arXiv subjects

Massimo Pietroni

Publications and source records attributed to Massimo Pietroni.

At least 19 recordsLinked to original sources

arXiv2026

Probing nonlinear structure formation beyond $\Lambda$CDM with the LSS bootstrap: a joint power spectrum and bispectrum analysis

We present the first MCMC-derived constraints on the parameters of the Large Scale Structure (LSS) bootstrap, a model-independent framework that captures deviations from $\Lambda$CDM using symmetry arguments alone. Focusing on modifications to the linear growth rate and to the quadratic perturbation-theory kernel -- quantified by the fractional parameters $\varepsilon_f$ and $\varepsilon_{d_{\gamma}}$, respectively -- we carry out a joint analysis of the one-loop galaxy power spectrum and the tree-level bispectrum multipoles within the EFTofLSS, employing the \texttt{PyBird} code extended to implement the bootstrap parametrization. We apply this analysis pipeline to two datasets: the BOSS DR12 LRG sample and the large-volume ``PT Challenge'' simulations. For BOSS, combining the power spectrum with the bispectrum monopole yields $\sim 7\%$ constraints on $\varepsilon_f$ and $\sim 57\%$ constraints on $\varepsilon_{d_{\gamma}}$. For the PT Challenge, whose survey volume is about 100 times larger, we reach $\sim 1\%$ precision on $\varepsilon_f$ and $\sim 25\%$ on $\varepsilon_{d_{\gamma}}$, including the bispectrum quadrupole in the analysis. Our results underscore the complementary roles of $\varepsilon_f$ and $\varepsilon_{d_{\gamma}}$ in separating changes to the background expansion from those affecting nonlinear structure formation, and they show that the LSS bootstrap offers a competitive, model-agnostic method for probing physics beyond $\Lambda$CDM with existing and upcoming galaxy surveys.

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arXiv2026

On the Relation Between Field-Level Posteriors, Correlators, and their Likelihoods

We develop a field-level posterior for cosmological data by marginalizing over initial conditions and noise in a general forward model. While our focus is on large-scale structure data, the results generalize to any weakly non-Gaussian observable. Moreover, the construction is non-perturbative with respect to the forward model and applies equally well to perturbative calculations, simulation-based predictions, and more general effective descriptions. Expanding the FLP around its Gaussian limit, we derive a general expression for the Fisher matrix and reorganize the field-level information into contributions associated with the connected correlators of the evolved field. This makes explicit which terms are captured by likelihood analyses based on the power spectrum, the bispectrum, or finite sets of summary statistics, and which are lost under compression. We recover the standard Gaussian-covariance result for the power spectrum, show that the Gaussian bispectrum likelihood reproduces the corresponding field-level contribution, and show how cross-covariances among summaries progressively reconstruct more of the full field-level information. As an application to the BAO scale, we show how the field contains all the information required for its optimal reconstruction in the presence of noise, and identify the contributions in the FLP needed to attain this limit. We also show that the reconstruction of the initial field arises naturally as a byproduct of our approach, yielding the optimal estimate of the initial conditions given the data and the noise. Our results provide a unified framework to compare field-level and correlator-based inference, to quantify the information loss induced by compression, and to explore the role of stochasticity.

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arXiv2026

(1+1)-Dimensional Schr\"odinger-Poisson equation with contact interaction

We investigate the role of contact interactions in the dynamics of fuzzy dark matter (FDM) modeled through the Schr\"odinger-Poisson equation in one spatial dimension. While the $\Lambda$CDM paradigm successfully explains structure formation on large scales, its small-scale predictions remain in tension with observations. FDM offers an alternative framework, where local self-interactions can further influence the formation and evolution of structures. We explore both attractive and repulsive contact interactions in static and expanding backgrounds. Using numerical simulations, we examine their impact on three key scenarios: the properties of the lowest-energy stationary solution, the relaxation of localized initial states, and the gravitational collapse of nonlocalized states. Our results show that contact interactions modify the density profile of the stationary solution and affect the onset of characteristic stages of gravitational collapse, particularly the shell-crossing event. In the (1+1) model, we confirm that relaxation does not converge to the lowest-energy stationary solution, even when local self-interactions are included. Taken together, local self-interactions play a relevant role in shaping the nonlinear dynamics of FDM and motivate further studies in higher-dimensional and cosmologically realistic settings.

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arXiv2025

Renormalized Perturbation Theory at Field-level: the LSS bootstrap in GridSPT

We present a first step toward field-level cosmological inference beyond the standard $\Lambda$CDM model, focusing on optimizing precision tests in the nonlinear regime of large-scale structure (LSS). As an illustrative case, we study the model-independent ``bootstrap'' coefficient of the second-order perturbation theory (PT) kernel for matter in real space, which we use as a proxy for new physics effects in the nonlinear sector. We discuss in details the ultraviolet (UV) cutoff dependence induced by discretizing fields on a grid, which requires proper renormalization to eliminate grid artifacts. We formulate a Wilsonian perturbative framework in which the evolution from a UV theory defined at a high cutoff $\Lambda_\text{uv}$ down to lower cutoffs is computed analytically, even beyond the validity of a derivative expansion. Within this framework, we develop an extended version of the GridSPT code incorporating the bootstrap parameterization and demonstrate how cutoff-independent predictions can be achieved through the inclusion of appropriate counterterms. We validate our approach at third- and fifth-order in PT, emphasizing the importance of higher-derivative contributions for unbiased parameter extraction. Our framework is readily extendable to biased tracers and redshift-space distortions.

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arXiv2024

Constraints on dark energy and modified gravity from the BOSS Full-Shape and DESI BAO data

We constrain dark energy and modified gravity within the effective field theory of dark energy framework using the full-shape BOSS galaxy power spectrum, combined with Planck cosmic microwave background (CMB) data and recent baryon acoustic oscillations (BAO) measurements from DESI. Specifically, we focus on a varying braiding parameter $\alpha_{\rm B}$, a running of the ``effective'' Planck mass $\alpha_{\rm M}$, and a constant dark energy equation of state $w$. The analysis is performed with two of these parameters at a time, including all the other standard cosmological parameters and marginalizing over bias and nuisance parameters. The full-shape galaxy power spectrum is modeled using the effective field theory of large-scale structure up to 1-loop order in perturbation theory. We find that the CMB data is most sensitive to $\alpha_{\rm B}$, and that adding large-scale structure information only slightly changes the parameter constraints. However, the large-scale structure data significantly improve the bounds on $\alpha_{\rm M}$ and $w$ by a factor of two. This improvement is driven by background information contained in the BAO, which breaks the degeneracy with $H_0$ in the CMB. We confirm this by comparing the BOSS full-shape information with BOSS BAO, finding no significant differences. This is likely to change with future high-precision full-shape data from Euclid and DESI however, to which the pipeline developed here is immediately applicable.

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arXiv2024

Bootstrapping Lagrangian Perturbation Theory for the Large Scale Structure

We develop a model-independent approach to lagrangian perturbation theory for the large scale structure of the universe. We focus on the displacement field for dark matter particles, and derive its most general structure without assuming a specific form for the equations of motion, but implementing a set of general requirements based on symmetry principles and consistency with the perturbative approach. We present explicit results up to sixth order, and provide an algorithmic procedure for arbitrarily higher orders. The resulting displacement field is expressed as an expansion in operators built up from the linear density field, with time-dependent coefficients that can be obtained, in a specific model, by solving ordinary differential equations. The derived structure is general enough to cover a wide spectrum of models beyond $Λ$CDM, including modified gravity scenarios of the Hordenski type and models with multiple dark matter species. This work is a first step towards a complete model-independent lagrangian forward model, to be employed in cosmological analyses with power spectrum and bispectrum, other summary statistics, and field-level inference.

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arXiv2024

Constraining Primordial Non-Gaussianity from Large Scale Structure with the Wavelet Scattering Transform

We investigate the Wavelet Scattering Transform (WST) as a tool for the study of Primordial non-Gaussianity (PNG) in Large Scale Structure (LSS), and compare its performance with that achievable via a joint analysis with power spectrum and bispectrum (P+B). We consider the three main primordial bispectrum shapes - local, equilateral and orthogonal - and produce Fisher forecast for the corresponding fNL amplitude parameters, jointly with standard cosmological parameters. We analyze simulations from the publicly available "Quijote" and "Quijote-png" N-body suites, studying both the dark matter and halo fields. We find that the WST outperforms the power spectrum alone on all parameters, both on the fNL's and on cosmological ones. In particular, on fNL_loc for halos, the improvement is about 27%. When B is combined with P, halo constraints from WST are weaker for fNL_loc (at ~ 15% level), but stronger for fNL_eq (~ 25%) and fNL_ortho (~ 28%). Our results show that WST, both alone and in combination with P+B, can improve the extraction of information on PNG from LSS data over the one attainable by a standard P+B analysis. Moreover, we identify a class of WST in which the origin of the extra information on PNG can be cleanly isolated.

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arXiv2023

Improving precision and accuracy in cosmology with model-independent spectrum and bispectrum

A new and promising avenue was recently developed for analyzing large-scale structure data with a model-independent approach, in which the linear power spectrum shape is parametrized with a large number of freely varying wavebands rather than by assuming specific cosmological models. We call this method FreePower. Here we show, using a Fisher matrix approach, that precision of this method for the case of the one-loop power spectrum is greatly improved with the inclusion of the tree-level bispectrum. We also show that accuracy can be similarly improved by employing perturbation theory kernels whose structure is entirely determined by symmetries instead of evolution equations valid in particular models (like in the usual Einstein-deSitter approximation). The main result is that with the Euclid survey one can precisely measure the Hubble function, distance and ($k$-independent) growth rate $f(z)$ in seven redshift bins in the range $z\in [0.6,\, 2.0]$. The typical errors for the lowest $z$bins are around 1\% (for $H$), 0.5--1\% (for $D$), and 1--3\% (for $f$). The use of general perturbation theory allows us, for the first time, to study constraints on the nonlinear kernels of cosmological perturbations, that is, beyond the linear growth factor, showing that they can be probed at the 10--20\% level. We find that the combination of spectrum and bispectrum is particularly effective in constraining the perturbation parameters, both at linear and quadratic order.

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arXiv2023

Constraints on modified gravity from the BOSS galaxy survey

We develop a pipeline to set new constraints on scale-independent modified gravity, from the galaxy power spectrum in redshift space of BOSS DR12. The latter is modelled using the effective field theory of large-scale structure up to 1-loop order in perturbation theory. We test our pipeline on synthetic and simulated data, to assess systematic biases on the inferred cosmological parameters due to marginalization and theoretical errors, and we apply it to the normal branch of the DGP model with a $Λ$CDM background. When applied to synthetic data and cosmological simulations, we observe biased posteriors due to the strong degeneracy between the nDGP parameter $Ω_{\rm rc}$ and the primordial amplitude of fluctuations $A_s$. Fixing the latter to the Planck central value, we obtain a posterior distribution with $Ω_{\rm rc}\lesssim 0.65$ at 95$\%$ C.L., under the assumption of a flat prior on $\log_{10} Ω_{\rm rc}$. This upper bound, however, depends strongly on the prior on $Ω_{\rm rc}$. To alleviate this effect, we provide an upper bound based on the Bayes factor between the nDGP model and $Λ$CDM model, which gives $Ω_{\rm rc}\lesssim 0.2$ at 95$\%$ C.L..

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arXiv2022

Fisher matrix for the one-loop galaxy power spectrum: measuring expansion and growth rates without assuming a cosmological model

We introduce a methodology to extend the Fisher matrix forecasts to mildly non-linear scales without the need of selecting a cosmological model. We make use of standard non-linear perturbation theory for biased tracers complemented by counterterms, and assume that the cosmological distances can be measured accurately with standard candles. Instead of choosing a specific model, we parametrize the linear power spectrum and the growth rate in several $k$ and $z$ bins. We show that one can then obtain model-independent constraints of the expansion rate $E(z)=H(z)/H_0$ and the growth rate $f(k,z)$, besides the bias functions. We apply the technique to both Euclid and DESI public specifications in the range $0.6\le z \le 1.8$ and show that the gain in precision when going from $k_{\rm max} = 0.1$ to $0.2\,h$/Mpc is around two- to threefold, while it reaches four- to ninefold when extending to $k_{\rm max} = 0.3\,h$/Mpc. In absolute terms, with $k_{\rm max}=0.2\,h/$Mpc, one can reach high precision on $E(z)$ at each $z$-shell: 8-10% for DESI with $Δz=0.1$, 5-6% for Euclid with $Δz=0.2-0.3$. This improves to 1-2% if the growth rate $f$ is taken to be $k$-independent. The growth rate itself has in general much weaker constraints, unless assumed to be $k$-independent, in which case the gain is similar to the one for $E(z)$ and uncertainties around 5-15% can be reached at each $z$-bin. We also discuss how neglecting the non-linear corrections can have a large effect on the constraints even for $k_{\rm max}=0.1\,h/$Mpc, unless one has independent strong prior information on the non-linear parameters.

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arXiv2021

The Large Scale Structure Bootstrap: perturbation theory and bias expansion from symmetries

We investigate the role played by symmetries in the perturbative expansion of the large-scale structure. In particular, we establish which of the coefficients of the perturbation theory kernels are dictated by symmetries and which not. Up to third order in perturbations, for the dark matter density contrast (and for the dark matter velocity) only three coefficients are not fixed by symmetries and depend on the particular cosmology. For generic biased tracers, where number/mass and momentum conservation cannot be imposed in general, this number rises to seven in agreement with other bias expansions discussed in the literature. A crucial role in our analysis is provided by extended Galilean invariance, which follows from diffeomorphism invariance in the non-relativistic limit. We identify a full hierarchy of extended Galilean invariance constraints, which fix the analytic structure of the perturbation theory kernels as the sums of an increasing number of external momenta vanish. Our approach is especially relevant for non-standard models that respect the same symmetries as $Λ$CDM and where perturbation theory at higher orders has not been exhaustively explored, such as dark energy and modified gravity scenarios. In this context, our results can be used to systematically extend the bias expansion to higher orders and set up model independent analyses.

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arXiv2021

One-Dimensional Fuzzy Dark Matter Models: Structure Growth and Asymptotic Dynamics

This paper investigates the feasibility of simulating Fuzzy Dark Matter (FDM) with a reduced number of spatial dimensions. Our aim is to set up a realistic, yet numerically inexpensive, toy model in $(1+1)$-dimensional space time, that - under well controlled system conditions - is capable of realizing important aspects of the full-fledged $(3+1)$-FDM phenomenology by means of one-dimensional analogues. Based on the coupled, nonlinear and nonlocal $(3+1)$-Schrödinger-Poisson equation under periodic boundary conditions, we derive two distinct one-dimensional models that differ in their transversal matter distribution and consequently in their nonlocal interaction along the single dimension of interest. We show that these discrepancies change the relaxation process of initial states as well as the asymptotic, i.e., thermalized and virialized, equilibrium state. Our investigation includes the dynamical evolution of artificial initial conditions for non-expanding space, as well as cosmological initial conditions in expanding space. The findings of this work are relevant for the interpretation of numerical simulation data modelling nonrelativistic fuzzy cold dark matter in reduced dimensions, in the quest for testing such models and for possible laboratory implementations of them.

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arXiv2020

Model independent measurement of the growth rate from the consistency relations of the LSS

The Consistency Relations for the Large Scale Structure provide a link between the amplitude of Baryonic Acoustic Oscillations in the squeezed bispectrum (BS) and in the power spectrum (PS). This relation depends on the large scale bias of the considered tracer, $b_α$, and on the growth rate of structures, $f$. Remarkably, originating from basic symmetry principles, this relation is exact and independent on the underlying cosmological model. By analysing data from large volume simulations, both for dark matter and for haloes, we illustrate how BS and PS measurements can be used to extract $b_α$ and $f$ without the need of any theoretical approximation scheme for the computation of the BS and the PS. We show that, combining measurements of the squeezed BS with the quadrupole to monopole ratios for the PS at large scales can successfully break the $b_α-f$ degeneracy. We forecast that this method, applied to a Euclid-like survey, will be able to measure bias, and then the growth rate, at better than $10\%$ level, with no extra assumption.

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arXiv2020

Measuring Bias via the Consistency Relations of the Large Scale Structure

Consistency Relations (CR) for the Large Scale Structure are exact equalities between correlation functions of different order. These relations descend from the equivalence principle and hold for primordial perturbations generated by single-field models of inflation. They are not affected by nonlinearities and hold also for biased tracers and in redshift space. We show that Baryonic Acoustic Oscillations (BAO) in the bispectrum (BS) in the squeezed limit are suppressed with respect to those in the power spectrum (PS) by a coefficient that depends on the BS configuration and on the bias parameter (and, in redshift space, also on the growth rate). We test these relations using large volume N-body simulations and show that they provide a novel way to measure large scale halo bias and, potentially, the growth rate. Since bias is obtained by comparing two directly observable quantities, the method is free from theoretical uncertainties both on the computational scheme and on the underlying cosmological model.

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arXiv2020

Extracting the BAO scale from BOSS DR12 dataset

We present the first application to real data from the BOSS DR12 dataset of the Extractor procedure to determine the acoustic scale imprinted on Baryonic Acoustic Oscillations (BAO). We show that, being largely insensitive to the broadband shape of the Power Spectrum, this procedure requires a lower number of nuisance parameters than those used by the BOSS collaboration, For non-reconstructed data our analysis improves the accuracy on the acoustic scale by about 20 %, while for reconstructed ones we get essentially the same level of accuracy as the BOSS analysis.

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arXiv2020

Asymptotic expansions for the Large Scale Structure

We explore the deep ultraviolet (that is, short-distance) limit of the power spectrum (PS) and of the correlation function of a cold dark matter dominated Universe. While for large scales the PS can be written as a double series expansion, in powers of the linear PS and of the wavenumber $k$, we show that, in the opposite limit, it can be expressed via an expansion in powers of the form $1/k^{d+2n}$, where $d$ is the number of spatial dimensions, and $n$ is a non negative integer. The coefficients of the terms of the expansion are nonperturbative in the linear PS, and can be interpreted in terms of the probability density function for the displacement field, evaluated around specific configurations of the latter, that we identify. In the case of the Zel'dovich dynamics, these coefficients can be determined analytically, whereas for the exact dynamics they can be treated as fit, or nuisance, parameters. We confirm our findings with numerical simulations and discuss the necessary steps to match our results to those obtained for larger scales and to actual measurements.

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arXiv2018

Structure formation beyond shell-crossing: nonperturbative expansions and late-time attractors

Structure formation in 1+1 dimensions is considered, with emphasis on the effects of shell-crossing. The breakdown of the perturbative expansion beyond shell-crossing is discussed, and it is shown, in a simple example, that the perturbative series can be extended to a transseries including nonperturbative terms. The latter converges to the exact result well beyond the range of validity of perturbation theory. The crucial role of the divergences induced by shell-crossing is discussed. They provide constraints on the structure of the transseries and act as a bridge between the perturbative and the nonperturbative sectors. Then, we show that the dynamics in the deep multistreaming regime is governed by attractors. In the case of simple initial conditions, these attractors coincide with the asymptotic configurations of the adhesion model, but in general they may differ. These results are applied to a cosmological setting, and an algorithm to build the attractor solution starting from the Zel'dovich approximation is developed. Finally, this algorithm is applied to the search of `haloes' and the results are compared with those obtained from the exact dynamical equations.

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arXiv2018

BAO Extractor: bias and redshift space effects

We study a new procedure to measure the sound horizon scale via Baryonic Acoustic Oscillations (BAO). Instead of fitting the measured power spectrum (PS) to a theoretical model containing the cosmological informations and all the nonlinear effects, we define a procedure to project out (or to "extract") the oscillating component from a given nonlinear PS. We show that the BAO scale extracted in this way is extremely robust and, moreover, can be reproduced by simple theoretical models at any redshift. By using N-body simulations, we discuss the effect of the nonlinear evolution of the matter field, of redshift space distortions and of scale-dependent halo bias, showing that all these effects can be reproduced with sub-percent accuracy. We give a one-parameter theoretical model based on a simple (IR) modification of 1-loop perturbation theory, which reproduces the BAO scale from measurements of halo clustering in redshift space at better than $0.1\%$ level and does not need any external UV input, such as coefficients measured from N-body simulations.

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