arXiv subjects

Fabien Lacasa

Publications and source records attributed to Fabien Lacasa.

At least 19 recordsLinked to original sources

arXiv2024

Fast and spurious: a robust determination of our peculiar velocity with future galaxy surveys

To date, the most precise measurement of the observer's peculiar velocity comes from the dipole in the Cosmic Microwave Background (CMB). This velocity also generates a dipole in the source number counts, whose amplitude is governed not only by the observer velocity, but also by specific properties of the sources, that are difficult to determine precisely. Quantitative studies of the source number counts currently give dipoles which are reasonably well aligned with the CMB dipole, but with a significantly larger amplitude than that of the CMB dipole. In this work, we explore an alternative way of measuring the observer velocity from the source number counts, using correlations between neighboring spherical harmonic coefficients, induced by the velocity. We show that these correlations contain both a term sensitive to the source properties and another one directly given by the observer velocity. We explore the potential of a Euclid-like survey to directly measure this second contribution, independently of the characteristics of the population of sources. We find that the method can reach a precision of 4%, corresponding to a detection significance of 24 sigma, on the observer velocity. This will settle with precision the present "dipole tension".

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arXiv2023

Statistical effects of the observer's peculiar velocity on source number counts

The velocity of the Sun with respect to the cosmic microwave background (CMB) can be extracted from the CMB dipole, provided its intrinsic dipole is assumed to be small in comparison. This interpretation is consistent, within fairly large error bars, with the measurement of the correlations between neighboring CMB multipoles induced by the velocity of the observer, which effectively breaks isotropy. In contrast, the source number count dipole was reported to privilege a velocity of the observer with an amplitude which is about twice as large as the one extracted from the entirely kinematic interpretation of the CMB dipole, with error bars which indicate a more and more significant tension. In this work, we study the effect of the peculiar velocity of the observer on correlations of nearby multipoles in the source number counts. We provide an unbiased estimator for the kinetic dipole amplitude, which is proportional to the peculiar velocity of the observer and we compute the expected signal to noise ratio. Near future experiments can achieve better than 5$\%$ constraints on the velocity of the Sun with our estimator.

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arXiv2023

Efficient computation of the super-sample covariance for stage IV galaxy surveys

Super-sample covariance (SSC) is an important effect for cosmological analyses that use the deep structure of the cosmic web; it may, however, be nontrivial to include it practically in a pipeline. We solve this difficulty by presenting a formula for the precision (inverse covariance) matrix and show applications to update likelihood or Fisher forecast pipelines. The formula has several advantages in terms of speed, reliability, stability, and ease of implementation. We present an analytical application to show the formal equivalence between three approaches to SSC: (i) at the usual covariance level, (ii) at the likelihood level, and (iii) with a quadratic estimator. We then present an application of this computationally efficient framework for studying the impact of inaccurate modelling of SSC responses for cosmological constraints from stage IV surveys. We find that a weak-lensing-only analysis is very sensitive to inaccurate modelling of the scale dependence of the response, which needs to be calibrated at the $\sim15\%$ level. The sensitivity to this scale dependence is less severe for the joint weak-lensing and galaxy clustering analysis (also known as 3x2pt). Nevertheless, we find that both the amplitude and scale-dependence of the responses have to be calibrated at better than 30\%.

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arXiv2022

Cosmology in the non-linear regime : the small scale miracle

Interest rises to exploit the full shape information of the galaxy power spectrum, as well as pushing analyses to smaller non-linear scales. Here I use the halo model to quantify the information content in the tomographic angular power spectrum of galaxies, for future high resolution surveys : Euclid and SKA2. I study how this information varies as a function of the scale cut applied, either with angular cut $\ell_{max}$ or physical cut kmax. For this, I use analytical covariances with the most complete census of non-Gaussian terms, which proves critical. I find that the Fisher information on most cosmological and astrophysical parameters follows a striking behaviour. Beyond the perturbative regime we first get decreasing returns : the information keeps rising but the slope slows down until reaching a saturation. The location of this plateau is a bit beyond the reach of current modeling methods : k $\sim$ 2 Mpc$^{-1}$ and slightly depends on the parameter and redshift bin considered. I explain the origin of this plateau, which is due to non-linear effects both on the power spectrum, and more importantly on non-Gaussian covariance terms. Then, pushing further we see the information rising again in the highly non-linear regime, with a steep slope. This is the small scale miracle, for which I give interpretation and discuss the properties. Hints are shown that this information should be disentanglable from the astrophysical content, and could improve Dark Energy constraints. Finally, more hints are shown that high order statistics may yield significant improvements over the power spectrum in this regime, with the improvements increasing with kmax. Data and notebooks reproducing all plots and results will be made available at \url{https://github.com/fabienlacasa/SmallScaleMiracle}

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arXiv2021

A new estimator for gravitational lensing using galaxy and intensity mapping surveys

We introduce the Galaxy Intensity Mapping cross-COrrelation estimator (GIMCO), which is a new tomographic estimator for the gravitational lensing potential, based on a combination of intensity mapping (IM) and galaxy number counts. The estimator can be written schematically as IM$(z_f)\times$galaxy$(z_b)$ $-$ galaxy$(z_f)\times$IM$(z_b)$ for a pair of distinct redshifts $(z_f,z_b)$; this combination allows to greatly reduce the contamination by density-density correlations, thus isolating the lensing signal. As an estimator constructed only from cross-correlations, it is additionally less susceptible to systematic effects. We show that the new estimator strongly suppresses cosmic variance and consequently improves the signal-to-noise ratio (SNR) for the detection of lensing, especially on linear scales and intermediate redshifts. %This makes it particularly valuable for future studies of dark energy and modified gravity. For cosmic variance dominated surveys, the SNR of our estimator is a factor 30 larger than the SNR obtained from the correlation of galaxy number counts only. Shot noise and interferometer noise reduce the SNR. For the specific example of the Dark Energy Survey (DES) cross-correlated with the Hydrogen Intensity mapping and Real time Analysis eXperiment (HIRAX), the SNR is around 4, whereas for Euclid cross-correlated with HIRAX it reaches 52. This corresponds to an improvement of a factor 4-5 compared to the SNR from DES alone. For Euclid cross-correlated with HIRAX the improvement with respect to Euclid alone strongly depends on the redshift. We find that the improvement is particularly important for redshifts below 1.6, where it reaches a factor of 5. This makes our estimator especially valuable to test dark energy and modified gravity, that are expected to leave an impact at low and intermediate redshifts.

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arXiv2020

Breaking degeneracies with the Sunyaev-Zeldovich full bispectrum

Non-Gaussian (NG) statistics of the thermal Sunyaev-Zeldovich (tSZ) effect carry significant information which is not contained in the power spectrum. Here, we perform a joint Fisher analysis of the tSZ power spectrum and bispectrum to verify how much the full bispectrum can contribute to improve parameter constraints. We go beyond similar studies of this kind in several respects: first of all, we include the complete power spectrum and bispectrum (auto- and cross-) covariance in the analysis, computing all NG contributions; furthermore we consider a multi-component foreground scenario and model the effects of component separation in the forecasts; finally, we consider an extended set of both cosmological and intra-cluster medium parameters. We show that the tSZ bispectrum is very efficient at breaking parameter degeneracies, making it able to produce even stronger cosmological constraints than the tSZ power spectrum: e.g. the standard deviation on $σ_8$ shrinks from $σ^\text{PS}(σ_8)=0.35$ to $σ^\text{BS}(σ_8)=0.065$ when we consider a multi-parameter analysis. We find that this is mostly due to the different response of separate triangle types (e.g. equilateral and squeezed) to changes in model parameters. While weak, this shape dependence is clearly non-negligible for cosmological parameters, and it is even stronger, as expected, for intra-cluster medium parameters.

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arXiv2020

Tomographic weak lensing bispectrum: a thorough analysis towards the next generation of galaxy surveys

We address key points for an efficient implementation of likelihood codes for modern weak lensing large-scale structure surveys. Specifically, we focus on the joint weak lensing convergence power spectrum-bispectrum probe and we tackle the numerical challenges required by a realistic analysis. Under the assumption of (multivariate) Gaussian likelihoods, we have developed a high performance code that allows highly parallelised prediction of the binned tomographic observables and of their joint non-Gaussian covariance matrix accounting for terms up to the 6-point correlation function and super-sample effects. This performance allows us to qualitatively address several interesting scientific questions. We find that the bispectrum provides an improvement in terms of signal-to-noise ratio (S/N) of about 10% on top of the power spectrum, making it a non-negligible source of information for future surveys. Furthermore, we are capable to test the impact of theoretical uncertainties in the halo model used to build our observables; with presently allowed variations we conclude that the impact is negligible on the S/N. Finally, we consider data compression possibilities to optimise future analyses of the weak lensing bispectrum. We find that, ignoring systematics, 5 equipopulated redshift bins are enough to recover the information content of a Euclid-like survey, with negligible improvement when increasing to 10 bins. We also explore principal component analysis and dependence on the triangle shapes as ways to reduce the numerical complexity of the problem.

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arXiv2020

Modelling the matter bispectrum at small scales in modified gravity

Future large-scale structure surveys will measure three-point statistics with high statistical significance. This will offer significant improvements on our understanding of gravity, provided we can model these statistics accurately. We assess the performance of several schemes for theoretical modelling of the matter bispectrum, including halo-model based approaches and fitting formulae. We compare the model predictions against N-body simulations, considering scales up to $k_{\rm max} = 4 h/{\rm Mpc}$, well into non-linear regime of structure formation. Focusing on the equilateral configuration, we conduct this analysis for three theories of gravity: general relativity, $f(R)$ gravity, and the DGP braneworld model. Additionally, we compute the lensing convergence bispectrum for these models. We find that all current modelling prescriptions in modified gravity, in particular for theories with scale-dependent linear growth, fail to attain the accuracy required by the precision of the Stage IV surveys such as \emph{Euclid}. Among these models, we find that a halo-model corrected fitting formula achieves the best overall performance.

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arXiv2020

The impact of braiding covariance and in-survey covariance on next-generation galaxy surveys

As galaxy surveys become more precise and push to smaller scales, the need for accurate covariances beyond the classical Gaussian formula becomes more acute. Here, I investigate the analytical implementation and impact of non-Gaussian covariance terms that I previously derived for galaxy clustering. Braiding covariance is such a class of terms and it gets contribution both from in-survey and super-survey modes. I present an approximation for braiding covariance which speeds up the numerical computation. I show that including braiding covariance is a necessary condition for including other non-Gaussian terms: the in-survey 2-, 3- and 4-halo covariance, which yield covariance matrices with negative eigenvalues if considered on their own. I then quantify the impact on parameter constraints, with forecasts for a Euclid-like survey. Compared to the Gaussian case, braiding and in-survey covariances significantly increase the error bars on cosmological parameters, in particular by 50% for w. The Halo Occupation Distribution (HOD) error bars are also affected between 12% and 39%. Accounting for super-sample covariance (SSC) also increases parameter errors, by 90% for w and between 7% and 64% for HOD. In total, non-Gaussianity increases the error bar on w by 120% (between 15% and 80% for other cosmological parameters), and the error bars on HOD parameters between 17% and 85%. Accounting for the 1-halo trispectrum term on top of SSC is not sufficient for capturing the full non-Gaussian impact: braiding and the rest of in-survey covariance have to be accounted for. Finally, I discuss why the inclusion of non-Gaussianity generally eases up parameter degeneracies, making cosmological constraints more robust to astrophysical uncertainties. The data and a Python notebook reproducing the results and plots of the article are available at \url{https://github.com/fabienlacasa/BraidingArticle}. [Abridged]

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arXiv2019

Fast and easy super-sample covariance of large scale structure observables

We present a numerically cheap approximation to super-sample covariance (SSC) of large scale structure cosmological probes, first in the case of angular power spectra. It necessitates no new elements besides those used for the prediction of the considered probes, thus relieving analysis pipelines from having to develop a full SSC modeling, and reducing the computational load. The approximation is asymptotically exact for fine redshift bins $Δz \rightarrow 0$. We furthermore show how it can be implemented at the level of a Gaussian likelihood or a Fisher matrix forecast, as a fast correction to the Gaussian case without needing to build large covariance matrices. Numerical application to a Euclid-like survey show that, compared to a full SSC computation, the approximation recovers nicely the signal-to-noise ratio as well as Fisher forecasts on cosmological parameters of the $w$CDM cosmological model. Moreover it allows for a fast prediction of which parameters are going to be the most affected by SSC and at which level. In the case of photometric galaxy clustering with Euclid-like specifications, we find that $σ_8$, $n_s$ and the dark energy equation of state $w$ are particularly heavily affected. We finally show how to generalize the approximation for probes other than angular spectra (correlation functions, number counts and bispectra), and at the likelihood level, allowing for the latter to be non-Gaussian if needs be. We release publicly a Python module allowing to implement the SSC approximation, as well as a notebook reproducing the plots of the article, at https://github.com/fabienlacasa/PySSC

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arXiv2018

Secondary CMB anisotropies from magnetized halos --I: Power spectra of the Faraday rotation angle and conversion rate

Magnetized plasmas within halos of galaxies leave their footprint on the polarized anisotropies of the cosmic microwave background. The two dominant effects for astrophysical halos are Faraday rotation generating rotation of the plane of linear polarization, and Faraday conversion inducing a leakage from linear polarization to circular polarization. We revisit these sources of secondary anisotropies by computing the angular power spectra of the Faraday rotation angle and of the Faraday conversion rate by the large scale structures. To this end, we use the halo model and we pay special attention to the impact of magnetic field projections. Assuming magnetic fields of halos to be uncorrelated, we found a vanishing 2-halo term, and angular power spectra peaking at multipoles $\ell\sim10^4$. The Faraday rotation angle is dominated by the contribution of thermal electrons. For the Faraday conversion rate, we found that both thermal electrons and relativistic, non-thermal electrons contribute equally in the most optimistic case for the density and Lorentz factor of relativistic electrons, while in more pessimistic cases the thermal electrons give the dominant contribution. Assuming the magnetic field to be independent of the halo mass, the angular power spectra for both effects roughly scale with the amplitude of matter perturbations as $\simσ_8^3$, and with a very mild dependence with the density of cold dark matter. Introducing a dependence of the magnetic field strength with the halo mass leads to an increase of the scaling with the amplitude of matter fluctuations, up to $\simσ_8^{9.5}$ for Faraday rotation and $\simσ_8^{15}$ for Faraday conversion for a magnetic field strength scaling linearly with the halo mass.

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arXiv2018

Covariance of the galaxy angular power spectrum with the halo model

As the determination of density fluctuations becomes more precise with larger surveys, it becomes more important to account for the increased covariance due to the non-linearity of the field. Here I have focussed on the galaxy density, with analytical prediction of the non-Gaussianity using the halo model coupled with standard perturbation theory in real space. I carried out an exact and exhaustive derivation of all tree-level terms of the non-Gaussian covariance of the galaxy $C_\ell$, with the computation developed up to the third order in perturbation theory and local halo bias, including the non-local tidal tensor effect. A diagrammatic method was used to derive the involved galaxy 3D trispectra, including shot-noise contributions. The projection to the angular covariance was derived in all trispectra cases with and without Limber's approximation, with the formulae being of potential interest for other observables than galaxies. The effect of subtracting shot-noise from the measured spectrum is also discussed, and does simplify the covariance, though some non-Gaussian shot-noise terms still remain. I make the link between this complete derivation and partial terms which have been used previously in the literature, including super-sample covariance (SSC). I uncover a wealth of additional terms which were not previously considered, including a whole new class which I dub braiding terms as it contains multipole-mixing kernels. The importance of all these new terms is discussed with analytical arguments. I find that they become comparable to, if not bigger than, SSC if the survey is large or deep enough to probe scales comparable with the matter-radiation equality $k_\mathrm{eq}$. A short self-contained summary of the equations is provided in Section 9 for the busy reader, ready to be implemented numerically for analysis of current and future galaxy surveys.

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arXiv2018

Super-sample covariance approximations and partial sky coverage

Super-sample covariance (SSC) is the dominant source of statistical error on large scale structure (LSS) observables for both current and future galaxy surveys. In this work, we concentrate on the SSC of cluster counts, also known as sample variance, which is particularly useful for the self-calibration of the cluster observable-mass relation; our approach can similarly be applied to other observables, such as galaxy clustering and lensing shear. We first examined the accuracy of two analytical approximations proposed in the literature for the flat sky limit, finding that they are accurate at the 15% and 30-35% level, respectively, for covariances of counts in the same redshift bin. We then developed a harmonic expansion formalism that allows for the prediction of SSC in an arbitrary survey mask geometry, such as large sky areas of current and future surveys. We show analytically and numerically that this formalism recovers the full sky and flat sky limits present in the literature. We then present an efficient numerical implementation of the formalism, which allows fast and easy runs of covariance predictions when the survey mask is modified. We applied our method to a mask that is broadly similar to the Dark Energy Survey footprint, finding a non-negligible negative cross-z covariance, i.e. redshift bins are anti-correlated. We also examined the case of data removal from holes due to, for example bright stars, quality cuts, or systematic removals, and find that this does not have noticeable effects on the structure of the SSC matrix, only rescaling its amplitude by the effective survey area. These advances enable analytical covariances of LSS observables to be computed for current and future galaxy surveys, which cover large areas of the sky where the flat sky approximation fails.

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arXiv2018

Inadequacy of internal covariance estimation for super-sample covariance

We give an analytical interpretation of how subsample-based internal covariance estimators lead to biased estimates of the covariance, due to underestimating the super-sample covariance (SSC). This includes the jackknife and bootstrap methods as estimators for the full survey area, and subsampling as an estimator of the covariance of subsamples. The limitations of the jackknife covariance have been previously presented in the literature because it is effectively a rescaling of the covariance of the subsample area. However we point out that subsampling is also biased, but for a different reason: the subsamples are not independent, and the corresponding lack of power results in SSC underprediction. We develop the formalism in the case of cluster counts that allows the bias of each covariance estimator to be exactly predicted. We find significant effects for a small-scale area or when a low number of subsamples is used, with auto-redshift biases ranging from 0.4% to 15% for subsampling and from 5% to 75% for jackknife covariance estimates. The cross-redshift covariance is even more affected; biases range from 8% to 25% for subsampling and from 50% to 90% for jackknife. Owing to the redshift evolution of the probe, the covariances cannot be debiased by a simple rescaling factor, and an exact debiasing has the same requirements as the full SSC prediction. These results thus disfavour the use of internal covariance estimators on data itself or a single simulation, leaving analytical prediction and simulations suites as possible SSC predictors.

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arXiv2016

Combining cluster number counts and galaxy clustering

The abundance of clusters and the clustering of galaxies are two of the important cosmological probes for current and future large scale surveys of galaxies, such as the Dark Energy Survey. In order to combine them one has to account for the fact that they are not independent quantities, since they probe the same density field. It is important to develop a good understanding of their correlation in order to extract parameter constraints. We present a detailed modelling of the joint covariance matrix between cluster number counts and the galaxy angular power spectrum. We employ the framework of the halo model complemented by a Halo Occupation Distribution model (HOD). We demonstrate the importance of accounting for non-Gaussianity to produce accurate covariance predictions. Indeed, we show that the non-Gaussian covariance becomes dominant at small scales, low redshifts or high cluster masses. We discuss in particular the case of the super-sample covariance (SSC), including the effects of galaxy shot-noise, halo second order bias and non-local bias. We demonstrate that the SSC obeys mathematical inequalities and positivity. Using the joint covariance matrix and a Fisher matrix methodology, we examine the prospects of combining these two probes to constrain cosmological and HOD parameters. We find that the combination indeed results in noticeably better constraints, with improvements of order 20\% on cosmological parameters compared to the best single probe, and even greater improvement on HOD parameters, with reduction of error bars by a factor 1.4-4.8. This happens in particular because the cross-covariance introduces a synergy between the probes on small scales. We conclude that accounting for non-Gaussian effects is required for the joint analysis of these observables in galaxy surveys.

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arXiv2015

Scaling of the 1-halo terms with bias

In the Halo Model, galaxies are hosted by dark matter halos, while the halos themselves are biased tracers of the underlying matter distribution. Measurements of galaxy correlation functions include contributions both from galaxies in different halos, and from galaxies in the same halo (the so-called 1-halo terms). We show that, for highly biased tracers, the 1-halo term of the power spectrum obeys a steep scaling relation in terms of bias. We also show that the 1-halo term of the trispectrum has a steep scaling with bias. The steepness of these scaling relations is such that the 1-halo terms can become key contributions to the $n$-point correlation functions, even at large scales. We interpret these results through analytical arguments and semi-analytical calculations in terms of the statistical properties of halos.

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arXiv2014

Combining cosmological constraints from cluster counts and galaxy clustering

Present and future large scale surveys offer promising probes of cosmology. For example the Dark Energy Survey (DES) is forecast to detect ~300 millions galaxies and thousands clusters up to redshift ~1.3. I here show ongoing work to combine two probes of large scale structure : cluster number counts and galaxy 2-point function (in real or harmonic space). The halo model (coupled to a Halo Occupation Distribution) can be used to model the cross-covariance between these probes, and I introduce a diagrammatic method to compute easily the different terms involved. Furthermore, I compute the joint non-Gaussian likelihood, using the Gram-Charlier series. Then I show how to extend the methods of Bayesian hyperparameters to Poissonian distributions, in a first step to include them in this joint likelihood.

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arXiv2014

Non-Gaussianity and extragalactic foregrounds to the Cosmic Microwave Background

[Abridged] This PhD thesis was defended in September 2013 at Université Paris-Sud, France. It studies the non-Gaussianity (NG) of extragalactic foregrounds to the Cosmic Microwave Background (CMB). This is particularly important for the analysis of CMB data from the Planck satellite, in which I was involved. I studied in particular the extragalactic foregrounds tracing the Large Scale Structure (LSS) of the universe : radio and infrared point-sources and the thermal Sunyaev-Zel'dovich effect (tSZ). The motivations and summary of this thesis cannot be shortened into the length constraints of this abstract and are thus described in an inner abstract and introduction. In a broad summary, this thesis is organised in the following parts : statistics of random variables and fields, spherical analysis in particular of polyspectra, some cosmology (inflation and its NG, CMB, LSS and halo model), extragalactic foregrounds (tSZ, point-sources), and measuring the NG of these foregrounds with Planck. More specifically and in a disorganised manner, the following were most of my contributions in the field : developments on the effect of masking on the angular bispectrum, introduction of an efficient bispectrum representation, derivation of the bispectrum covariance, generation of non-gaussian simulations, projection of 3D Fourier polyspectra onto 2D spherical ones, treatment of shot-noise terms with the halo model, introduction of a diagrammatic formalism for elegant and simple derivation of galaxy polyspectra, halo model description of the bispectrum of the tSZ effect and of the Cosmic Infrared Background (CIB), phenomenological prescription of the NG of clustered sources and corresponding KSW-like estimator, effect of point-sources NG for Planck, measurement of the CIB bispectrum with Planck data, measurement of the tSZ bispectrum with Planck data and cosmological constraints with it.

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