Normalization Of Power Spectrum Research Articles

Cosmology with galaxy cluster properties using machine learning

Context. Galaxy clusters are the largest gravitating structures in the universe, and their mass assembly is sensitive to the underlying cosmology. Their mass function, baryon fraction, and mass distribution have been used to infer cosmological parameters despite the presence of systematics. However, the complexity of the scaling relations among galaxy cluster properties has never been fully exploited, limiting their potential as a cosmological probe. Aims. We propose the first machine learning (ML) method using galaxy cluster properties from hydrodynamical simulations in different cosmologies to predict cosmological parameters combining a series of canonical cluster observables, such as gas mass, gas bolometric luminosity, gas temperature, stellar mass, cluster radius, total mass, and velocity dispersion at different redshifts. Methods. The ML model was trained on mock “measurements” of these observable quantities from Magneticum multi-cosmology simulations to derive unbiased constraints on a set of cosmological parameters. These include the mass density parameter, Ωm, the power spectrum normalization, σ8, the baryonic density parameter, Ωb, and the reduced Hubble constant, h0. Results. We tested the ML model on catalogs of a few hundred clusters taken, in turn, from each simulation and found that the ML model can correctly predict the cosmology from where they have been picked. The cumulative accuracy depends on the cosmology, ranging from 21% to 75%. We demonstrate that this is sufficient to derive unbiased constraints on the main cosmological parameters with errors on the order of ~14% for Ωm, ~8% for σ8, ~6% for Ωb, and ~3% for h0. Conclusions. This proof-of-concept analysis, though based on a limited variety of multi-cosmology simulations, shows that ML can efficiently map the correlations in the multidimensional space of the observed quantities to the cosmological parameter space and narrow down the probability that a given sample belongs to a given cosmological parameter combination. More large-volume, mid-resolution, multi-cosmology hydro-simulations need to be produced to expand the applicability to a wider cosmological parameter range. However, this first test is exceptionally promising, as it shows that these ML tools can be applied to cluster samples from multiwavelength observations from surveys such as Rubin/LSST, CSST, Euclid, and Roman in optical and near-infrared bands, and eROSITA in X-rays, to the constrain cosmology and effect of baryonic feedback.

The e-MANTIS emulator: fast predictions of the non-linear matter power spectrum in f(R)CDM cosmology

ABSTRACT In order to probe modifications of gravity at cosmological scales, one needs accurate theoretical predictions. N-body simulations are required to explore the non-linear regime of structure formation but are very time consuming. In this work, we release a new public emulator, dubbed e-mantis, that performs an accurate and fast interpolation between the predictions of f(R) modified gravity cosmological simulations, run with ecosmog. We sample a wide 3D parameter space given by the current background scalar field value $10^{-7}\lt \left|f_{R_0}\right|\lt 10^{-4}$, matter density 0.24 < Ωm < 0.39, and primordial power spectrum normalization 0.6 < σ8 < 1.0, with 110 points sampled from a Latin hypercube. For each model we perform pairs of f(R)CDM and ΛCDM simulations covering an effective volume of $\left(560 \, h^{-1}\, \mathrm{Mpc}\right)^3$ with a mass resolution of ∼2 × 1010h−1M⊙. We build an emulator for the matter power spectrum boost B(k) = Pf(R)(k)/PΛCDM(k) using a Gaussian process regression method. The boost is mostly independent of h, ns, and Ωb, which reduces the dimensionality of the relevant cosmological parameter space. Additionally, it is more robust against statistical and systematic errors than the raw power spectrum, thus strongly reducing our computational needs. According to our dedicated study of numerical systematics, the resulting emulator has an estimated maximum error of 3 per cent across the whole cosmological parameter space, for scales $0.03 \ h\, \mathrm{Mpc}^{-1} \lt k \lt 7 \ h\, \mathrm{Mpc}^{-1}$, and redshifts 0 < z < 2, while in most cases the accuracy is better than 1 per cent. Such an emulator could be used to constrain f(R) gravity with weak lensing analyses.

Natural Chain Inflation

In Chain Inflation the universe tunnels along a series of false vacua of ever-decreasing energy. The main goal of this paper is to embed Chain Inflation in high energy fundamental physics. We begin by illustrating a simple effective formalism for calculating Cosmic Microwave Background (CMB) observables in Chain Inflation. Density perturbations seeding the anisotropies emerge from the probabilistic nature of tunneling (rather than from quantum fluctuations of the inflation). To obtain the correct normalization of the scalar power spectrum and the scalar spectral index, we find an upper limit on the scale of inflation at horizon crossing of CMB scales, V⁎1/4<1012 GeV. We then provide an explicit realization of chain inflation, in which the inflaton is identified with an axion in supergravity. The axion enjoys a perturbative shift symmetry which is broken to a discrete remnant by instantons. The model, which we dub ‘natural chain inflation’ satisfies all cosmological constraints and can be embedded into a standard ΛCDM cosmology. Our work provides a major step towards the ultraviolet completion of chain inflation in string theory.

AMICO galaxy clusters in KiDS-DR3: measurement of the halo bias and power spectrum normalization from a stacked weak lensing analysis

ABSTRACT Galaxy clusters are biased tracers of the underlying matter density field. At very large radii beyond about 10 Mpc h−1, the shear profile shows evidence of a second-halo term. This is related to the correlated matter distribution around galaxy clusters and proportional to the so-called halo bias. We present an observational analysis of the halo bias–mass relation based on the AMICO galaxy cluster catalogue, comprising around 7000 candidates detected in the third release of the KiDS survey. We split the cluster sample into 14 redshift-richness bins and derive the halo bias and the virial mass in each bin by means of a stacked weak lensing analysis. The observed halo bias–mass relation and the theoretical predictions based on the Lambda cold dark matter standard cosmological model show an agreement within 2σ. The mean measurements of bias and mass over the full catalogue give $M_{200c} = (4.9 \pm 0.3) \times 10^{13}\, {\rm M}_{\odot }/{\it h}$ and $b_h \sigma _8^2 = 1.2 \pm 0.1$. With the additional prior of a bias–mass relation from numerical simulations, we constrain the normalization of the power spectrum with a fixed matter density Ωm = 0.3, finding σ8 = 0.63 ± 0.10.

C3 Cluster Clustering Cosmology I. New Constraints on the Cosmic Growth Rate at z ∼ 0.3 from Redshift-space Clustering Anisotropies

Abstract Redshift-space distortions in the clustering of galaxy clusters provide a novel probe to test the theory of gravity on cosmological scales. The aim of this work is to derive new constraints on the linear growth rate of cosmic structures from the redshift-space two-point correlation function of galaxy clusters. We construct a large spectroscopic catalog of optically selected clusters from the Sloan Digital Sky Survey. The selected sample consists of 43,743 clusters in the redshift range 0.1 &lt; z &lt; 0.42, with masses estimated from weak-lensing calibrated scaling relations. We measure the transverse and radial wedges of the two-point correlation function of the selected clusters. Modeling the redshift-space clustering anisotropies, we provide the first constraints on the linear growth rate from cluster clustering. The cluster masses are used to set a prior on the linear bias of the sample. This represents the main advantage in using galaxy clusters as cosmic probes, instead of galaxies. Assuming a standard cosmological model consistent with the latest cosmic microwave background constraints, we do not find any evidence of deviations from general relativity. Specifically, we get the value of the growth rate times the matter power spectrum normalization parameter fσ 8 = 0.44 ± 0.05, at an effective redshift of z = 0.275.

Dark sector interactions and the curvature of the universe in light of Planck's 2018 data

We investigate the observational viability of a class of interacting dark energy (iDE) models in the light of the latest observations of the Cosmic Microwave Background and type Ia supernovae, and the SH0ES measurement of the current expansion rate H 0. Our analysis explores both the assumptions of a non-zero spatial curvature and a free curvature density, the correlation between the interaction parameter α and H 0, and updates the results reported in [1].The results show that the best-fit of our joint analysis clearly favours a positive interaction, i.e., an energy flux from dark matter to dark energy, with α≈ 0.2, while the non-interacting case, α = 0, is ruled out by more than 3σ confidence level under the flat space assumption. On the other hand, considering a non-zero spatial curvature, we find a significant anti-correlation between the interaction parameter and the universe density curvature, which seems to relax the correlation between the parameters α and H 0, as well as between H 0 and the normalization of the matter power spectrum on scales of 8h -1 Mpc (σ8).Finally, we discuss the influence of considering the SH0ES prior on H 0 in the joint analyses performed, and find thatsuch a choice does not change considerably the standard cosmology predictions but has a significant influence on the results of the iDE model.

Linear perturbations spectra for dynamical dark energy inspired by modified gravity

In this paper, we study a particular modified gravity Equation of State (EoS), the so-called Jaime–Jaber–Escamilla, that emerges from the first gravity modified action principle and can reproduce three cosmological viable [Formula: see text] theories: the Starobinsky, Hu–Sawicki and Exponential models. This EoS is a suitable candidate to reproduce the dynamical dark energy behaviour already reconstructed by the current data sets. Based on the joint statistical analysis, we found that our results are still in good agreement (within [Formula: see text]) with the [Formula: see text]CDM, while at perturbative level, we note that the matter power spectrum normalisation factor [Formula: see text] shows an agreement with SDSS and SNeIa+IRAS at 1-[Formula: see text] for the Starobinsky model and with SDSS-vec for the Hu–Sawicki and Exponential models. Furthermore, we found that for the [Formula: see text] values, Starobinsky and Hu–Sawicki show the least tension in comparison with PL18 TT. All these aspects cannot be observed directly from other alternatives theories, where an equation of state is difficult to compute analytically.

Neutrino mass bounds from confronting an effective model with BOSS Lyman-α data

We present an effective model for the one-dimensional Lyman-α flux power spectrum far above the baryonic Jeans scale. The main new ingredient is constituted by a set of two parameters that encode the impact of small, highly non-linear scales on the one-dimensional power spectrum on large scales, where it is measured by BOSS. We show that, by marginalizing over the model parameters that capture the impact of the intergalactic medium, the flux power spectrum from both simulations and observations can be described with high precision. The model displays a degeneracy between the neutrino masses and the (unknown, in our formalism) normalization of the flux power spectrum. This degeneracy can be lifted by calibrating one of the model parameters with simulation data, and using input from Planck CMB data. We demonstrate that this approach can be used to extract bounds on the sum of neutrino masses with comparably low numerical effort, while allowing for a conservative treatment of uncertainties from the dynamics of the intergalactic medium. An explorative analysis yields an upper bound of 0.16eV at 95% C.L. when applied to BOSS data at 3 ≤ z ≤ 4.2. We also forecast that if the systematic and statistical errors will be reduced by a factor two the upper bound will become 0.1eV at 95% C.L, and 0.056eV when assuming a 1% error.

Arguments against using h−1 Mpc units in observational cosmology

It is common to express cosmological measurements in units of $h^{-1}{\rm Mpc}$. Here, we review some of the complications that originate from this practice. A crucial problem caused by these units is related to the normalization of the matter power spectrum, which is commonly characterized in terms of the linear-theory rms mass fluctuation in spheres of radius $8\,h^{-1}{\rm Mpc}$, $\sigma_8$. This parameter does not correctly capture the impact of $h$ on the amplitude of density fluctuations. We show that the use of $\sigma_8$ has caused critical misconceptions for both the so-called $\sigma_8$ tension regarding the consistency between low-redshift probes and cosmic microwave background data, and the way in which growth-rate estimates inferred from redshift-space distortions are commonly expressed. We propose to abandon the use of $h^{-1}{\rm Mpc}$ units in cosmology and to characterize the amplitude of the matter power spectrum in terms of $\sigma_{12}$, defined as the mass fluctuation in spheres of radius $12\,{\rm Mpc}$, whose value is similar to the standard $\sigma_8$ for $h\sim 0.67$.

Constraining neutrino masses with weak-lensing multiscale peak counts

Massive neutrinos influence the background evolution of the Universe as well as the growth of structure. Being able to model this effect and constrain the sum of their masses is one of the key challenges in modern cosmology. Weak-lensing cosmological constraints will also soon reach higher levels of precision with next-generation surveys like LSST, WFIRST and Euclid. We use the MassiveNus simulations to derive constraints on the sum of neutrino masses $M_{\nu}$, the present-day total matter density $\Omega_{\rm m}$, and the primordial power spectrum normalization $A_{\rm s}$ in a tomographic setting. We measure the lensing power spectrum as second-order statistics along with peak counts as higher-order statistics on lensing convergence maps generated from the simulations. We investigate the impact of multiscale filtering approaches on cosmological parameters by employing a starlet (wavelet) filter and a concatenation of Gaussian filters. In both cases peak counts perform better than the power spectrum on the set of parameters [$M_{\nu}$, $\Omega_{\rm m}$, $A_{\rm s}$] respectively by 63$\%$, 40$\%$ and 72$\%$ when using a starlet filter and by 70$\%$, 40$\%$ and 77$\%$ when using a multiscale Gaussian. More importantly, we show that when using a multiscale approach, joining power spectrum and peaks does not add any relevant information over considering just the peaks alone. While both multiscale filters behave similarly, we find that with the starlet filter the majority of the information in the data covariance matrix is encoded in the diagonal elements; this can be an advantage when inverting the matrix, speeding up the numerical implementation.

Unbiased cosmology inference from biased tracers using the EFT likelihood

We present updates on the cosmology inference using the effective field theory (EFT) likelihood presented previously in Schmidt et al., 2018, Elsner et al., 2019 \\cite{paperI,paperII}. Specifically, we add a cutoff to the initial conditions that serve as starting point for the matter forward model. We show that this cutoff, which was not employed in any previous related work, is important to regularize loop integrals that otherwise involve small-scale, non-perturbative modes. We then present results on the inferred value of the linear power spectrum normalization σ8 from rest-frame halo catalogs using both second- and third-order bias expansions, imposing uniform priors on all bias parameters. Due to the perfect bias-σ8 degeneracy at linear order, constraints on σ8 rely entirely on nonlinear information. The results show the expected convergence behavior when lowering the cutoff in wavenumber, L. When including modes up to k ⩽ Λ = 0.1 h Mpc−1 in the second-order case, σ8 is recovered to within ≲ 6% for a range of halo masses and redshifts. The systematic bias shrinks to 4% or less for the third-order bias expansion on the same range of scales. Together with additional evidence we provide, this shows that the residual mismatch in σ8 can be attributed to higher-order bias contributions. We conclude that the EFT likelihood is able to infer unbiased cosmological constraints, within expected theoretical systematic errors, from physical biased tracers on quasilinear scales.

Cosmology inference from a biased density field using the EFT-based likelihood

The effective-field-theory (EFT) approach to the clustering of galaxies and other biased tracers allows for an isolation of the cosmological information that is protected by symmetries, in particular the equivalence principle, and thus is robust to the complicated dynamics of dark matter, gas, and stars on small scales. All existing implementations proceed by making predictions for the lowest-order n-point functions of biased tracers, as well as their covariance, and comparing with measurements. Recently, we presented an EFT-based expression for the conditional probability of the density field of a biased tracer given the matter density field, which in principle uses information from arbitrarily high order n-point functions. Here, we report results based on this likelihood by applying it to halo catalogs in real space, specifically an inference of the power spectrum normalization σ8. We include bias terms up to second order as well as the leading higher-derivative term. For a cutoff value of Λ = 0.1 hMpc−1, we recover the ground-truth value of σ8 to within 95% CL for different halo samples and redshifts. We discuss possible sources for the remaining systematic bias in σ8 as well as future developments.

Cosmological exploitation of the size function of cosmic voids identified in the distribution of biased tracers

Abstract Cosmic voids are large underdense regions that, together with galaxy clusters, filaments and walls, build-up the large-scale structure of the Universe. The void size function provides a powerful probe to test the cosmological framework. However, to fully exploit this statistics, the void sample has to be properly cleaned from spurious objects. Furthermore, the bias of the mass tracers used to detect these regions has to be taken into account in the size function model. In our work, we test a cleaning algorithm and a new void size function model on a set of simulated dark matter halo catalogues, with different mass and redshift selections, to investigate the statistics of voids identified in a biased mass density field. We then investigate how the density field tracers’ bias affects the detected size of voids. The main result of this analysis is a new model of the size function, parametrized in terms of the linear effective bias of the tracers used, which is straightforwardly inferred from the large-scale two-point correlation function. This method is a crucial step in exploiting real surveys. The proposed size function model has been accurately calibrated on halo catalogues, and used to validate the possibility to provide forecasts on the cosmological constraints, namely on the matter density contrast, ΩM, and on the normalization of the linear matter power spectrum, σ8, at different redshifts.

A rigorous EFT-based forward model for large-scale structure

Conventional approaches to cosmology inference from galaxy redshift surveys are based on n-point functions, which are under rigorous perturbative control on sufficiently large scales. Here, we present an alternative approach, which employs a likelihood at the level of the galaxy density field. By integrating out small-scale modes based on effective-field theory arguments, we prove that this likelihood is under perturbative control if certain specific conditions are met. We further show that the information captured by this likelihood is equivalent to the combination of the next-to-leading order galaxy power spectrum, leading-order bispectrum, and BAO reconstruction. Combined with MCMC sampling and MAP optimization techniques, our results allow for fully Bayesian cosmology inference from large-scale structure that is under perturbative control. We illustrate this via a first demonstration of unbiased cosmology inference from nonlinear large-scale structure using this likelihood. In particular, we show unbiased estimates of the power spectrum normalization σ8 from a catalog of simulated dark matter halos, where nonlinear information is crucial in breaking the b1−σ8 degeneracy.

Weak-lensing peaks in simulated light cones: investigating the coupling between dark matter and dark energy

In this paper, we study the statistical properties of weak lensing peaks in light-cones generated from cosmological simulations. In order to assess the prospects of such observable as a cosmological probe, we consider simulations that include interacting Dark Energy (hereafter DE) models with coupling term between DE and Dark Matter. Cosmological models that produce a larger population of massive clusters have more numerous high signal-to-noise peaks; among models with comparable numbers of clusters those with more concentrated haloes produce more peaks. The most extreme model under investigation shows a difference in peak counts of about $20\%$ with respect to the reference $\mathrm{\Lambda}$CDM model. We find that peak statistics can be used to distinguish a coupling DE model from a reference one with the same power spectrum normalisation. The differences in the expansion history and the growth rate of structure formation are reflected in their halo counts, non-linear scale features and, through them, in the properties of the lensing peaks. For a source redshift distribution consistent with the expectations of future space-based wide field surveys, we find that typically seventy percent of the cluster population contributes to weak-lensing peaks with signal-to-noise ratios larger than two, and that the fraction of clusters in peaks approaches one-hundred percent for haloes with redshift z$\leq$0.5. Our analysis demonstrates that peak statistics are an important tool for disentangling DE models by accurately tracing the structure formation processes as a function of the cosmic time.

Tension and constraints on modified gravity parametrizations of Geff(z) from growth rate and Planck data

We construct an updated and extended compilation of growth rate data consisting of 34 points and including corrections for model dependence. In order to maximize the independence of the datapoints we also construct a subsample of this compilation (`Gold' growth dataset) which consists of 18 datapoints. We test the consistency of this dataset with the best fit Planck15/$\Lambda$CDM parameters in the context of General Relativity (GR) using the evolution equation for the growth factor $\delta(a)$ with a $w$CDM background. We find tension at the $\sim 3 \sigma$ level between the best fit parameters $w$ (the dark energy equation of state), $\Omega_{0m}$ (the matter density parameter) and $\sigma_8$ (the matter power spectrum normalization on scales $8h^{-1}$Mpc) and the corresponding Planck15/$\Lambda$CDM parameters. We show that the tension disappears if we allow for evolution of the effective Newton's constant, parametrized as $G_{eff}(a)/G_N = 1 + g_a(1-a)^n-g_a(1-a)^{2n}$ with $n\ge2$ where $g_a$, $n$ are parameters of the model, $a$ is the scale factor and $z = 1/a-1$ is the redshift. This parametrization satisfies three criteria: a. $G_{eff} > 0$, b. Consistency with Big Bang Nucleosynthesis ($G_{eff}(a\ll 1)/G_N=1$), c. Consistency with solar system tests ($G_{eff}(a=1)/G_N=1$ and $G_{eff}'(a=1)/G_N=0$). We show that the best fit form of $G_{eff}(z)$ obtained from the growth data corresponds to weakening gravity at recent redshifts (decreasing function of $z$) and we demonstrate that this behavior is not consistent with any scalar-tensor Lagrangian with a real scalar field. Finally, we use MGCAMB to find the best fit $G_{eff}(z)$ obtained from the Planck CMB power spectrum on large angular scales and show that it is a mildly increasing function of $z$, in $3\sigma$ tension with the corresponding decreasing best fit $G_{eff}(z)$ obtained from the growth data.

The VIMOS Public Extragalactic Redshift Survey (VIPERS)

We present measurements of the growth rate of cosmological structure from the modelling of the anisotropic galaxy clustering measured in the final data release of the VIPERS survey. The analysis is carried out in configuration space and based on measurements of the first two even multipole moments of the anisotropic galaxy auto-correlation function, in two redshift bins spanning the range $0.5 < z < 1.2$. We provide robust and cosmology-independent corrections for the VIPERS angular selection function, allowing recovery of the underlying clustering amplitude at the percent level down to the Mpc scale. We discuss several improvements on the non-linear modelling of redshift-space distortions (RSD) and perform detailed tests of a variety of approaches against a set of realistic VIPERS-like mock realisations. This includes using novel fitting functions to describe the velocity divergence and density power spectra $P_{\theta\theta}$ and $P_{\delta\theta}$ that appear in RSD models. These tests show that we are able to measure the growth rate with negligible bias down to separations of $5h^{-1}Mpc$. Interestingly, the application to real data shows a weaker sensitivity to the details of non-linear RSD corrections compared to mock results. We obtain consistent values for the growth rate times the matter power spectrum normalisation parameter of $f\sigma_8=0.55\pm 0.12$ and $0.40\pm0.11$ at effective redshifts of $z = 0.6$ and $z=0.86$ respectively. These results are in agreement with standard cosmology predictions assuming Einstein gravity in a $\Lambda \rm{CDM}$ background.

Fourier transform power spectrum is a potential measure of tissue alignment in standard MRI: A multiple sclerosis study.

Loss of tissue coherency in brain white matter is found in many neurological diseases such as multiple sclerosis (MS). While several approaches have been proposed to evaluate white matter coherency including fractional anisotropy and fiber tracking in diffusion-weighted imaging, few are available for standard magnetic resonance imaging (MRI). Here we present an image post-processing method for this purpose based on Fourier transform (FT) power spectrum. T2-weighted images were collected from 19 patients (10 relapsing-remitting and 9 secondary progressive MS) and 19 age- and gender-matched controls. Image processing steps included: computation, normalization, and thresholding of FT power spectrum; determination of tissue alignment profile and dominant alignment direction; and calculation of alignment complexity using a new measure named angular entropy. To test the validity of this method, we used a highly organized brain white matter structure, corpus callosum. Six regions of interest were examined from the left, central and right aspects of both genu and splenium. We found that the dominant orientation of each ROI derived from our method was significantly correlated with the predicted directions based on anatomy. There was greater angular entropy in patients than controls, and a trend to be greater in secondary progressive MS patients. These findings suggest that it is possible to detect tissue alignment and anisotropy using traditional MRI, which are routinely acquired in clinical practice. Analysis of FT power spectrum may become a new approach for advancing the evaluation and management of patients with MS and similar disorders. Further confirmation is warranted.

Constraints on shear and rotation with massive galaxy clusters

A precise determination of the mass function is an important tool to verify cosmological predictions of the $\Lambda$CDM model and to infer more precisely the better model describing the evolution of the Universe. Galaxy clusters have been currently used to infer cosmological parameters, in particular the matter density parameter $\Omega_{\rm m}$, the matter power spectrum normalization $\sigma_8$ and the equation of state parameter $w_{\rm de}$ of the dark energy fluid. In this work, using data on massive galaxy clusters ($M>8\times 10^{14}~h^{-1}~M_{\odot}$) in the redshift range $0.05\lesssim z\lesssim 0.83$ we put constraints on the parameter $\alpha$ introduced within the formalism of the extended spherical collapse model to quantify deviations from sphericity due to shear and rotation. Since at the moment there is no physical model describing its functional shape, we assume it to be a logarithmic function of the cluster mass. By holding $\sigma_8$ fixed and restricting our analysis to a $\Lambda$CDM model, we find, at $1-\sigma$ confidence level, $\Omega_{\rm m}=0.284\pm0.0064$, $h=0.678\pm0.017$ and $\beta=0.0019^{+0.0008}_{-0.0015}$, where $\beta$ represents the slope of the parameter $\alpha$. This results translates into a $9\%$ decrement of the number of massive clusters with respect to a standard $\Lambda$CDM mass function, but better data are required to better constrain this quantity, since at the $2-\sigma$ and $3-\sigma$ confidence level we are only able to infer upper limits.

Modelling galaxy clustering on small scales to tighten constraints on dark energy and modified gravity

We present a new approach to measuring cosmic expansion history and growth rate of large scale structure using the anisotropic two dimensional galaxy correlation function (2DCF) measured from data; it makes use of the empirical modeling of small-scale galaxy clustering derived from numerical simulations by Zheng et al. (2013). We validate this method using mock catalogues, before applying it to the analysis of the CMASS sample from the Sloan Digital Sky Survey Data Release 10 (DR10) of the Baryon Oscillation Spectroscopic Survey (BOSS). We find that this method enables accurate and precise measurements of cosmic expansion history and growth rate of large scale structure. Modeling the 2DCF fully including nonlinear effects and redshift space distortions (RSD) in the scale range of 16 to 144 Mpc/h, we find H(0.57)r_s(z_d)/c=0.0459 +/- 0.0006, D_A(0.57)/r_s(z_d)=9.011 +/- 0.073, and f_g(0.57)\sigma_8(0.57)=0.476 +/- 0.050, which correspond to precisions of 1.3%, 0.8%, and 10.5% respectively. We have defined r_s(z_d) to be the sound horizon at the drag epoch computed using a simple integral, f_g(z) as the growth rate at redshift z, and \sigma_8(z) as the matter power spectrum normalization on 8Mpc/h scale at z. We find that neglecting the small-scale information significantly weakens the constraints on H(z) and D_A(z), and leads to a biased estimate of f_g(z). Our results indicate that we can significantly tighten constraints on dark energy and modified gravity by reliably modeling small-scale galaxy clustering.