arXiv subjects

Björn Malte Schäfer

Publications and source records attributed to Björn Malte Schäfer.

At least 19 recordsLinked to original sources

arXiv2026

A Global Overview of Starobinsky Inflation beyond slow-roll with CMB-BAO data

We perform a global analysis of the Starobinsky inflation using most recent CMB data from ACT and SPT together with DESI BAO measurements. By directly solving the equations of motion, we find relatively stronger constraints on the model parameters than those obtained under the slow-roll approximation from the baseline $Λ$CDM parameters $A_s$ and $n_s$. We translate these constraints into limits on the reheating temperature. We also discuss the dependence of the prior choices of the model parameters. Further, the correlation of the model parameters with the BAO parameter $r_d h$ is also studied. We further investigate the impact of the global analysis on the dimension-six $R^3$ modified Starobinsky model, deriving constraints on its additional parameters. Finally, we also provide parameter limits on the effective inflationary Hubble slow-roll (HSR) and potential slow-roll (PSR) parametrization.

astro-ph.CO↗

arXiv2026

The Latent Information Geometry of Jet Classification

Latent representations are an important theme in modern machine learning. Any network training with the notion of locality introduces a latent geometry which we can analyze with the help of differential geometry, specifically information geometry. We introduce the main concepts needed to analyze learned latent geometries, specifically curvature and nonmetricities, and show how they can be used for decoder and classifier geometries. We then apply our new methods to understand the physics behind binary quark-gluon classification and three-fold fat jet tagging.

hep-ph↗

arXiv2025

A novel inversion algorithm for weak gravitational lensing using quasi-conformal geometry

The challenge in weak gravitational lensing caused by galaxies and clusters is to infer the projected mass density distribution from gravitational lensing measurements, known as the inversion problem. We introduce a novel theoretical approach to solving the inversion problem. The cornerstone of the proposed method lies in a complex formalism that describes the lens mapping as a quasi-conformal mapping with the Beltrami coefficient given by the negative of the reduced shear, which can, in principle, be observed from the image ellipticities. We propose an algorithm called QCLens that is based on this complex formalism. QCLens computes the underlying quasi-conformal mapping using a finite element approach by reducing the problem to two elliptic partial differential equations that solely depend on the reduced shear field. Experimental results for both the Schwarzschild and the singular isothermal lens demonstrate the agreement of our proposed method with the analytically computable solutions.

astro-ph.IM↗

arXiv2025

Starobinsky in Stereo: SKA-CMB Synergy in SBI

Modern machine learning techniques can unlock the vast cosmological information encoded in forthcoming Square Kilometre Array (SKA) observations. We show that tomographic 21 cm data from the reionisation era can yield stringent tests of inflationary models - here illustrated with Starobinsky $R+R^2$ inflation. Using a simulation-based inference (SBI) framework, we compare neural summaries (convolutional network and vision transformer) with a traditional power spectrum summary and perform a fully joint SBI analysis combining 21 cm data with data of the cosmic microwave background (CMB). Forecasts based on realistic mock observations indicate that SKA alone will achieve constraints competitive with Planck, and that the combined SKA + CMB dataset will tighten bounds on both inflationary and $Λ\mathrm{CDM}$ parameters considerably while improving precision on key astrophysical quantities.

astro-ph.CO↗

arXiv2025

Rényi-Induced Information Geometry and Hartigan's Prior Family

We derive the information geometry induced by the statistical Rényi divergence, namely its metric tensor, its dual parametrized connections, as well as its dual Laplacians. Based on these results, we demonstrate that the Rényi-geometry, though closely related, differs in structure from Amari's well-known $α$-geometry. Subsequently, we derive the canonical uniform prior distributions for a statistical manifold endowed with a Rényi-geometry, namely the dual Rényi-covolumes. We find that the Rényi-priors can be made to coincide with Takeuchi and Amari's $α$-priors by a reparameterization, which is itself of particular significance in statistics. Herewith, we demonstrate that Hartigan's parametrized ($α_H$) family of priors is precisely the parametrized ($ρ$) family of Rényi-priors ($α_H = ρ$).

math.ST↗

arXiv2025

Approximating non-Gaussian Bayesian partitions with normalising flows: statistics, inference and application to cosmology

Subject of this paper is the simplification of Markov chain Monte Carlo sampling as used in Bayesian statistical inference by means of normalising flows, a machine learning method which is able to construct an invertible and differentiable transformation between Gaussian and non-Gaussian random distributions. We use normalising flows to compute Bayesian partition functions for non-Gaussian distributions and show how normalising flows can be employed in finding analytical expressions for posterior distributions beyond the Gaussian limit. Flows offer advantages for the numerical evaluation of the partition function itself, as well as for cumulants and for the information entropy. We demonstrate how normalising flows in conjunction with Bayes partitions can be used in inference problems in cosmology and apply them to the posterior distribution for the matter density $Ω_m$ and a dark energy equation of state parameter $w_0$ on the basis of supernova data.

astro-ph.CO↗

arXiv2025

Partition function approach to non-Gaussian likelihoods: information theory and state variables for Bayesian inference

The significance of statistical physics concepts such as entropy extends far beyond classical thermodynamics. We interpret the similarity between partitions in statistical mechanics and partitions in Bayesian inference as an articulation of a result by Jaynes (1957), who clarified that thermodynamics is in essence a theory of information. In this, every sampling process has a mechanical analogue. Consequently, the divide between ensembles of samplers in parameter space and sampling from a mechanical system in thermodynamic equilibrium would be artificial. Based on this realisation, we construct a continuous modelling of a Bayes update akin to a transition between thermodynamic ensembles. This leads to an information theoretic interpretation of Jazinsky's equality, relating the expenditure of work to the influence of data via the likelihood. We propose one way to transfer the vocabulary and the formalism of thermodynamics (energy, work, heat) and statistical mechanics (partition functions) to statistical inference, starting from Bayes' law. Different kinds of inference processes are discussed and relative entropies are shown to follow from suitably constructed partitions as an analytical formulation of sampling processes. Lastly, we propose an effective dimension as a measure of system complexity. A numerical example from cosmology is put forward to illustrate these results.

cond-mat.stat-mech↗

arXiv2024

Partition function approach to non-Gaussian likelihoods: macrocanonical partitions and replicating Markov-chains

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 $μ$, 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 $Ω_m$ and $w$ on the basis of data from the supernova distance redshift relation.

astro-ph.CO↗

arXiv2024

A unified linear intrinsic alignment model for elliptical and disc galaxies and the resulting ellipticity spectra

Alignments of spiral 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 an Euclid-like survey.

astro-ph.CO↗

arXiv2024

PINNferring the Hubble Function with Uncertainties

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.

astro-ph.CO↗

arXiv2024

Partition function approach to non-Gaussian likelihoods: partitions for the inference of functions and the Fisher-functional

Motivated by constraints on the dark energy equation of state from supernova-data, we propose a formalism for the Bayesian inference of functions: Starting at a functional variant of the Kullback-Leibler divergence we construct a functional Fisher-matrix and a suitable partition functional which takes on the shape of a path integral. After showing the validity of the Cramér-Rao bound and unbiasedness for functional inference in the Gaussian case, we construct Fisher-functionals for the dark energy equation of state constrained by the cosmological redshift-luminosity relationship of supernovae of type Ia, for both the linearised and the lowest-order non-linear model. Introducing Fourier-expansions and expansions into Gegenbauer-polynomials as discretisations of the dark energy equation of state function shows how the uncertainty on the inferred function scales with model complexity and how functional assumptions can lead to errors in extrapolation to poorly constrained redshift ranges.

astro-ph.CO↗

arXiv2023

A weak lensing perspective on nonlinear structure formation with fuzzy dark matter

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 $χ^2$-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.

astro-ph.CO↗

arXiv2023

Partition function approach to non-Gaussian likelihoods: physically motivated convergence criteria for Markov-chains

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.

astro-ph.CO↗

arXiv2023

Cornering Extended Starobinsky Inflation with CMB and SKA

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.

astro-ph.CO↗

arXiv2023

On the Cosmic Web Elongation in Fuzzy Dark Matter Cosmologies: Effects on Density Profiles, Shapes and Alignments of Halos

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 ($Λ$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 $Λ$CDM as a function of the particle mass $m$. Compared to $Λ$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 $Λ$CDM. The intermediate-to-major and minor-to-major shape parameter profiles are monotonically increasing with ellipsoidal radius in $N$-body simulations of $Λ$CDM. In FDM-like cosmologies, the monotonicity is broken, halos are more elongated around the virial radius than their $Λ$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 $6.4 σ$-significance in the fractional differences between the isotropised linear alignment magnitudes $D_{\text{iso}}$ in the $m=10^{-22}$ eV model and $Λ$CDM. Such FDM-like imprints on the internal properties of virialised halos are expected to be strikingly visible in the high-$z$ Universe.

astro-ph.CO↗

arXiv2022

Partition function approach to non-Gaussian likelihoods: Formalism and expansions for weakly non-Gaussian cosmological inference

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 $Ω_m$ 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 Cramér-Rao boundary and to information entropies.

astro-ph.CO↗

arXiv2022

Etherington duality breaking: gravitational lensing in non-metric spacetimes versus intrinsic alignments

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 $Σ(\ell) \geq 3$ 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.

astro-ph.CO↗

arXiv2022

Probing the Inflaton Potential with SKA

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.

astro-ph.CO↗