated convergence criteria with clearly defined target values indicating convergence. As a numerical tool, we employ physics-informed neural networks for speeding up the sampling process., Comment: 12 pages, 6 figures

Alignments of disc galaxies were thought to result from tidal torquing, where tidal field of the cosmic large-scale structure exert torquing moments onto dark matter haloes, determining their angular momentum and ultimately the orientation of galactic discs. In this model, resulting intrinsic ellipticity correlations are typically present on small scales, but neither observations nor simulations have found empirical evidence; instead, simulations point at the possibility that alignments of disc galaxies follow a similar alignment model as elliptical galaxies, but with a weaker alignment amplitude. In our article we make the case for the theory of linear alignments resulting from tidal distortions of the galactic disc, investigate the physical properties of this model and derive the resulting angular ellipticity spectra, as they would appear as a contribution to weak gravitational lensing in surveys such as Euclid's. We discuss in detail on the statistical and physical properties of tidally induced alignments in disc galaxies, as they are relevant for mitigation of alignment contamination in weak lensing data, comment on the consistency between the alignment amplitude in spiral and elliptical galaxies and finally, estimate their observability with a Euclid-like survey., Comment: 10 pages, 7 figures

Monte-Carlo techniques are standard numerical tools for exploring non-Gaussian and multivariate likelihoods. Many variants of the original Metropolis-Hastings algorithm have been proposed to increase the sampling efficiency. Motivated by Ensemble Monte Carlo we allow the number of Markov chains to vary by exchanging particles with a reservoir, controlled by a parameter analogous to a chemical potential $\mu$, which effectively establishes a random process that samples microstates from a macrocanonical instead of a canonical ensemble. In this paper, we develop the theory of macrocanonical sampling for statistical inference on the basis of Bayesian macrocanonical partition functions, thereby bringing to light the relations between information-theoretical quantities and thermodynamic properties. Furthermore, we propose an algorithm for macrocanonical sampling, $\texttt{Avalanche Sampling}$, and apply it to various toy problems as well as the likelihood on the cosmological parameters $\Omega_m$ and $w$ on the basis of data from the supernova distance redshift relation., Comment: 13 pages, 9 figures

Starobinsky inflation is an attractive, fundamental model to explain the Planck measurements, and its higher-order extension may allow us to probe quantum gravity effects. We show that future CMB data combined with the 21cm intensity map from SKA will meaningfully probe such an extended Starobinsky model. A combined analysis will provide a precise measurement and intriguing insight into inflationary dynamics, even accounting for correlations with astrophysical parameters., Comment: Matches with published version

We investigate nonlinear structure formation in the fuzzy dark matter (FDM) model in comparison to cold dark matter (CDM) models from a weak lensing perspective using perturbative methods. We use Eulerian perturbation theory (PT) up to fourth order to compute the tree-level matter trispectrum and the one-loop matter spectrum and bispectrum from consistently chosen initial conditions. In addition, we predict the non-linear matter power spectra using $N$-body simulations with CDM and FDM initial conditions. We go on to derive the respective lensing spectra, bispectra and trispectra in CDM and FDM in the context of a Euclid-like weak lensing survey. Finally, we compute the attainable cumulative signal-to-noise ratios and an estimate of the attainable $\chi^2$-functionals for distinguishing FDM from CDM at particle masses $m=10^{-21}$ eV, $m = 10^{-22}$ eV and $m = 10^{-23}$ eV. We find that PT predictions cannot be used to reliably distinguish the three models in a weak lensing survey. Assuming that $N$-body simulations overestimate the late-time small-scale power in the FDM model, future weak lensing survey might be used to distinguish between the FDM and CDM cases up to a mass of $m = 10^{-23}$ eV. However, observations probing the local high-$z$ universe are probably more suited to constrain the FDM mass., Comment: 20 pages, 25 figures; added references for section 2.1; revision after feedback from review; submitted to MNRAS

Non-Gaussian likelihoods, ubiquitous throughout cosmology, are a direct consequence of nonlinearities in the physical model. Their treatment requires Monte-Carlo Markov-chain or more advanced sampling methods for the determination of confidence contours. As an alternative, we construct canonical partition functions as Laplace-transforms of the Bayesian evidence, from which MCMC-methods would sample microstates. Cumulants of order $n$ of the posterior distribution follow by direct $n$-fold differentiation of the logarithmic partition function, recovering the classic Fisher-matrix formalism at second order. We connect this approach for weakly non-Gaussianities to the DALI- and Gram-Charlier expansions and demonstrate the validity with a supernova-likelihood on the cosmological parameters $\Omega_m$ and $w$. We comment on extensions of the canonical partition function to include kinetic energies in order to bridge to Hamilton Monte-Carlo sampling, and on ensemble Markov-chain methods, as they would result from transitioning to macrocanonical partition functions depending on a chemical potential. Lastly we demonstrate the relationship of the partition function approach to the Cram\'er-Rao boundary and to information entropies., Comment: 12 pages 2 figures, Affiliation updated

The Etherington distance duality relation is well-established for metric theories of gravity, and confirms the duality between the luminosity distance and the angular diameter distance through the conservation of surface brightness. A violation of the Etherington distance duality due to lensing in a non-metric spacetime would lead to fluctuations in surface brightness of galaxies. Likewise, fluctuations of the surface brightness can arise in classical astrophysics as a consequence of intrinsic tidal interaction of galaxies with their environment. Therefore, we study these in two cases in detail: Firstly, for intrinsic size fluctuations and the resulting changes in surface brightness, and secondly, for an area-metric spacetime as an example of a non-metric spacetime where the distance duality relation itself acquires modifications. The aim of this work is to quantify whether a surface brightness fluctuation effect due to area-metric gravity would be resolvable compared to the similar effect caused by intrinsic alignment. We thus compare the auto- and cross-correlations of the angular spectra in these two cases and show that the fluctuations in intrinsic brightness can potentially be measured with a cumulative signal-to-noise ratio $\Sigma(\ell) \geq 3$ in a Euclid-like survey. The measurement in area-metric spacetimes, however, depends on the specific parameter choices, which also determine the shape and amplitude of the spectra. While lensing surveys do have sensitivity to lensing-induced surface brightness fluctuations in area-metric spacetimes, the measurement does not seem to be possible for natural values of the Etherington-breaking parameters., Comment: 12 pages, 6 figures, submitted to MNRAS

The fuzzy dark matter (FDM) scenario has received increased attention in recent years due to the small-scale challenges of the vanilla Lambda cold dark matter ($\Lambda$CDM) cosmological model and the lack of any experimental evidence for any candidate particle. In this study, we use cosmological $N$-body simulations to investigate high-redshift dark matter halos and their responsiveness to an FDM-like power spectrum cutoff on small scales in the primordial density perturbations. We study halo density profiles, shapes and alignments in FDM-like cosmologies (the latter two for the first time) by providing fits and quantifying departures from $\Lambda$CDM as a function of the particle mass $m$. Compared to $\Lambda$CDM, the concentrations of FDM-like halos are lower, peaking at an $m$-dependent halo mass and thus breaking the approximate universality of density profiles in $\Lambda$CDM. The intermediate-to-major and minor-to-major shape parameter profiles are monotonically increasing with ellipsoidal radius in $N$-body simulations of $\Lambda$CDM. In FDM-like cosmologies, the monotonicity is broken, halos are more elongated around the virial radius than their $\Lambda$CDM counterparts and less elongated closer to the center. Finally, intrinsic alignment correlations, stemming from the deformation of initially spherically collapsing halos in an ambient gravitational tidal field, become stronger with decreasing $m$. At $z\sim 4$, we find a $6.4 \sigma$-significance in the fractional differences between the isotropised linear alignment magnitudes $D_{\text{iso}}$ in the $m=10^{-22}$ eV model and $\Lambda$CDM. Such FDM-like imprints on the internal properties of virialised halos are expected to be strikingly visible in the high-$z$ Universe., Comment: 20 pages, 10 figures, 3 tables

SKA will be a major step forward not only in astrophysics, but also in precision cosmology. We show how the neutral hydrogen intensity map can be combined with the Planck measurements of the CMB power spectrum, to provide a precision test of the inflaton potential. For a conservative range of redshifts we find that SKA can significantly improve current constraints on the Hubble slow-roll parameters., Comment: 25 pages, 14 figures

We study the impact of modified gravity of the Horndeski class, on intrinsic shape correlations in cosmic shear surveys. As intrinsic shape correlations (IAs) are caused by tidal gravitational fields acting on galaxies as a collection of massive non-relativistic test particles, they are only sensitive to the gravitational potential, which forms in conjunction with the curvature perturbation. In contrast, the cosmic shear signal probes the sum of these two, i.e. both Bardeen-potentials. Combining these probes therefore constitutes a test of gravity, derived from a single measurement. Focusing on linear scales and alignments of elliptical galaxies, we study the impact on inference of the braiding $\hat{\alpha}_B$ and the time evolution of the Planck mass $\hat{\alpha}_M$ by treating IAs as a genuine signal contributing to the overall ellipticity correlation. We find that for \textsc{Euclid}, IAs can help to improve constraints on modified gravity of the Horndeski-class by 10 per cent if the alignment parameter needed for the linear alignment model is provided by simulations. If, however, the IA needs to be self calibrated, all of the sensitivity is put into the inference of the alignment strength $D$ since there is a very strong correlation with the evolution of the Planck mass. Thus diminishing the benefit of IA for probing modified gravitational theories. While the present paper shows results mainly for modified gravity parameters, similar deductions can be drawn for the investigation of anisotropic stresses, parameterised modifications to the Poisson-equation, the phenomenology of gravitational slip and to breaking degeneracies in a standard cosmology., Comment: 7 pages, 2 figures

Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and empirical Gaussianisation transforms can reduce the amount of non-Gaussianity in a distribution. Alternatively, in this work, we employ methods from information geometry. The latter formulates a set of probability distributions for some given model as a manifold employing a Riemannian structure, equipped with a metric, the Fisher information. In this framework we study the differential geometrical meaning of non-Gaussianities in a higher order Fisher approximation, and their respective transformation behaviour under re-parameterisation, which corresponds to a chart transition on the statistical manifold. While weak non-Gaussianities vanish in normal coordinates in a first order approximation, one can in general not find transformations that discard non-Gaussianities globally. As an application we consider the likelihood of the supernovae distance-redshift relation in cosmology for the parameter pair ($\Omega_{\mathrm{m_0}}$, $w$). We demonstrate the connection between confidence intervals and geodesic length and demonstrate how the Lie-derivative along the degeneracy directions gives hints at possible isometries of the Fisher metric., Comment: 20 pages, 5 figures, figures modified, discussion added, matches journal version

Accurate measurements of the cosmic shear signal require a separation of the true weak gravitational lensing signal from intrinsic shape correlations of galaxies. These `intrinsic alignments' of galaxies originate from galaxy formation processes and are expected to be correlated with the gravitational field through tidal processes affecting the galaxies, such as tidal shearing for elliptical galaxies and tidal torquing for spiral galaxies. In this study, we use morphologically selected samples of elliptical and spiral galaxies from the IllustrisTNG simulation at z=0 and z=1 to test the commonly employed linear (tidal shearing) and quadratic (tidal torquing) models for intrinsic alignments. We obtain local measurements of the linear and quadratic alignment parameters, including corrections for large-scale anisotropies of the cosmologically small simulation volume, and study their dependence on galaxy and environmental properties. We find a significant alignment signal for elliptical galaxies (linear model), that increases with mass and redshift. Spiral galaxies (quadratic model) on the other hand exhibit a significant signal only for the most massive objects at z=1. We show the quadratic model for spiral galaxies to break down at its fundamental assumptions, and simultaneously obtain a significant signal of spiral galaxies to align according to the linear model. We use the derived alignment parameters to compute intrinsic alignment spectra and estimate the expected contamination in the weak lensing signal obtained by Euclid., Comment: 23 pages, 24 figures, submitted to MNRAS, comments welcome

We present constraints on Horndeski gravity from a combined analysis of cosmic shear, galaxy-galaxy lensing and galaxy clustering from $450\,\mathrm{deg}^2$ of the Kilo-Degree Survey (KiDS) and the Galaxy And Mass Assembly (GAMA) survey. The Horndeski class of dark energy/modified gravity models includes the majority of universally coupled extensions to $\Lambda$CDM with one scalar field in addition to the metric. We study the functions of time that fully describe the evolution of linear perturbations in Horndeski gravity. Our results are compatible throughout with a $\Lambda$CDM model. By imposing gravitational wave constraints, we fix the tensor speed excess to zero and consider a subset of models including e.g. quintessence and $f(R)$ theories. Assuming proportionality of the Horndeski functions $\alpha_B$ and $\alpha_M$ (kinetic braiding and the Planck mass run rate, respectively) to the dark energy density fraction $\Omega_{\mathrm{DE}}(a) = 1 - \Omega_{\mathrm{m}}(a)$, we find for the proportionality coefficients $\hat{\alpha}_B = 0.20_{-0.33}^{+0.20} \,$ and $\, \hat{\alpha}_M = 0.25_{-0.29}^{+0.19}$. Our value of $S_8 \equiv \sigma_8 \sqrt{\Omega_{\mathrm{m}}/0.3}$ is in better agreement with the $Planck$ estimate when measured in the enlarged Horndeski parameter space than in a pure $\Lambda$CDM scenario. In our joint three-probe analysis we report a downward shift of the $S_8$ best fit value from the $Planck$ measurement of $\Delta S_8 = 0.016_{-0.046}^{+0.048}$ in Horndeski gravity, compared to $\Delta S_8 = 0.059_{-0.039}^{+0.040}$ in $\Lambda$CDM. Our constraints are robust to the modelling uncertainty of the non-linear matter power spectrum in Horndeski gravity. Our likelihood code for multi-probe analysis in both $\Lambda$CDM and Horndeski gravity is publicly available at http://github.com/alessiospuriomancini/KiDSHorndeski ., Comment: 18 pages, 7 figures, matches version published in MNRAS. Likelihood code available at http://github.com/alessiospuriomancini/KiDSHorndeski