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Since the discovery of the accelerated expansion of the Universe in 1998, modified gravity (MG) theories have attracted considerable attention as alternatives to dark energy (DE). While distinguishing the effects of MG from those of DE using cosmic background expansion alone is difficult, the large-scale structure is expected to differ significantly. Among the plethora of MG models, we are particularly interested in those that introduce a scale dependence in the growth of perturbations; specifically, theories that introduce fifth forces mediated by scalar fields with a finite range accessible to cosmological probes. This is the case with $f(R)$ gravity, which is widely regarded as the most studied model in cosmology. In this work, we utilize, for the first time, the full-shape power spectrum of galaxies to constrain scale-dependent modified gravity theories. By using BOSS DR12 dataset, along with a BBN prior on $ \omega_b $ and a Planck 2018 prior on $ n_s $, we obtain an upper bound of $ |f_{R0}| < 5.89 \times 10^{-6} $ at 68% confidence level (c.l.) and $ < 1.53 \times 10^{-5} $ at 95% c.l. for the Hu-Sawicki ($ n=1 $) model. We discuss that it is highly unlikely these constraints will be significantly improved by future galaxy spectroscopic catalogs, such as DESI and Euclid., Comment: 7 pages, 3 figures

One of the main obstacles for the signal extraction of the three point correlation function using photometric surveys, such as the Rubin Observatory Legacy Survey of Space and Time (LSST), will be the prohibitive computation time required for dealing with a vast quantity of sources. Brute force algorithms, which naively scales as $\mathcal{O}(N^3)$ with the number of objects, can be further improved with tree methods but not enough to deal with large scale correlations of Rubin's data. However, a harmonic basis decomposition of these higher order statistics reduces the time dramatically, to scale as a two-point correlation function with the number of objects, so that the signal can be extracted in a reasonable amount of time. In this work, we aim to develop the framework to use these expansions within the Limber approximation for scalar (or spin-0) fields, such as galaxy counts, weak lensing convergence or aperture masses. We develop an estimator to extract the signal from catalogs and different phenomenological and theoretical models for its description. The latter includes halo model and standard perturbation theory, to which we add a simple effective field theory prescription based on the short range of non-locality of cosmic fields, significantly improving the agreement with simulated data. In parallel to the modeling of the signal, we develop a code that can efficiently calculate three points correlations of more than 200 million data points (a full sky simulation with Nside=4096) in $\sim$40 minutes on a single high-performance computing node, enabling a feasible analysis for the upcoming LSST data., Comment: 31 pages, 10 figures

Recent findings from DESI BAO combined with Planck CMB data have set an upper limit on the total neutrino mass of $\sum m_\nu < 0.072\, \text{eV}$ (95% confidence level), ruling out the inverted hierarchy. Indeed, methods that rely on the background expansion of the Universe tend to suggest negative neutrino masses. In this work, we contribute to the quest for accurately constraining neutrino mass using cosmological probes. By conducting a full-shape analysis on data from BOSS, eBOSS, and synthetic power spectra, we showed that projection effects can significantly influence constraints on neutrino mass, rendering these measurements largely unreliable. Our results highlight the need for better techniques to measure the neutrino mass accurately. Based on the large-scale structure suppression, we identified a critical blind spot in the full-shape analysis. By splitting the galaxy power spectrum into broadband and wiggles, we noticed that information on neutrino mass is primarily extracted from the suppressed wiggles rather than broadband suppression. This opens the possibility of developing alternative methods based only on the wiggles of the power spectrum that can be more robust than those heavily reliant on background evolution., Comment: 10 pages

Modified gravity models with scale-dependent linear growth typically exhibit an enhancement in the power spectrum beyond a certain scale. The conventional methods for extracting cosmological information usually involve inferring modified gravity effects via Redshift Space Distortions (RSD), particularly through the time evolution of $f\sigma_8$. However, classical galaxy RSD clustering analyses encounter difficulties in accurately capturing the spectrum's enhanced power, which is better obtained from the broad-band power spectrum. In this sense, full-shape analyses aim to consider survey data using comprehensive and precise models of the whole power spectrum. Yet, a major challenge in this approach is the slow computation of non-linear loop integrals for scale-dependent modified gravity, precluding the estimation of cosmological parameters using Markov Chain Monte Carlo methods. Based on recent studies, in this work we develop a perturbation theory tailored for Modified Gravity, or analogous scenarios introducing additional scales, such as in the presence of massive neutrinos. Our approach only needs the calculation of the scale-dependent growth rate $f(k,t)$ and the limit of the perturbative kernels at large scales. We called this approximate technique as fk-Perturbation Theory and implemented it into the code fkpt, capable of computing the redshift space galaxy power spectrum in a fraction of a second. We validate our modeling and code with the $f(R)$ theory MG-GLAM and General Relativity NSeries sets of simulations. The code is available at https://github.com/alejandroaviles/fkpt, Comment: 34 pages, 9 figures. v2

Recently, a new wave of full modeling analyses have emerged within the Large-Scale Structure community, leading mostly to tighter constraints on the estimation of cosmological parameters, when compared with standard approaches used over the last decade by collaboration analyses of stage III experiments. However, the majority of these full-shape analyses have primarily been conducted in Fourier space, with limited emphasis on exploring the configuration space. Investigating n-point correlations in configuration space demands a higher computational cost compared to Fourier space because it typically requires an additional integration step. This can pose a limitation when using these approaches, especially when considering higher-order statistics. One avenue to mitigate the high computation time is to take advantage of neural network acceleration techniques. In this work, we present a full shape analysis of Sloan Digital Sky Survey III/BOSS in configuration space using a neural network accelerator. We show that the efficacy of the pipeline is enhanced by a time factor $10^{3}$ without sacrificing precision, making it possible to reduce the error associated with the surrogate modeling to below $10^{-2}$ percent which is compatible with the precision required for current stage IV experiments such as DESI. We find $\Omega_m=0.286\pm 0.009$, $H_0=68.8\pm 1.2$ $\mathrm{km} \mathrm{s^{-1}}\mathrm{Mpc^{-1}}$ and $A_s \times 10^9 =2.09 ^{+0.25}_{-0.29}$. Our results on public BOSS data are in good agreement with BOSS official results and compatible with other independent full modeling analyses. We explore relaxing the prior on $\omega_b$ and varying $n_s$, without significant changes in the mean values of the cosmological parameters posterior distributions, but enlarging their widths. Finally, we explore the information content of the multipoles when constraining cosmological parameters.

Upcoming imaging surveys will allow for high signal-to-noise measurements of galaxy clustering at small scales. In this work, we present the results of the LSST bias challenge, the goal of which is to compare the performance of different nonlinear galaxy bias models in the context of LSST Y10 data. Specifically, we compare two perturbative approaches, Lagrangian perturbation theory (LPT) and Eulerian PT (EPT) to two variants of Hybrid Effective Field Theory (HEFT), with our fiducial implementation of these models including terms up to second order in the bias expansion as well as nonlocal bias and deviations from Poissonian stochasticity. We consider different simulated galaxy samples and test the performance of the bias models in a tomographic joint analysis of LSST-Y10-like galaxy clustering, galaxy-galaxy-lensing and cosmic shear. We find both HEFT methods as well as LPT and EPT combined with non-perturbative predictions for the matter power spectrum to yield unbiased constraints on cosmological parameters up to at least a maximal scale of $k_{\mathrm{max}}=0.4 \; \mathrm{Mpc}^{-1}$ for all samples considered, even in the presence of assembly bias. While we find that we can reduce the complexity of the bias model for HEFT without compromising fit accuracy, this is not generally the case for the perturbative models. We find significant detections of non-Poissonian stochasticity in all cases considered, and our analysis shows evidence that small-scale galaxy clustering predominantly improves constraints on galaxy bias rather than cosmological parameters. These results therefore suggest that the systematic uncertainties associated with current nonlinear bias models are likely to be subdominant compared to other sources of error for tomographic analyses of upcoming photometric surveys, which bodes well for future galaxy clustering analyses using these high signal-to-noise data. [abridged], Comment: 47 pages, 19 figures, 1 table, to be submitted to JCAP

The next generation of galaxy surveys will provide highly accurate measurements of the large-scale structure of the Universe, allowing for more stringent tests of gravity on cosmological scales. Higher order statistics are a valuable tool to study the non-Gaussianities in the matter field and to break degeneracies between modified gravity and other physical or nuisance parameters. However, understanding from first principles the behaviour of these correlations is essential to characterise deviations from General Relativity (GR), and the purpose of this work. This work uses contemporary ideas of Standard Perturbation Theory on biased tracers to characterize the three point correlation function (3PCF) at tree level for Modified Gravity models with a scale-dependent gravitational strength, and applies the theory to two specific models ($f(R)$ and DGP) that are representative for Chameleon and Vainshtein screening mechanisms. Additionally, we use a multipole decomposition, which apart from speeding up the algorithm to extract the signal from data, also helps to visualize and characterize GR deviations., Comment: 25 pages, 5 figures

We study dark energy cosmological models, extensions of the standard model of particles, characterized by having an extra relativistic energy density at very early times, and that rapidly dilute after a phase transition occurs. These models generate well localized features (or bumps) in the matter power spectrum for modes crossing the horizon around and before the phase transition epoch. This is because the presence of the additional energy component enhances the growth of matter fluctuations during the radiation dominated epoch. Instead of considering a particular model, we focus on a parametric family of Gaussian bumps in the matter power spectrum, which otherwise would be a $\Lambda$CDM one. We study the evolution of such bump cosmologies and their effects in the halo mass function and halo power spectrum using N-body simulations, the halo-model based HMcode method, and the peak background split framework. The bumps are subject to different nonlinear effects that become physically well understood, and from them we are able to predict that the most distinctive features will show up for intermediate halo masses $10^{12.3} \,h^{-1}M_{\odot} < M < 10^{13.6} \,h^{-1}M_{\odot}$. Out of this range, we expect halos are not significantly affected regardless of the location of the primordial bump in the matter power spectrum. Our analytical results are accurate and in very satisfactory agreement with the simulated data., Comment: 17 pages, 7 figures

We compute 1-loop corrections to the redshift space galaxy power spectrum in cosmologies containing additional scales, and hence kernels different from Einstein-de Sitter (EdS). Specifically, our method is tailored for cosmologies in the presence of massive neutrinos and some modified gravity models; in this article we concentrate on the former case. The perturbative kernels have contributions that we notice appear either from the logarithmic growth factor $f(k,t)$, which is scale-dependent because of the neutrino free-streaming, or from the failure of the commonly used approximation $f^2=\Omega_m$. The latter contributions make the computation of loop corrections quite slow, precluding full-shape analyses for parameter estimation. However, we identify that the dominant pieces of the kernels come from the growth factor, allowing us to simplify the kernels but retaining the characteristic free-streaming scale introduced by the neutrinos' mass. Moreover, with this simplification one can exploit FFTLog methods to speed up the computations even more. We validate our analytical modeling and numerical method with halo catalogs extracted from the Quijote simulations finding good agreement with the, a priori, known cosmological parameters. We make public our Python code FOLPS$\nu$ to compute the redshift space power spectrum in a fraction of second. Code available at https://github.com/henoriega/FOLPS-nu., Comment: 38 pages + appendices, 13 figures. v2: Adds fits at redshift z=1

The Dark Energy Spectroscopic Instrument (DESI) has embarked on an ambitious five-year survey to explore the nature of dark energy with spectroscopy of 40 million galaxies and quasars. DESI will determine precise redshifts and employ the Baryon Acoustic Oscillation method to measure distances from the nearby universe to z > 3.5, as well as measure the growth of structure and probe potential modifications to general relativity. In this paper we describe the significant instrumentation we developed for the DESI survey. The new instrumentation includes a wide-field, 3.2-deg diameter prime-focus corrector that focuses the light onto 5020 robotic fiber positioners on the 0.812 m diameter, aspheric focal surface. The positioners and their fibers are divided among ten wedge-shaped petals. Each petal is connected to one of ten spectrographs via a contiguous, high-efficiency, nearly 50 m fiber cable bundle. The ten spectrographs each use a pair of dichroics to split the light into three channels that together record the light from 360 - 980 nm with a resolution of 2000 to 5000. We describe the science requirements, technical requirements on the instrumentation, and management of the project. DESI was installed at the 4-m Mayall telescope at Kitt Peak, and we also describe the facility upgrades to prepare for DESI and the installation and functional verification process. DESI has achieved all of its performance goals, and the DESI survey began in May 2021. Some performance highlights include RMS positioner accuracy better than 0.1", SNR per \sqrt{\AA} > 0.5 for a z > 2 quasar with flux 0.28e-17 erg/s/cm^2/A at 380 nm in 4000s, and median SNR = 7 of the [OII] doublet at 8e-17 erg/s/cm^2 in a 1000s exposure for emission line galaxies at z = 1.4 - 1.6. We conclude with highlights from the on-sky validation and commissioning of the instrument, key successes, and lessons learned. (abridged), Comment: 78 pages, 32 figures, submitted to AJ

In the last two decades, Modified Gravity (MG) models have been proposed to explain the accelerated expansion of the Universe. However, one of the main difficulties these theories face is that they must reduce to General Relativity (GR) at sufficiently high energy densities, such as those found in the solar system. To achieve this, MG theories typically employ so-called screening mechanisms: nonlinear effects that bring them to GR at the appropriate limits. For this reason, low-energy regions where the screenings do not operate efficiently, such as cosmic voids, are identified as ideal laboratories for testing GR. Hence, the use of marked statistics that up-weight low energy densities have been proposed for being implemented with data from future galaxy surveys. In this proceeding note, we show how to construct theoretical templates for such statistics and test their accuracy with the use of N-body simulations., Comment: Proceeding note for the Sixteenth Marcel Grossmann Meeting - MG16

We introduce an Eulerian Perturbation Theory to study the clustering of tracers for cosmologies in the presence of massive neutrinos. Our approach is based on mapping recently-obtained Lagrangian Perturbation Theory results to the Eulerian framework. We add Effective Field Theory counterterms, IR-resummations and a biasing scheme to compute the one-loop redshift-space power spectrum. To assess our predictions, we compare the power spectrum multipoles against synthetic halo catalogues from the Quijote simulations, finding excellent agreement on scales $k\lesssim 0.25 \,h \text{Mpc}^{-1}$. One can obtain the same fitting accuracy using higher wave-numbers, but then the theory fails to give a correct estimation of the linear bias parameter. We further discuss the implications for the tree-level bispectrum. Finally, calculating loop corrections is computationally costly, hence we derive an accurate approximation wherein we retain only the main features of the kernels, as produced by changes to the growth rate. As a result, we show how FFTLog methods can be used to further accelerate the loop computations with these reduced kernels., Comment: 42 pages, 10 figures

We develop a framework to compute the redshift space power spectrum (PS), with kernels beyond Einstein-de Sitter (EdS), that can be applied to a wide variety of generalized cosmologies. We build upon a formalism that was recently employed for standard cosmology in Chen, Vlah & White (2020), and utilize an expansion of the density-weighted velocity moment generating function that explicitly separates the magnitude of the $k$-modes and their angle to the line-of-sight direction dependencies. We compute the PS for matter and biased tracers to 1-loop Perturbation Theory (PT) and show that the expansion has a correct infrared and ultraviolet behavior, free of unwanted divergences. We also add Effective Field Theory (EFT) counterterms, necessary to account for small-scale contributions to PT, and employ an IR-resummation prescription to properly model the smearing of the BAO due to large scale bulk flows within Standard-PT. To demonstrate the applicability of our formalism, we apply it on the $\Lambda$CDM and the Hu-Sawicki $f(R)$ models, and compare our numerical results against the ELEPHANT suite of $N$-body simulations, finding very good agreement up to $k= 0.27\, \text{Mpc}^{-1} h$ at $z=0.5$ for the first three non-vanishing Legendre multipoles of the PS. To our knowledge, the model presented in this work is the most accurate theoretical EFT-PT for modified gravity to date, being the only one that accounts for beyond linear local biasing in redshift-space. Hence, we argue our RSD modeling is a promising tool to construct theoretical templates in order to test deviations from $\Lambda$CDM using real data obtained from the next stage of cosmological surveys such as DESI and LSST., Comment: 56 pages, 11 figures, version 2 with minor changes

Shortly after its discovery, General Relativity (GR) was applied to predict the behavior of our Universe on the largest scales, and later became the foundation of modern cosmology. Its validity has been verified on a range of scales and environments from the Solar system to merging black holes. However, experimental confirmations of GR on cosmological scales have so far lacked the accuracy one would hope for -- its applications on those scales being largely based on extrapolation and its validity sometimes questioned in the shadow of the unexpected cosmic acceleration. Future astronomical instruments surveying the distribution and evolution of galaxies over substantial portions of the observable Universe, such as the Dark Energy Spectroscopic Instrument (DESI), will be able to measure the fingerprints of gravity and their statistical power will allow strong constraints on alternatives to GR. In this paper, based on a set of $N$-body simulations and mock galaxy catalogs, we study the predictions of a number of traditional and novel estimators beyond linear redshift distortions in two well-studied modified gravity models, chameleon $f(R)$ gravity and a braneworld model, and the potential of testing these deviations from GR using DESI. These estimators employ a wide array of statistical properties of the galaxy and the underlying dark matter field, including two-point and higher-order statistics, environmental dependence, redshift space distortions and weak lensing. We find that they hold promising power for testing GR to unprecedented precision. The major future challenge is to make realistic, simulation-based mock galaxy catalogs for both GR and alternative models to fully exploit the statistic power of the DESI survey and to better understand the impact of key systematic effects. Using these, we identify future simulation and analysis needs for gravity tests using DESI., Comment: 69 pages, 36 figures, 6 tables; accepted for publication in JCAP. The modified gravity HOD galaxy catalogues used in this paper can be downloaded from http://icc.dur.ac.uk/data/, by searching for the title of this paper from the dataset table

We present the one-loop perturbation theory for the power spectrum of the marked density field of matter and biased tracers in real- and redshift-space. The statistic has been shown to yield impressive constraints on cosmological parameters; to exploit this, we require an accurate and computationally inexpensive theoretical model. Comparison with $N$-body simulations demonstrates that linear theory fails on all scales, but inclusion of one-loop Effective Field Theory terms gives a substantial improvement, with $\sim 5\%$ accuracy at $z = 1$. The expansion is less convergent in redshift-space (achieving $\sim 10\%$ accuracy), but there are significant improvements for biased tracers due to the freedom in the bias coefficients. The large-scale theory contains non-negligible contributions from all perturbative orders; we suggest a reorganization of the theory that contains all terms relevant on large-scales, discussing both its explicit form at one-loop and structure at infinite-loop. This motivates a low-$k$ correction term, leading to a model that is sub-percent accurate on large scales, albeit with the inclusion of two (three) free coefficients in real- (redshift-)space. We further consider the effects of massive neutrinos, showing that beyond-EdS corrections to the perturbative kernels are negligible in practice. It remains to see whether the purported gains in cosmological parameters remain valid for biased tracers and can be captured by the theoretical model., Comment: 40 pages, 11 figures, accepted by JCAP

We study the cosmological signatures of having extra energy density, $\rho_{ex}$, beyond the $\Lambda$CDM model that dilutes rapidly, faster than radiation, at a scale factor $a_c$ with a corresponding mode $k_c=a_c H(a_c)$ crossing the horizon at that time. These types of models are motivated by phase transitions of the underlying elementary particles, for example the creation of protons and neutrons from almost massless quarks or the recently proposed Bound Dark Energy model. The rapidly dilution of $\rho_{ex}$ leaves distinctive imprints in the Universe not only in the expansion history with a clear impact on the acoustic scale, $r_s(a_cc)$, and angular distances, $D_A(a)$, but also in the matter and CMB power spectra. The rapidly diluted energy density $\rho_{ex}$, (RDED) generates characteristic signatures that can be observed with current and future precision cosmological data. In particular, we find a bump in the matter power spectrum compared to the standard $\Lambda$CDM. We identify the amplitude, width, and time scale of the bump to the physical properties of the transition. We study these effects with linear theory, standard perturbation theory, and the correlated impact on cosmological distances, allowing for independent measurements of these extensions of the standard $\Lambda$CDM model., Comment: 17 pages, 7 figures

Some beyond $\Lambda$CDM cosmological models have dark-sector energy densities that suffer phase transitions. Fluctuations entering the horizon during such a transition can receive enhancements that ultimately show up as a distinctive bump in the power spectrum relative to a model with no phase transition. In this work, we study the non-linear evolution of such signatures in the matter power spectrum and correlation function using N-body simulations, perturbation theory and HMcode - a halo-model based method. We focus on modelling the response, computed as the ratio of statistics between a model containing a bump and one without it, rather than in the statistics themselves. Instead of working with a specific theoretical model, we inject a parametric family of Gaussian bumps into otherwise standard $\Lambda$CDM spectra. We find that even when the primordial bump is located at linear scales, non-linearities tend to produce a second bump at smaller scales. This effect is understood within the halo model due to a more efficient halo formation. In redshift space these nonlinear signatures are partially erased because of the damping along the line-of-sight direction produced by non-coherent motions of particles at small scales. In configuration space, the bump modulates the correlation function reflecting as oscillations in the response, as it is clear in linear Eulerian theory; however, they become damped because large scale coherent flows have some tendency to occupy regions more depleted of particles. This mechanism is explained within Lagrangian Perturbation Theory and well captured by our simulations., Comment: 15 pages, 8 figures

We develop a Lagrangian Perturbation Theory (LPT) framework to study the clustering of cold dark matter (CDM) in cosmologies with massive neutrinos. We follow the trajectories of CDM particles with Lagrangian displacements fields up to third order in perturbation theory. Once the neutrinos become non-relativistic, their density fluctuations are modeled as being proportional to the CDM density fluctuations, with a scale-dependent proportionality factor. This yields a gravitational back-reaction that introduces additional scales to the linear growth function, which is accounted for in the higher order LPT kernels. Through non-linear mappings from Eulerian to Lagrangian frames, we ensure that our theory has a well behaved large scale behavior free of unwanted UV divergences, which are common when neutrino and CDM densities are not treated on an equal footing, and in resummation schemes that manifestly break Galilean invariance. We use our theory to construct correlation functions for both the underlying matter field, as well as for biased tracers using Convolution-LPT. Redshift-space distortions effects are modeled using the Gaussian Streaming Model. When comparing our analytical results to simulated data from the Quijote simulation suite, we find good accuracy down to $r=20 \,\text{Mpc} \, h^{-1}$ at redshift $z=0.5$, for the real space and redshift space monopole particle correlation functions with no free parameters. The same accuracy is reached for the redshift space quadrupole if we additionally consider an effective field theory parameter that shifts the pairwise velocity dispersion. For modeling the correlation functions of tracers we adopt a simple Lagrangian biasing scheme with only density and curvature operators, which we find sufficient to reach down to $r=20 \,\text{Mpc} \, h^{-1}$ when comparing to simulated halos., Comment: 34 pages, 8 figures

We study the effects of dark energy (DE) anisotropic stress on features of the matter power spectrum (PS). We employ the Parametrized Post-Friedmannian (PPF) formalism to emulate an effective DE, and model its anisotropic stress properties through a two-parameter equation that governs its overall amplitude ($g_0$) and transition scale ($c_g$). For the background cosmology, we consider different equations of state to model DE including a constant $w_0$ parameter, and models that provide thawing (CPL) and freezing (nCPL) behaviors. We first constrain these parameters by using the Pantheon, BAO, $H_0$ and CMB Planck data. Then, we analyze the role played by these parameters in the linear PS. In order for the anisotropic stress not to provoke deviations larger than $10\%$ and $5\%$ with respect to the $\Lambda$CDM PS at $k \sim 0.01 \,h/\text{Mpc}$, the parameters have to be in the range $-0.30< g_0 < 0.32$, $0 \leq c_g^2 < 0.01$ and $-0.15 < g_0 < 0.16$, $0 \leq c_g^2 < 0.01$, respectively. Additionally, we compute the leading nonlinear corrections to the PS using standard perturbation theory in real and redshift space, showing that the differences with respect to the $\Lambda$CDM are enhanced, especially for the quadrupole and hexadecapole RSD multipoles., Comment: 19 pages, 13 figures, 1 table

We develop perturbation theory approaches to model the marked correlation function constructed to up-weight low density regions of the Universe, which might help distinguish modified gravity models from the standard cosmology model based on general relativity. Working within Convolution Lagrangian Perturbation Theory, we obtain that weighted correlation functions are expressible as double convolution integrals that we approximate using a combination of Eulerian and Lagrangian schemes. We find that different approaches agree within 1$\%$ on quasi non-linear scales. Compared with {\it N}-body simulations, the perturbation theory is found to provide accurate predictions for the marked correlation function of dark matter fields, dark matter halos as well as Halo Occupation Distribution galaxies down to $30$ Mpc/h. These analytic approaches help to understand the degeneracy between the mark and the galaxy bias and find a way to maximize the differences among various cosmological models., Comment: 36 pages, 12 figures

We extend the scale-dependent Gaussian Streaming Model (GSM) to produce analytical predictions for the anisotropic redshift-space correlation function for biased tracers in modified gravity models. Employing the Convolution Lagrangian Perturbation Theory (CLPT) re-summation scheme, with a local Lagrangian bias schema provided by the peak-background split formalism, we predict the necessary ingredients that enter the GSM, the real-space halo pairwise velocity and the pairwise velocity dispersion. We further consider effective field theory contributions to the pairwise velocity dispersion in order to model correctly its large scale behavior. We apply our method on two widely-considered modified gravity models, the chameleon-screened f(R) Hu-Sawicki model and the nDGP Vainshtein model and compare our predictions against state-of-the-art N-body simulations for these models. We demonstrate that the GSM approach to predict the monopole and the quadrupole of the redshift-space correlation function for halos, gives very good agreement with the simulation data, for a wide range of screening mechanisms, levels of screening and halo masses at z=0.5 and z=1. Our work shows the applicability of the GSM, for cosmologies beyond GR, demonstrating that it can serve as a powerful predictive tool for the next stage of cosmological surveys like DESI, Euclid, LSST and WFIRST., Comment: 43 pages, 9 figures. Updated to match published version in JCAP

We present a formalism to study screening mechanisms in modified theories of gravity via perturbative methods in different cosmological scenarios. We consider Einstein frame posed theories that are recast as Jordan frame theories, where a known formalism is employed, though the resulting non-linearities of the Klein-Gordon equation acquire an explicit coupling between matter and the scalar field, which is not present in Jordan frame theories. The obtained growth functions are then separated in screening and non-screened contributions to facilitate its analysis. This allows us to compare several theoretical models and to recognize patterns which can be used to differentiate models and their screening mechanisms. In particular, we find anti-screening features in the Symmetron model. In opposition, chameleon type theories, both in the Jordan and in the Einstein frame, always present a screening behaviour. Up to third order in perturbation, we find no anti-screening behaviour in theories with a Vainshtein mechanism, such as the DGP and the cubic Galileon., Comment: 12 pages, 9 figures. Replaced to match version accepted for publication in A&A

In this work we extend the perturbation theory for modified gravity (MG) in two main aspects. First, the construction of matter overdensities from Lagrangian displacement fields is shown to hold in a general framework, allowing us to find Standard Perturbation Theory (SPT) kernels from known Lagrangian Perturbation Theory (LPT) kernels. We then develop a theory of biased tracers for generalized cosmologies, extending already existing formalisms for $\Lambda$CDM. We present the correlation function in Convolution-LPT and the power spectrum in SPT for $\Lambda$CDM, $f(R)$ Hu-Sawicky, and DGP braneworld models. Our formalism can be applied to many generalized cosmologies and to facilitate it, we are making public a code to compute these statistics. We further study the relaxation of bias with the use of a simple model and of excursion set theory, showing that in general the bias parameters have smaller values in MG than in General Relativity., Comment: 38 pages, 8 figures. v2: matches the published version

We extend the definition of Lagrangian local bias proposed by Matsubara (2008) to include curvature and higher-derivative bias operators. Evolution of initially biased tracers using perturbation theory (PT) generates multivariate bias parameters as soon as nonlinear fluctuations become important. We present a procedure that reparametrize a set of spectral parameters, the arguments of the Fourier transformed Lagrangian bias function, from which multivariate renormalized biases can be derived at any order in bias expansion and PT. We find our method simpler than previous renormalization schemes because it only relies on the definition of bias, fixed from the beginning, and in one equation relating renormalized and unrenormalized spectral parameters. We also show that our multivariate biases can be obtained within the peak background split framework, in that sense this work extends that of Schmidt, Jeong and Desjacques (2013); however, we restrict our method to Gaussian initial conditions. Non-linear evolution also leads to the appearance of products of correlators evaluated at the same point, commonly named contact terms, yielding divergent contributions to the power spectrum, in this work we present an explicit method to remove these divergences by introducing stochastic fields., Comment: 15 pages, 1 figure. v2: Typos corrected to match the published version

We present a formalism to compute Lagrangian displacement fields for a wide range of cosmologies in the context of perturbation theory up to third order. We emphasize the case of theories with scale dependent gravitational strengths, such as chameleons, but our formalism can be accommodated to other modified gravity theories. In the non-linear regime two qualitative features arise. One, as is well known, is that nonlinearities lead to a screening of the force mediated by the scalar field. The second is a consequence of the transformation of the Klein-Gordon equation from Eulerian to Lagrangian coordinates, producing frame-lagging terms that are important especially at large scales, and if not considered, the theory does not reduce to the $\Lambda$CDM model in that limit. We apply our formalism to compute the 1-loop power spectrum and the correlation function in $f(R)$ gravity by using different resummation schemes. We further discuss the IR divergences of these formalisms., Comment: 32 pages, 10 figures. v2: CLPT scheme added, IR divergences discussed. v3: Matches published version

With the use of simulated supernova catalogs, we show that the statefinder parameters turn out to be poorly and biased estimated by standard cosmography. To this end, we compute their standard deviations and several bias statistics on cosmologies near the concordance model, demonstrating that these are very large, making standard cosmography unsuitable for future and wider compilations of data. To overcome this issue, we propose a new method that consists in introducing the series of the Hubble function into the luminosity distance, instead of considering the usual direct Taylor expansions of the luminosity distance. Moreover, in order to speed up the numerical computations, we estimate the coefficients of our expansions in a hierarchical manner, in which the order of the expansion depends on the redshift of every single piece of data. In addition, we propose two hybrids methods that incorporates standard cosmography at low redshifts. The methods presented here perform better than the standard approach of cosmography both in the errors and bias of the estimated statefinders. We further propose a one-parameter diagnostic to reject non-viable methods in cosmography., Comment: 13 pages, 11 figures. V2: Extended discussion and references added

We compute the dark matter velocity dispersion tensor up to third order in perturbation theory using the Lagrangian formalism, revealing growing solutions at the third and higher orders. Our results are general and can be used for any other perturbative formalism. As an application, corrections to the matter power spectrum are calculated, and we find that some of them have the same structure as those in the effective field theory of large-scale structure, with "EFT-like" coefficients that grow quadratically with the linear growth function and are further suppressed by powers of the logarithmic linear growth factor $f$; other corrections present additional $k$ dependence. Due to the velocity dispersions, there exists a free-streaming scale that suppresses the whole 1-loop power spectrum. Furthermore, we find that as a consequence of the nonlinear evolution, the free-streaming length is shifted towards larger scales, wiping out more structure than that expected in linear theory. Therefore, we argue that the formalism developed here is better suited for a perturbation treatment of warm dark matter or neutrino clustering, where the velocity dispersion effects are well known to be important. We discuss implications related to the nature of dark matter., Comment: 20 pages, 2 figures. Matches version accepted to PRD

We have continued the development of Lagrangian, cosmological perturbation theory for the low-order correlators of the matter density field. We provide a new route to understanding how the effective field theory (EFT) of large-scale structure can be formulated in the Lagrandian framework and a new resummation scheme, comparing our results to earlier work and to a series of high-resolution N-body simulations in both Fourier and configuration space. The `new' terms arising from EFT serve to tame the dependence of perturbation theory on small-scale physics and improve agreement with simulations (though with an additional free parameter). We find that all of our models fare well on scales larger than about two to three times the non-linear scale, but fail as the non-linear scale is approached. This is slightly less reach than has been seen previously. At low redshift the Lagrangian model fares as well as EFT in its Eulerian formulation, but at higher $z$ the Eulerian EFT fits the data to smaller scales than resummed, Lagrangian EFT. All the perturbative models fare better than linear theory., Comment: 19 pages, 3 figures

We investigate the thermodynamics of general fluids that have the constriction that their pressure is constant. For example, this happens in the case of pure dust matter, for which the pressure vanishes and also in the case of standard dark matter phenomenology. Assuming a finite non-zero pressure, the corresponding dynamics is richer than one naively would expect. In particular, it can be considered as a unified description of dark energy and dark matter. We first consider the more general thermodynamic properties of this class of fluids finding the important result that for them adiabatic and isothermal processes should coincide. We therefore study their behaviors in curved space-times where local thermal equilibrium can be appealed. Thus, we show that this dark fluid degenerates with the dark sector of the LCDM model only in the case of adiabatic evolution. We demonstrate that, adding dissipative processes, a phantom behavior can occur and finally we further highlight that an arbitrary decomposition of the dark sector, into ad hoc dark matter and dark energy terms, may give rise to phantom dark energy, whereas the whole dark sector remains non-phantom., Comment: 20 pages, 6 figures

We review the hydrodynamics of the dark sector components in Cosmology. For this purpose we use the approach of Newtonian gravitational instability, and thereafter we add corrections to arrive to a full relativistic description. In Cosmology and Astrophysics, it is usual to decompose the dark sector into two species, dark matter and dark energy. We will use instead a unified approach by describing a single unified dark fluid with very simple assumptions, namely the dark fluid is barotropic and its sound speed vanishes., Comment: 13 pages, To be published in 'Selected Topics of Computational and Experimental Fluid Mechanics' Springer Book Series: Environmental Science and Engineering: Environmental Science

We propose a novel approach for parameterizing the luminosity distance, based on the use of rational "Pad\'e" approximations. This new technique extends standard Taylor treatments, overcoming possible convergence issues at high redshifts plaguing standard cosmography. Indeed, we show that Pad\'e expansions enable us to confidently use data over a larger interval with respect to the usual Taylor series. To show this property in detail, we propose several Pad\'e expansions and we compare these approximations with cosmic data, thus obtaining cosmographic bounds from the observable universe for all cases. In particular, we fit Pad\'e luminosity distances with observational data from different uncorrelated surveys. We employ union 2.1 supernova data, baryonic acoustic oscillation, Hubble space telescope measurements and differential age data. In so doing, we also demonstrate that the use of Pad\'e approximants can improve the analyses carried out by introducing cosmographic auxiliary variables, i.e. a standard technique usually employed in cosmography in order to overcome the divergence problem. Moreover, for any drawback related to standard cosmography, we emphasize possible resolutions in the framework of Pad\'e approximants. In particular, we investigate how to reduce systematics, how to overcome the degeneracy between cosmological coefficients, how to treat divergences and so forth. As a result, we show that cosmic bounds are actually refined through the use of Pad\'e treatments and the thus derived best values of the cosmographic parameters show slight departures from the standard cosmological paradigm. Although all our results are perfectly consistent with the $\Lambda$CDM model, evolving dark energy components different from a pure cosmological constant are not definitively ruled out., Comment: 24 pages, 9 figures

Dark matter and dark energy are essential in the description of the late Universe, since at least the epoch of equality. On the other hand, the inflation is also necessary and demands a "dark" component, usually associated to a scalar field that dominated the dynamics and kinematics in the very early Universe. Yet, these three dark components of standard model of cosmology are independent from each other, although there are alternative models that pursue to achieve a triple unification, or at least a double. In the present work we present an update of two models that we have considered in recent years. The first is the "dark fluid" model in which dark matter and dark energy are the same thing, achieving a double unification with specific properties that exactly emulate the standard model of cosmology, given the dark degeneracy that exists in the LCDM model. The second model is given by a single F(X) scalar field Lagrangian, with which one is able to model the whole cosmological dynamics, from inflation to today, representing a triple unification model. We highlight the main properties of these models, as well as we test them against known cosmological probes., Comment: 20 pages, 5 figures, 1 table. arXiv admin note: substantial text overlap with arXiv:1108.2457

A cosmographic reconstruction of $f(\mathcal T)$ models is here revised in a model independent way by fixing observational bounds on the most relevant terms of the $f(\mathcal T)$ Taylor expansion. We relate the $f(\mathcal T)$ models and their derivatives to the cosmographic parameters and then adopt a Monte Carlo analysis. The experimental bounds are thus independent of the choice of a particular $f(\mathcal T)$ model. The advantage of such an analysis lies on constraining the dynamics of the universe by reconstructing the form of $f(\mathcal T)$, without any further assumptions apart from the validity of the cosmological principle and the analyticity of the $f(\mathcal T)$ function. The main result is to fix model independent cosmographic constraints on the functional form of $f(\mathcal T)$ which are compatible with the theoretical predictions. Furthermore, we infer a phenomenological expression for $f(\mathcal T)$, compatible with the current cosmographic bounds and show that small deviations are expected from a constant $f(\mathcal T)$ term, indicating that the equation of state of dark energy could slightly evolve from the one of the $\Lambda$CDM model., Comment: Accepted in Phys. Rev. D

We use cosmography to present constraints on the kinematics of the Universe without postulating any underlying theoretical model a priori. To this end, we use a Markov Chain Monte Carlo analysis to perform comparisons to the supernova Ia union 2 compilation, combined with the Hubble Space Telescope measurements of the Hubble constant, and the Hubble parameter datasets. The cosmographic approach to our analysis is revisited and extended for new notions of redshift presented as alternatives to the redshift z. Furthermore, we introduce a new set of fitting parameters describing the kinematical evolution of the Universe in terms of the equation of state of the Universe and derivatives of the total pressure. Our results are consistent with the \Lambda CDM model, although alternative models, with nearly constant pressure and no cosmological constant, match the results accurately as well., Comment: 3 pages, no figures, Proceedings of the 13th Marcel Grossmann Meeting