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The dispersion measure (DM) of fast radio bursts (FRBs) is sensitive to the electron distribution in the Universe, making it a promising probe of cosmology and astrophysical processes such as baryonic feedback. However, cosmological analyses of FRBs require knowledge of the contribution to the observed DM coming from the FRB host. The size and distribution of this contribution is still uncertain, thus significantly limiting current cosmological FRB analyses. In this study, we extend the baryonification (BCM) approach to derive a physically-motivated, analytic model for predicting the host contribution to FRB DMs. By focusing on the statistical properties of FRB host DMs, we find that our simple model is able to reproduce the probability distribution function (PDF) of host halo DMs measured from the CAMELS suite of hydrodynamic simulations, as well as their mass- and redshift dependence. Furthermore, we demonstrate that our model allows for self-consistent predictions of the host DM PDF and the matter power spectrum suppression due to baryonic effects, as observed in these simulations, making it promising for modelling host-DM-related systematics in FRB analyses. In general, we find that the shape of the host DM PDF is determined by the interplay between the FRB and gas distributions in halos. Our findings indicate that more compact FRB profiles require shallower gas profiles (and vice versa) in order to match the observed DM distributions in hydrodynamic simulations. Furthermore, the analytic model presented here shows that the shape of the host DM PDF is highly sensitive to the parameters of the BCM. This suggests that this observable could be used as an interesting test bed for baryonic processes, complementing other probes due to its sensitivity to feedback on galactic scales. We further discuss the main limitations of our analysis, and point out potential avenues for future work., Comment: 13 pages, 12 figures, to be submitted to OJA, comments welcome

Photometric galaxy surveys, despite their limited resolution along the line of sight, encode rich information about the large-scale structure (LSS) of the Universe thanks to the large number density and extensive depth of the data. However, the complicated selection effects in wide and deep surveys will potentially cause significant bias in the angular two-point correlation function (2PCF) measured from those surveys. In this paper, we measure the 2PCF from the newly published KiDS-Legacy sample. Given an $r$-band $5\sigma$ magnitude limit of $24.8$ and survey footprint of $1347$ deg$^2$, it achieves an excellent combination of sky coverage and depth for such a measurement. We find that complex selection effects, primarily induced by varying seeing, introduce over-estimation of the 2PCF by approximately an order of magnitude. To correct for such effects, we apply a machine learning-based method to recover an ``organised random'' (OR) that presents the same selection pattern as the galaxy sample. The basic idea is to find the selection-induced clustering of galaxies using a combination of self-organising maps (SOM) and hierarchical clustering (HC). This unsupervised machine learning method is able to recover complicated selection effects without specifying their functional forms. We validate this ``SOM+HC'' method on mock deep galaxy samples with realistic systematics and selections derived from the KiDS-Legacy catalogue. Using mock data, we demonstrate that the OR delivers unbiased 2PCF cosmological parameter constraints, removing the $27\sigma$ offset in the galaxy bias parameter that is recovered when adopting uniform randoms. Blinded measurements on the real KiDS-Legacy data show that the corrected 2PCF is robust to the SOM+HC configuration near the optimal setup suggested by the mock tests. Our software is open-source for future usage., Comment: 29 pages, 27 figures, 4 tables

We use the dispersion measure (DM) of localised Fast Radio Bursts (FRBs) to constrain cosmological and host galaxy parameters using simulation-based inference (SBI) for the first time. By simulating the large-scale structure of the electron density with the Generator for Large-Scale Structure (GLASS), we generate log-normal realisations of the free electron density field, accurately capturing the correlations between different FRBs. For the host galaxy contribution, we rigorously test various models, including log-normal, truncated Gaussian and Gamma distributions, while modelling the Milky Way component using pulsar data. Through these simulations, we employ the truncated sequential neural posterior estimation method to obtain the posterior. Using current observational data, we successfully recover the amplitude of the DM-redshift relation, consistent with Planck, while also fitting both the mean host contribution and its shape. Notably, we find no clear preference for a specific model of the host galaxy contribution. Although SBI may not yet be strictly necessary for FRB inference, this work lays the groundwork for the future, as the increasing volume of FRB data will demand precise modelling of both the host and large-scale structure components. Our modular simulation pipeline offers flexibility, allowing for easy integration of improved models as they become available, ensuring scalability and adaptability for upcoming analyses using FRBs. The pipeline is made publicly available under https://github.com/koustav-konar/FastNeuralBurst., Comment: Submitted to OJA, 14 pages, 10 figures, comments welcome

We introduce OneCovariance, an open-source software designed to accurately compute covariance matrices for an arbitrary set of two-point summary statistics across a variety of large-scale structure tracers. Utilising the halo model, we estimate the statistical properties of matter and biased tracer fields, incorporating all Gaussian, non-Gaussian, and super-sample covariance terms. The flexible configuration permits user-specific parameters, such as the complexity of survey geometry, the halo occupation distribution employed to define each galaxy sample, or the form of the real-space and/or Fourier space statistics to be analysed. We illustrate the capabilities of OneCovariance within the context of a cosmic shear analysis of the final data release of the Kilo-Degree Survey (KiDS-Legacy). Upon comparing our estimated covariance with measurements from mock data and calculations from independent software, we ascertain that OneCovariance achieves accuracy at the per cent level. When assessing the impact of ignoring complex survey geometry in the cosmic shear covariance computation, we discover misestimations at approximately the $10\%$ level for cosmic variance terms. Nonetheless, these discrepancies do not significantly affect the KiDS-Legacy recovery of cosmological parameters. We derive the cross-covariance between real-space correlation functions, bandpowers, and COSEBIs, facilitating future consistency tests among these three cosmic shear statistics. Additionally, we calculate the covariance matrix of photometric-spectroscopic galaxy clustering measurements, validating Jackknife covariance estimates for calibrating KiDS-Legacy redshift distributions. The OneCovariance can be found on github Hub together with a comprehensive documentation and examples., Comment: 37 pages, 11 figures, to be submitted to A&A, code available at https://github.com/rreischke/OneCovariance

We explore the enhanced self-calibration of photometric galaxy redshift distributions, $n(z)$, through the combination of up to six two-point functions. Our $\rm 3\times2pt$ configuration is comprised of photometric shear, spectroscopic galaxy clustering, and spectroscopic-photometric galaxy-galaxy lensing (GGL). We further include spectroscopic-photometric cross-clustering; photometric GGL; and photometric auto-clustering, using the photometric shear sample as density tracer. We perform simulated likelihood forecasts of the cosmological and nuisance parameter constraints for Stage-III- and Stage-IV-like surveys. For the Stage-III-like case, we employ realistic but perturbed redshift distributions, and distinguish between "coherent" shifting in one direction, versus more internal scattering and full-shape errors. For perfectly known $n(z)$, a $\rm 6\times2pt$ analysis gains $\sim40\%$ in Figure of Merit (FoM) in the $S_8\equiv\sigma_8\sqrt{\Omega_{\rm m}/0.3}$ and $\Omega_{\rm m}$ plane relative to the $\rm 3\times2pt$ analysis. If untreated, coherent and incoherent redshift errors lead to inaccurate inferences of $S_8$ and $\Omega_{\rm m}$, respectively. Employing bin-wise scalar shifts $\delta{z}_i$ in the tomographic mean redshifts reduces cosmological parameter biases, with a $\rm 6x2pt$ analysis constraining the shift parameters with $2-4$ times the precision of a photometric $\rm 3^{ph}\times2pt$ analysis. For the Stage-IV-like survey, a $\rm 6\times2pt$ analysis doubles the FoM($\sigma_8{-}\Omega_{\rm m}$) compared to any $\rm 3\times2pt$ or $\rm 3^{ph}\times2pt$ analysis, and is only $8\%$ less constraining than if the $n(z)$ were perfectly known. A Gaussian mixture model for the $n(z)$ reduces mean-redshift errors and preserves the $n(z)$ shape. It also yields the most accurate and precise cosmological constraints for any $N\rm\times2pt$ configuration given $n(z)$ biases., Comment: 38 pages, 20 figures, to be submitted to A&A

We explore the potential for improving constraints on gravity by leveraging correlations in the dispersion measure derived from Fast Radio Bursts (FRBs) in combination with cosmic shear. Specifically, we focus on Horndeski gravity, inferring the kinetic braiding and Planck mass run rate from a stage-4 cosmic shear mock survey alongside a survey comprising $10^4$ FRBs. For the inference pipeline, we utilise hi_class to predict the linear matter power spectrum in modified gravity scenarios, while non-linear corrections are modelled with HMcode, including feedback mechanisms. Our findings indicate that FRBs can disentangle degeneracies between baryonic feedback and cosmological parameters, as well as the mass of massive neutrinos. Since these parameters are also degenerate with modified gravity parameters, the inclusion of FRBs can enhance constraints on Horndeski parameters by up to $40$ percent, despite being a less significant measurement. Additionally, we apply our model to current FRB data and use the uncertainty in the $\mathrm{DM}-z$ relation to impose limits on gravity. However, due to the limited sample size of current data, constraints are predominantly influenced by theoretical priors. Despite this, our study demonstrates that FRBs will significantly augment the limited set of cosmological probes available, playing a critical role in providing alternative tests of feedback, cosmology, and gravity. All codes used in this work are made publically available., Comment: 14 pages, 10 figures

We present a simulation-based inference (SBI) cosmological analysis of cosmic shear two-point statistics from the fourth weak gravitational lensing data release of the ESO Kilo-Degree Survey (KiDS-1000). KiDS-SBI efficiently performs non-Limber projection of the matter power spectrum via Levin's method, and constructs log-normal random matter fields on the curved sky for arbitrary cosmologies, including effective prescriptions for intrinsic alignments and baryonic feedback. The forward model samples realistic galaxy positions and shapes based on the observational characteristics, incorporating shear measurement and redshift calibration uncertainties, as well as angular anisotropies due to variations in depth and point-spread function. To enable direct comparison with standard inference, we limit our analysis to pseudo-angular power spectra. The SBI is based on sequential neural likelihood estimation to infer the posterior distribution of spatially-flat $\Lambda$CDM cosmological parameters from 18,000 realisations. We infer a mean marginal of the growth of structure parameter $S_{8} \equiv \sigma_8 (\Omega_\mathrm{m} / 0.3)^{0.5} = 0.731\pm 0.033$ ($68 \%$). We present a measure of goodness-of-fit for SBI and determine that the forward model fits the data well with a probability-to-exceed of $0.42$. For fixed cosmology, the learnt likelihood is approximately Gaussian, while constraints widen compared to a Gaussian likelihood analysis due to cosmology dependence in the covariance. Neglecting variable depth and anisotropies in the point spread function in the model can cause $S_{8}$ to be overestimated by ${\sim}5\%$. Our results are in agreement with previous analysis of KiDS-1000 and reinforce a $2.9 \sigma$ tension with constraints from cosmic microwave background measurements. This work highlights the importance of forward-modelling systematic effects in upcoming galaxy surveys., Comment: 44 pages, 30 figures. Submitted to Astronomy & Astrophysics

Fast Radio Bursts (FRBs) are a sensitive probe of the electron distribution in both the large-scale structure and their host galaxies through the dispersion measure (DM) of the radio pulse. Baryonic feedback models are crucial for modelling small scales for ongoing cosmological surveys that are expected to change the electron distribution in galaxies in a way that can be probed by FRB observations. In this paper, we explore the impact of baryonic feedback on FRB hosts using numerical simulations and make a detailed study of the host galaxy dispersion as a function of redshift, galaxy type, feedback model and how these properties vary in independent simulation codes. We find that the host galaxy dispersion varies dramatically between different implementations of baryonic feedback, allowing FRBs with host identification to be a valuable probe of feedback physics and thus provide necessary priors for upcoming analysis of the statistical properties of the large-scale structure. We further find that any dependency on the exact location of events within the halo is small. While there exists an evolution of the dispersion measure with redshift and halo mass, it is largely driven by varying star formation rates of the halo. Spectral information from FRB hosts can therefore be used to put priors on the host galaxy dispersion measure, and FRBs can be used to distinguish between competing models of baryonic feedback in future studies., Comment: 8 pages, 8 figures

One of the key limitations of large-scale structure surveys of the current and future generation, such as Euclid, LSST-Rubin or Roman, is the influence of feedback processes on the distribution of matter in the Universe. This effect, called baryonic feedback, modifies the matter power spectrum on non-linear scales much stronger than any cosmological parameter of interest. Constraining these modifications is therefore key to unlock the full potential of the upcoming surveys, and we propose to do so with the help of Fast Radio Bursts (FRBs). FRBs are short, astrophysical radio transients of extragalactic origin. Their burst signal is dispersed by the free electrons in the large-scale-structure, leading to delayed arrival times at different frequencies characterised by the dispersion measure (DM). Since the dispersion measure is sensitive to the integrated line-of-sight electron density, it is a direct probe of the baryonic content of the Universe. We investigate how FRBs can break the degeneracies between cosmological and feedback parameters by correlating the observed Dispersion Measure with the weak gravitational lensing signal of a Euclid-like survey. In particular we use a simple one-parameter model controlling baryonic feedback, but we expect similar findings for more complex models. Within this model we find that $\sim 10^4$ FRBs are sufficient to constrain the baryonic feedback 10 times better than cosmic shear alone. Breaking this degeneracy will tighten the constraints considerably, for example we expect a factor of two improvement on the sum of neutrino masses, Comment: 18 pages, 7 figures

We present refined cosmological parameter constraints derived from a cosmic shear analysis of the fourth data release of the Kilo-Degree Survey (KiDS-1000). Our main improvements include enhanced galaxy shape measurements made possible by an updated version of the lensfit code and improved shear calibration achieved with a newly developed suite of multi-band image simulations. Additionally, we incorporated recent advancements in cosmological inference from the joint Dark Energy Survey Year 3 and KiDS-1000 cosmic shear analysis. Assuming a spatially flat standard cosmological model, we constrain $S_8\equiv\sigma_8(\Omega_{\rm m}/0.3)^{0.5} = 0.776_{-0.027-0.003}^{+0.029+0.002}$, where the second set of uncertainties accounts for the systematic uncertainties within the shear calibration. These systematic uncertainties stem from minor deviations from realism in the image simulations and the sensitivity of the shear measurement algorithm to the morphology of the galaxy sample. Despite these changes, our results align with previous KiDS studies and other weak lensing surveys, and we find a ${\sim}2.3\sigma$ level of tension with the Planck cosmic microwave background constraints on $S_8$., Comment: 20 pages, 13 figures, 4 tables, minor revisions to match the final accepted version

The superposition of many astrophysical gravitational wave (GW) signals below typical detection thresholds baths detectors in a stochastic gravitational wave background (SGWB). In this work, we present a Fourier space approach to compute the frequency-domain distribution of stochastic gravitational wave backgrounds produced by discrete sources. Expressions for the moment-generating function and the distribution of observed (discrete) Fourier modes are provided. The results are first applied to the signal originating from all the mergers of compact stellar remnants (black holes and neutron stars) in the Universe, which is found to exhibit a $-4$ power-law tail. This tail is verified in the signal-to-noise ratio distribution of GWTC events. The extent to which the subtraction of bright (loud) mergers gaussianizes the resulting confusion noise of unresolved sources is then illustrated. The power-law asymptotic tail for the unsubtracted signal, and an exponentially decaying tail in the case of the SGWB, are also derived analytically. Our results generalize to any background of gravitational waves emanating from discrete, individually coherent, sources., Comment: (v1) Comments welcome. (v2) Updated to match version accepted to PRD

Fast Radio Bursts (FRBs) are short astrophysical transients of extragalactic origin. Their burst signal is dispersed by the free electrons in the large-scale-structure (LSS), leading to delayed arrival times at different frequencies. Another potential source of time delay is the well known Shapiro delay, which measures the space-space and time-time metric perturbations along the line-of-sight. If photons of different frequencies follow different trajectories, i.e. if the universality of free fall guaranteed by the weak equivalence principle (WEP) is violated, they would experience an additional relative delay. This quantity, however, is not an observable on the background level as it is not gauge independent, which has led to confusion in previous papers. Instead, an imprint can be seen in the correlation between the time delays of different pulses. In this paper, we derive robust and consistent constraints from twelve localised FRBs on the violation of the WEP in the energy range between 4.6 and 6 meV. In contrast to a number of previous studies, we consider our signal to be not in the model, but in the covariance matrix of the likelihood. To do so, we calculate the covariance of the time delays induced by the free electrons in the LSS, the WEP breaking terms, the Milky Way and host galaxy. By marginalising over both host galaxy contribution and the contribution from the free electrons, we find that the parametrised post-Newtonian parameter $\gamma$ characterising the WEP violation must be constant in this energy range to 1 in $10^{13}$ at 68$\;\%$ confidence. These are the tightest constraints to-date on $\Delta\gamma$ in this low energy range., Comment: 8 pages, 4 figures, accepted by MNRAS, matches final submitted

Photometric redshifts are a key ingredient in the analysis and interpretation of large-scale structure (LSS) surveys. The accuracy and precision of these redshift estimates are directly linked to the constraining power of photometric surveys. It is hence necessary to define precision and accuracy requirements for the redshift calibration \revision{to not} infer biased results in the final analysis. For weak gravitational lensing of the LSS, the photometry culminates in the estimation of the source redshift distribution (SRD) in each of the tomographic bins used in the analysis. The focus has been on shifts of the mean of the SRDs and how well the calibration must be able to recover those. Since the estimated SRDs are usually given as a normalized histogram with corresponding errors, it would be advantageous to propagate these uncertainties accordingly to see whether the requirements of the given survey are indeed fulfilled. Here we propose the use of functional derivatives to calculate the sensitivity of the final observables, e.g. the lensing angular power spectrum, with respect to the SRD at a specific redshift. This allows the propagation of arbitrarily shaped small perturbations to the SRD, without having to run the whole analysis pipeline for each realization again. We apply our method to an EUCLID survey and demonstrate it with SRDs of the KV450 data set, recovering previous results. Lastly, we note that the moments of the SRD of order larger than two will probably not be relevant when propagating redshift uncertainties in cosmic shear analysis., Comment: 10 pages, 9 figures, matches accepted version in MNRAS

The dispersion of fast radio bursts (FRBs) is a measure of the large-scale electron distribution. It enables measurements of cosmological parameters, especially of the expansion rate and the cosmic baryon fraction. The number of events is expected to increase dramatically over the coming years, and of particular interest are bursts with identified host galaxy and therefore redshift information. In this paper, we explore the covariance matrix of the dispersion measure (DM) of FRBs induced by the large-scale structure, as bursts from a similar direction on the sky are correlated by long wavelength modes of the electron distribution. We derive analytical expressions for the covariance matrix and examine the impact on parameter estimation from the FRB dispersion measure - redshift relation. The covariance also contains additional information that is missed by analysing the events individually. For future samples containing over $\sim300$ FRBs with host identification over the full sky, the covariance needs to be taken into account for unbiased inference, and the effect increases dramatically for smaller patches of the sky. Also forecasts must consider these effects as they would yield too optimistic parameter constraints. Our procedure can also be applied to the DM of the afterglow of Gamma Ray Bursts., Comment: 8 pages, 5 figures, accepted by MNRAS, matches final submitted version

We present constraints on the flat $\Lambda$CDM cosmological model through a joint analysis of galaxy abundance, galaxy clustering and galaxy-galaxy lensing observables with the Kilo-Degree Survey. Our theoretical model combines a flexible conditional stellar mass function, to describe the galaxy-halo connection, with a cosmological N-body simulation-calibrated halo model to describe the non-linear matter field. Our magnitude-limited bright galaxy sample combines 9-band optical-to-near-infrared photometry with an extensive and complete spectroscopic training sample to provide accurate redshift and stellar mass estimates. Our faint galaxy sample provides a background of accurately calibrated lensing measurements. We constrain the structure growth parameter $S_8=\sigma_8\sqrt{\Omega_{\mathrm{m}}/0.3}=0.773^{+0.028}_{-0.030}$, and the matter density parameter $\Omega_{\mathrm{m}}=0.290^{+0.021}_{-0.017}$. The galaxy-halo connection model adopted in the work is shown to be in agreement with previous studies. Our constraints on cosmological parameters are comparable to, and consistent with, joint $3\times2{\mathrm{pt}}$ clustering-lensing analyses that additionally include a cosmic shear observable. This analysis therefore brings attention to the significant constraining power in the often-excluded non-linear scales for galaxy clustering and galaxy-galaxy lensing observables. By adopting a theoretical model that accounts for non-linear halo bias, halo exclusion, scale-dependent galaxy bias and the impact of baryon feedback, this work demonstrates the potential and a way forward to include non-linear scales in cosmological analyses. Varying the width of the satellite galaxy distribution with an additional parameter yields a strong preference for sub-Poissonian variance, improving the goodness of fit by 0.18 in reduced $\chi^{2}$ value compared to a fixed Poisson distribution., Comment: 25 pages, 16 figures, accepted for publication in A&A, v3 with updated figure from Corrigendum (https://www.aanda.org/articles/aa/full_html/2024/08/aa50702e-24/aa50702e-24.html, https://doi.org/10.1051/0004-6361/202450702e)

We determine the error introduced in a joint halo model analysis of galaxy-galaxy lensing and galaxy clustering observables when adopting the standard approximation of linear halo bias. Considering the Kilo-Degree Survey, we forecast that ignoring the non-linear halo bias would result in up to 5$\sigma$ offsets in the recovered cosmological parameters describing structure growth, $S_8$, and the matter density parameter, $\Omega_{\mathrm{m}}$. We include the scales $10^{-1.3}

Developing analysis pipelines based on statistics beyond two-point functions is critical for extracting a maximal amount of cosmological information from current and upcoming weak lensing surveys. In this paper, we study the impact of the intrinsic alignment of galaxies (IA) on three promising probes measured from aperture mass maps -- the lensing peaks, minima and full PDF, in comparison and in combination with the shear two-point correlation functions ($\gamma$-2PCFs). Our two-dimensional IA infusion method converts the light-cone-projected mass sheets into projected tidal tensors, which are then linearly coupled to an intrinsic ellipticity component with a strength controlled by the coupling parameter $A_{\rm IA}$. We validate our method with the $\gamma$-2PCFs statistics, recovering well the analytical calculations from the linear alignment model of Bridle \& King in a full tomographic setting, and for different $A_{\rm IA}$ values. We next use our method to infuse at the galaxy catalogue level a non-linear IA model that includes the density-weighting term introduced in \citet{Blazek2015}, and compute the impact on the three aperture mass map statistics. We find that large \snr peaks are maximally affected, with deviations reaching 30\% (10\%) for a {\it Euclid}-like (KiDS-like) survey. Modelling the signal in a $w$CDM cosmology universe with $N$-body simulations, we forecast the cosmological bias caused by unmodelled IA for 100 deg$^2$ of {\it Euclid}-like data, finding very large offsets in $w_0$ (5-10$\sigma_{\rm stat}$), $\Omega_{\rm m}$ (4-6$\sigma_{\rm stat}$), and $S_8 \equiv \sigma_8\sqrt{\Omega_{\rm m}/0.3}$ ($\sim$3$\sigma_{\rm stat}$). The method presented in this paper offers a compelling avenue to account for IA in beyond-two-point weak lensing statistics, with a flexibility comparable to that of current $\gamma$-2PCFs IA analytical models., Comment: 21 pages, 12 figures, accepted version

Fast radio bursts (FRBs) are very short and bright transients visible over extragalactic distances. The radio pulse undergoes dispersion caused by free electrons along the line of sight, most of which are associated with the large-scale structure (LSS). The total dispersion measure therefore increases with the line of sight and provides a distance estimate to the source. We present the first measurement of the Hubble constant using the dispersion measure -- redshift relation of FRBs with identified host counterpart and corresponding redshift information. A sample of nine currently available FRBs yields a constraint of $H_0 = 62.3 \pm 9.1 \,\rm{km} \,\rm{s}^{-1}\,\rm{Mpc}^{-1}$, accounting for uncertainty stemming from the LSS, host halo and Milky Way contributions to the observed dispersion measure. The main current limitation is statistical, and we estimate that a few hundred events with corresponding redshifts are sufficient for a per cent measurement of $H_0$. This is a number well within reach of ongoing FRB searches. We perform a forecast using a realistic mock sample to demonstrate that a high-precision measurement of the expansion rate is possible without relying on other cosmological probes. FRBs can therefore arbitrate the current tension between early and late time measurements of $H_0$ in the near future., Comment: 6 pages, 3 figures. Submitted to MNRAS

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

Fast radio bursts (FRBs) are astrophysical transients of still debated origin. So far several hundred events have been detected, mostly at extragalactic distances, and this number is expected to grow significantly over the next years. The radio signals from the burst experience dispersion as they travel through the free electrons along the line-of-sight characterised by the dispersion measure (DM) of the radio pulse. In addition, each photon also experiences a gravitational Shapiro time delay while travelling through the potentials generated by the large-scale structure. If the equivalence principle (EP) holds, the Shapiro delay is the same for photons of all frequencies. In case the EP is broken, one would expect an additional dispersion to occur which could be either positive or negative for individual sources. Here we suggest to use angular statistics of the DM fluctuations to put constraints on the EP parametrized by the post-Newtonian parameter $\gamma$. Previous studies suffer from the problem that the gravitational potential responsible for the delay diverges in a cosmological setting, which our approach avoids. We carry out a forecast for a population of FRBs observable within the next years and show that any significant detection of the DM angular power spectrum will place constraints on the EP that are by a few orders of magnitude more stringent than current limits., Comment: 6 pages, 2 figures

We explore the implications of a single observer's viewpoint on measurements of galaxy clustering statistics. We focus on the Bardeen potentials, which imprint characteristic scale-dependent signatures in the observed galaxy power spectrum. The existence of an observer breaks homogeneity as it singles out particular field values at her/his position, like a spontaneous symmetry breaking. As a result, spatial averaging of the data must be performed while holding the Bardeen potentials fixed at the observer's position. In practice, this can be implemented with the formalism of constrained random fields. In the traditional Cartesian Fourier decomposition, this constraint imprints a signature in the observed galaxy power spectrum at wavenumber comparable to the fundamental mode of the survey. This effect, which is well within the cosmic variance, is the same for all observers regardless of their local environment because differences of potential solely are observable. In a spherical Bessel Fourier decomposition, this constraint affects the monopole of the observed galaxy distribution solely, like in CMB data. As a corollary, the scale-dependence of the non-Gaussian bias induced by a local primordial non-Gaussianity is not significantly affected by the observer's viewpoint., Comment: 10 pages, one figure (v1) submitted to MNRAS (v2) in press in MNRAS

Fast radio bursts (FRBs) are astrophysical transients of currently unknown origin, and so far several events have been detected at extragalactic distances. The dispersion measure (DM) of the radio signal is a probe of the integrated electron density along the line of sight and therefore allows to map the electron distribution within the large-scale structure. Since a fraction of electrons gets expelled from galaxies by feedback, they are anticorrelated with halos at large scales and hence the angular DM correlations show a scale-dependent bias caused by primordial non-Gaussianity. Although the signal is weaker than in other probes like galaxy clustering, FRBs can potentially probe considerably larger volumes. We show that while studying the FRB clustering signal requires very large samples, correlations in the DM are cosmic-variance limited on large angular scales with only $\sim 10^{3-4}$ events. A tomographic analysis of the angular DM correlation function can constrain the local primordial bispectrum shape parameter $f_\mathrm{NL}$ to a precision down to ${f_\mathrm{NL}}\sim \mathcal{O}(1)$ depending on assumptions about the FRB redshift distribution and the astrophysical feedback on large scales. This makes FRBs a competitive probe to constrain inflationary physics., Comment: 9 pages, 5 figures

The subject of this paper is a quantification of the information content of cosmological probes of the large-scale structures, specifically of temperature and polarisation anisotropies in the cosmic microwave background, CMB-lensing, weak cosmic shear and galaxy clustering, in terms of Information theory measures like information entropies. We aim to establish relationships for Gaussian likelihoods, between conventional measures of statistical uncertainties and information entropies. Furthermore, we extend these studies to the computation of (Bayesian) evidences and the power of measurement to distinguish between competing models. We investigate in detail how cosmological data decreases information entropy by reducing statistical errors and by breaking degeneracies. In addition, we work out how tensions between data sets increase information entropy and quantify this effect in three examples: the discrepancy in $\Omega_m$ and $\sigma_8$ between the CMB and weak lensing, the role of intrinsic alignments in weak lensing data when attempting the dark energy equation of state parameters, and the famous $H_0$-tension between Cepheids in the Hubble keystone project and the cosmic microwave background as observed by Planck., Comment: 12 pages, 5 figures, submitted to MNRAS

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

Dark matter comprised of axion-like particles (ALPs) generated by the realignment mechanism in the post-inflationary scenario leads to primordial isocurvature fluctuations. The power spectrum of these fluctuations is flat for small wave numbers, extending to scales accessible with cosmological surveys. We use the latest measurements of Cosmic Microwave Background (CMB) primary anisotropies together with CMB lensing, Baryonic Acoustic Oscillations (BAO) and Sunyaev Zel'dovich (SZ) cluster counts to measure the amplitude and tilt of the isocurvature component. We find preference for a white-noise isocurvature component in the CMB primary anisotropies; this conclusion is, however, weakened by current large-scale structure (LSS) data. Interpreting the result as a conservative upper limit on the isocurvature component, the combined bound on the ALP mass from all probes is $m_{a} \gtrsim 10^{-19}$ eV, with some dependence on how $m_{a}$ evolves with temperature. The expected sensitivity of cosmic shear and galaxy clustering from future LSS experiments and CMB lensing suggests improved bounds of $m_{a} \gtrsim 10^{-18}$-$10^{-13}$ eV, depending on scale cuts used to avoid non-linearities and the ALP mass-temperature dependence., Comment: 25 pages, 11 figures. Matches accepted version

The subject of this paper is optimisation of weak lensing tomography: We carry out numerical minimisation of a measure of total statistical error as a function of the redshifts of the tomographic bin edges by means of a Nelder-Mead algorithm in order to optimise the sensitivity of weak lensing with respect to different optimisation targets. Working under the assumption of a Gaussian likelihood for the parameters of a $w_0 w_a$CDM-model and using Euclid's conservative survey specifications, we compare an equipopulated, equidistant and optimised bin setting and find that in general the equipopulated setting is very close to the optimal one, while an equidistant setting is far from optimal and also suffers from the ad hoc choice of a maximum redshift. More importantly, we find that nearly saturated information content can be gained using already few tomographic bins. This is crucial for photometric redshift surveys with large redshift errors. We consider a large range of targets for the optimisation process that can be computed from the parameter covariance (or equivalently, from the Fisher-matrix), extend these studies to information entropy measures such as the Kullback-Leibler-divergence and conclude that in many cases equipopulated binning yields results close to the optimum, which we support by analytical arguments.

We study the parameter estimation bias induced by intrinsic alignments on a Euclid-like weak lensing survey. For the intrinsic alignment signal we assume a composite alignment model for elliptical and spiral galaxies using tidal shearing and tidal torquing as the alignment generating mechanism, respectively. The parameter estimation bias is carried out analytically with a Gaussian bias model and through running Monte-Carlo-Markov-chains on synthetic data including the alignment signal with a likelihood only including the cosmic shear signal. In particular, we study the impact of $II$ and $GI$ alignment terms individually as well as the more realistic situation where both types of alignment are present, and investigate the scaling of the estimation biases with varying strength of the alignment signal. Our results show that intrinsic alignments can cause substantial biases in cosmological parameters even if the coupling of galaxies to the ambient large is small. Especially $GI$-contributions strongly bias key cosmological parameters such as the dark energy equation of state. We also correct the analytic expression for the Gaussian bias model and find that the biases induced by intrinsic alignments are not accurately recovered by the simple analytic model., Comment: submitted for publication, 17 pages, 5 figures

The coalescence of compact binary stars is expected to produce a stochastic background of gravitational waves (GW) observable with future GW detectors. Such backgrounds are usually characterized by their power spectrum as a function of frequency. Here, we present a method to calculate the full 1-point distribution of strain fluctuations. We focus on time series data, but our approach generalizes to the frequency domain. We illustrate how this probability distribution can be evaluated numerically. In addition, we derive accurate analytical asymptotic expressions for the large strain tail, which demonstrate that it is dominated by the nearest source. As an application, we calculate the distribution of strain fluctuations for the astrophysical GW background produced by binary mergers of compact stars in the Universe, and the distribution of the observed confusion background obtained upon subtracting bright, resolved sources from the signal. We quantify the extent to which they deviate from a Gaussian distribution. Our approach could be useful for the spectral shape reconstruction of stochastic GW backgrounds., Comment: (v1): Submitted for publication. Comments welcome (v2): 18 pages, 6 figures. Revised version accepted for publication in PRD

We use analytic computations to predict the power spectrum as well as the bispectrum of Cosmic Infrared Background (CIB) anisotropies. Our approach is based on the halo model and takes into account the mean luminosity-mass relation. The model is used to forecast the possibility to simultaneously constrain cosmological, CIB and halo occupation distribution (HOD) parameters in the presence of foregrounds. For the analysis we use wavelengths in eight frequency channels between 200 and 900$\;\mathrm{GHz}$ with survey specifications given by Planck and LiteBird. We explore the sensitivity to the model parameters up to multipoles of $\ell =1000$ using auto- and cross-correlations between the different frequency bands. With this setting, cosmological, HOD and CIB parameters can be constrained to a few percent. Galactic dust is modeled by a power law and the shot noise contribution as a frequency dependent amplitude which are marginalized over. We find that dust residuals in the CIB maps only marginally influence constraints on standard cosmological parameters. Furthermore, the bispectrum yields tighter constraints (by a factor four in $1\sigma$ errors) on almost all model parameters while the degeneracy directions are very similar to the ones of the power spectrum. The increase in sensitivity is most pronounced for the sum of the neutrino masses. Due to the similarity of degeneracies a combination of both analysis is not needed for most parameters. This, however, might be due to the simplified bias description generally adopted in such halo model approaches., Comment: 14 pages, 7 figures

We assume that dark matter is comprised of axion-like particles (ALPs) generated by the realignment mechanism in the post-inflationary scenario. This leads to isocurvature fluctuations with an amplitude of order one for scales comparable to the horizon at the time when the ALP field starts oscillating. The power spectrum of these fluctuations is flat for small wave numbers, extending to scales relevant for cosmological observables. Denoting the relative isocurvature amplitude at $k_*$ = 0.05 Mpc$^{-1}$ by $f_{\rm iso}$, Planck observations of the cosmic microwave background (CMB) yield $f_{\rm iso}$ < 0.31 at the 2$\sigma$-level. This excludes the hypothesis of post-inflationary ALP dark matter with masses $m_{a}$ < 10$^{-20}-$10$^{-16}$ eV, where the range is due to details of the ALP mass-temperature dependence. Future CMB stage IV and 21-cm intensity mapping experiments may improve these limits by 1$-$2 orders of magnitude in $m_{a}$., Comment: 24 pages, 6 figures, 2 tables; minor changes, references added

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

In this work we investigate the environmental dependence of the intrinsic ellipticity correlations in cosmic shear surveys. We use the quadratic and linear alignment model to describe the contributions by spiral and elliptical galaxies, respectively. The density field is in both cases described by a Gaussian random field and ellipticity correlation functions that are conditional on the environment of the galaxies are constructed by sampling random values for the tidal tensor and inertial tensor. The covariance of the Gaussian random process from which the tensor entries are drawn is decomposed by means of a spherical Fourier-Bessel transformation of the density field. The dependence on environment is modelled by the number of positive eigenvalues of the tidal tensor, which allows a differentiation between voids, sheets, filaments and superclusters. We find that elliptical galaxies align strongest in elongated structures such as sheets and filaments with an amplitude almost an order of magnitude higher compared to the alignment in clusters or voids. In contrast to this, spiral galaxies align equally strong in all environments. Cross-alignments between different environments are smaller than the respective auto-correlations subject to the Cauchy-Schwarz inequality which is an effective bound on their amplitude. Furthermore, we find misalignment between inertial and tidal tensor to be stronger in anisotropic regions compared to clusters or voids. While the imprint of weak lensing on galaxy ellipticities is agnostic about the environment, using environment information can help to distinguish between lensing and the intrinsic alignment signal.

Observations of the large-scale structure (LSS) implicitly assume an ideal FLRW observer with the ambient structure having no influence on the observer. However, due to correlations in the LSS, cosmological observables are dependent on the position of an observer. We investigate this influence in full generality for a weakly non-Gaussian random field, for which we derive expressions for angular spectra of large-scale structure observables conditional on a property of the large-scale structure that is typical for the observer's location. As an application, we then apply to the formalism to angular spectra of the weak gravitational lensing effect and provide numerical estimates for the resulting change on the spectra using linear structure formation. For angular weak lensing spectra we find the effect to be of order of a few percent, for instance we estimate for an overdensity of $\delta =0.5$ and multipoles up to $\ell=100$ the change in the weak lensing spectra to be approximately 4 percent. We show that without accounting for correlation between the density at observer's location and the weak gravitational lensing spectra, the values of the parameters $\Omega_m$ and $\sigma_8$ are underestimated by a few percent. Thus, this effect will be important when analysing data from future surveys such as Euclid, which aim at the percent-level precision. The effect is difficult to capture in simulations, as estimates of the number of numerical simulations necessary to quantify the effect are high., Comment: 13 pages, 7 figures, figure added

Intrinsic alignments of galaxies are recognised as one of the most important systematic in weak lensing surveys on small angular scales. In this paper we investigate ellipticity correlation functions that are measured separately on elliptical and spiral galaxies, for which we assume the generic alignment mechanisms based on tidal shearing and tidal torquing, respectively. Including morphological information allows to find linear combinations of measured ellipticity correlation functions which suppress the gravitational lensing signal completely or which show a strongly boosted gravitational lensing signal relative to intrinsic alignments. Specifically, we find that $(i)$ intrinsic alignment spectra can be measured in a model-independent way at a significance of $\Sigma\simeq 60$ with a wide-angle tomographic survey such as Euclid's, $(ii)$ intrinsic alignment model parameters can be determined at percent-level precision, $(iii)$ this measurement is not impeded by misclassifying galaxies and assuming a wrong alignment model, $(iv)$ parameter estimation from a cleaned weak lensing spectrum is possible with almost no bias and $(v)$ the misclassification would not strongly impact parameter estimation from the boosted weak lensing spectrum.

Future observations of the large-scale structure have the potential to investigate cosmological models with a high degree of complexity, including the properties of gravity on large scales, the presence of a complicated dark energy component, and the addition of neutrinos changing structures on small scales. Here we study Horndeski theories of gravity, the most general minimally coupled scalar-tensor theories of second order. While the cosmological background evolution can be described by an effective equation of state, the perturbations are characterised by four free functions of time. We consider a specific parametrisation of these functions tracing the dark energy component. The likelihood of the full parameter set resulting from combining cosmic microwave background primary anisotropies including their gravitational lensing signal, tomographic angular galaxy clustering and weak cosmic shear, together with all possible non-vanishing cross-correlations is evaluated; both with the Fisher-formalism as well as without the assumption of a specific functional form of the posterior through Monte-Carlo Markov-chains (MCMCs). Our results show that even complex cosmological models can be constrained and could exclude variations of the effective Newtonian gravitational coupling larger than 10\% over the age of the Universe. In particular, we confirm strong correlations between parameter groups. Furthermore, we find that the expected contours from MCMC are significantly larger than those from the Fisher analysis even with the vast amount of signal provided by stage IV experiments, illustrating the importance of a proper treatment of non-Gaussian likelihoods and the high level of precision needed for unlocking the sensitivity on gravitational parameters., Comment: 15 pages, 5 figures, in press, bibliography and figures updated

When the gravitational lensing of the large-scale structure is calculated from a cosmological model a few assumptions enter: $(i)$ one assumes that the photons follow unperturbed background geodesics, which is usually referred to as the Born-approximation, $(ii)$ the lenses move slowly, $(iii)$ the source-redshift distribution is evaluated relative to the background quantities and $(iv)$ the lensing effect is linear in the gravitational potential. Even though these approximations are small individually they could sum up, especially since they include local effects such as the Sachs-Wolfe and peculiar motion, but also non-local ones like the Born-approximation and the integrated Sachs-Wolfe effect. In this work we will address all points mentioned and perturbatively calculate the effect on a tomographic cosmic shear power spectrum of each effect individually as well as all cross-correlations. Our findings show that each effect is at least 4 to 5 orders of magnitude below the leading order lensing signal. Finally we sum up all effects to estimate the overall impact on parameter estimation by a future cosmological weak lensing survey such as Euclid in a $w$CDM cosmology with parametrisation $\Omega_\mathrm{m}$, $\sigma_8$,$n_\mathrm{s}$, $h$, $w_0$ and $w_\mathrm{a}$, using 5 tomographic bins. We consistently find a parameter bias of $10^{-5}$, which is therefore completely negligible for all practical purposes, confirming that other effects such as intrinsic alignments and magnification bias will be the dominant systematic source in future surveys.

Traditionally the spherical collapse of objects is studied with respect to a uniform background density, yielding the critical over-density $\delta_\mathrm{c}$ as key ingredient to the mass function of virialized objects. Here we investigate the shear and rotation acting on a peak in a Gaussian random field. By assuming that collapsing objects mainly form at those peaks, we use this shear and rotation as external effects changing the dynamics of the spherical collapse, which is described by the Raychaudhuri equation. We therefore assume that the shear and rotation have no additional dynamics on top of their cosmological evolution and thus only appear as inhomogeneities in the differential equation., Comment: 8 pages, 5 figures, MNRAS accepted

We extend a previous work by Reischke et al., 2016 by studying the effects of tidal shear on clustering dark energy models within the framework of the extended spherical collapse model and using the Zel'dovich approximation. As in previous works on clustering dark energy, we assumed a vanishing effective sound speed describing the perturbations in dark energy models. To be self-consistent, our treatment is valid only on linear scales since we do not intend to introduce any heuristic models. This approach makes the linear overdensity $\delta_{\rm c}$ mass dependent and similarly to the case of smooth dark energy, its effects are predominant at small masses and redshifts. Tidal shear has effects of the order of percent or less, regardless of the model and preserves a well known feature of clustering dark energy: When dark energy perturbations are included, the models resemble better the $\Lambda$CDM evolution of perturbations. We also showed that effects on the comoving number density of halos are small and qualitatively and quantitatively in agreement with what previously found for smooth dark energy models., Comment: 9 pages, 2 figures. Accepted for publications on MNRAS

The likelihood function for cosmological parameters, given by e.g. weak lensing shear measurements, depends on contributions to the covariance induced by the nonlinear evolution of the cosmic web. As nonlinear clustering to date has only been described by numerical $N$-body simulations in a reliable and sufficiently precise way, the necessary computational costs for estimating those covariances at different points in parameter space are tremendous. In this work we describe the change of the matter covariance and of the weak lensing covariance matrix as a function of cosmological parameters by constructing a suitable basis, where we model the contribution to the covariance from nonlinear structure formation using Eulerian perturbation theory at third order. We show that our formalism is capable of dealing with large matrices and reproduces expected degeneracies and scaling with cosmological parameters in a reliable way. Comparing our analytical results to numerical simulations we find that the method describes the variation of the covariance matrix found in the SUNGLASS weak lensing simulation pipeline within the errors at one-loop and tree-level for the spectrum and the trispectrum, respectively, for multipoles up to $\ell\leq 1300$. We show that it is possible to optimize the sampling of parameter space where numerical simulations should be carried out by minimising interpolation errors and propose a corresponding method to distribute points in parameter space in an economical way., Comment: 10 pages, 6 figures, submitted to MNRAS

We study the spherical collapse model in the presence of external gravitational tidal shear fields for different dark energy scenarios and investigate the impact on the mass function and cluster number counts. While previous studies of the influence of shear and rotation on $\delta_\mathrm{c}$ have been performed with heuristically motivated models, we try to avoid this model dependence and sample the external tidal shear values directly from the statistics of the underlying linearly evolved density field based on first order Lagrangian perturbation theory. Within this self-consistent approach, in the sense that we restrict our treatment to scales where linear theory is still applicable, only fluctuations larger than the scale of the considered objects are included into the sampling process which naturally introduces a mass dependence of $\delta_\mathrm{c}$. We find that shear effects are predominant for smaller objects and at lower redshifts, i. e. the effect on $\delta_\mathrm{c}$ is at or below the percent level for the $\Lambda$CDM model. For dark energy models we also find small but noticeable differences, similar to $\Lambda$CDM. The virial overdensity $\Delta_\mathrm{V}$ is nearly unaffected by the external shear. The now mass dependent $\delta_c$ is used to evaluate the mass function for different dark energy scenarios and afterwards to predict cluster number counts, which indicate that ignoring the shear contribution can lead to biases of the order of $1\sigma$ in the estimation of cosmological parameters like $\Omega_\mathrm{m}$, $\sigma_8$ or $w$., Comment: 12 pages, 10 figures, submitted to MNRAS

Forecasts in cosmology, both with Monte-Carlo Markov-chain methods and with the Fisher matrix formalism, depend on the choice of the fiducial model because both the signal strength of any observable as well as the model nonlinearities linking observables to cosmological parameters vary in the general case. In this paper we propose a method for extrapolating Fisher-forecasts across the space of cosmological parameters by constructing a suitable ba- sis. We demonstrate the validity of our method with constraints on a standard dark energy model extrapolated from a {\Lambda}CDM-model, as can be expected from 2-bin weak lensing to- mography with a Euclid-like survey, in the parameter pairs $(\Omega_\text{m},\sigma_8)$, $(\Omega_\text{m}, w_0)$ and $(w_0, w_\text{a})$. Our numerical results include very accurate extrapolations across a wide range of cosmo- logical parameters in terms of shape, size and orientation of the parameter likelihood, and a decomposition of the change of the likelihood contours into modes, which are straightforward to interpret in a geometrical way. We find that in particular the variation of the dark energy figure of merit is well captured by our formalism., Comment: 9 pages, 3+1 figures, reference and discussion added

The statistics of peaks in weak gravitational lensing maps is a promising technique to constrain cosmological parameters in present and future surveys. Here we investigate its power when using general extreme value statistics which is very sensitive to the exponential tail of the halo mass function. To this end, we use an analytic method to quantify the number of weak lensing peaks caused by galaxy clusters, large-scale structures and observational noise. Doing so, we further improve the method in the regime of high signal-to-noise ratios dominated by non-linear structures by accounting for the embedding of those counts into the surrounding shear caused by large scale structures. We derive the extreme value and order statistics for both over-densities (positive peaks) and under-densities (negative peaks) and provide an optimized criterion to split a wide field survey into sub-fields in order to sample the distribution of extreme values such that the expected objects causing the largest signals are mostly due to galaxy clusters. We find good agreement of our model predictions with a ray-tracing $N$-body simulation. For a Euclid-like survey, we find tight constraints on $\sigma_8$ and $\Omega_\text{m}$ with relative uncertainties of $\sim 10^{-3}$. In contrast, the equation of state parameter $w_0$ can be constrained only with a $10\%$ level, and $w_\text{a}$ is out of reach even if we include redshift information., Comment: 14 pages, 11 figures, Accepted for publication in MNRAS, one figure added, little changes in the manuscript, added references