We develop a code to produce the power spectrum in redshift space based on standard perturbation theory (SPT) at 1-loop order. The code can be applied to a wide range of modified gravity and dark energy models using a recently proposed numerical method by A.Taruya to find the SPT kernels. This includes Horndeski's theory with a general potential, which accommodates both chameleon and Vainshtein screening mechanisms and provides a non-linear extension of the effective theory of dark energy up to the third order. Focus is on a recent non-linear model of the redshift space power spectrum which has been shown to model the anisotropy very well at relevant scales for the SPT framework, as well as capturing relevant non-linear effects typical of modified gravity theories. We provide consistency checks of the code against established results and elucidate its application within the light of upcoming high precision RSD data.

We present constraints on extensions to the standard cosmological model of a spatially flat Universe governed by general relativity, a cosmological constant (Λ), and cold dark matter (CDM) by varying the spatial curvature ΩK, the sum of the neutrino masses ∑mν, the dark energy equation of state parameter w, and the Hu-Sawicki f(R) gravity fR0 parameter. With the combined 3 × 2 pt measurements of cosmic shear from the Kilo-Degree Survey (KiDS-1000), galaxy clustering from the Baryon Oscillation Spectroscopic Survey (BOSS), and galaxy-galaxy lensing from the overlap between KiDS-1000, BOSS, and the spectroscopic 2-degree Field Lensing Survey, we find results that are fully consistent with a flat ΛCDM model with ΩK = 0.011−0.057+0.054, ∑mν < 1.76 eV (95% CL), and w = −0.99−0.13+0.11. The fR0 parameter is unconstrained in our fully non-linear f(R) cosmic shear analysis. Considering three different model selection criteria, we find no clear preference for either the fiducial flat ΛCDM model or any of the considered extensions. In addition to extensions to the flat ΛCDM parameter space, we also explore restrictions to common subsets of the flat ΛCDM parameter space by fixing the amplitude of the primordial power spectrum to the Planck best-fit value, as well as adding external data from supernovae and lensing of the cosmic microwave background (CMB). Neither the beyond-ΛCDM models nor the imposed restrictions explored in this analysis are able to resolve the ∼3σ tension in S8 between the 3 × 2 pt constraints and the Planck temperature and polarisation data, with the exception of wCDM, where the S8 tension is resolved. The tension in the wCDM case persists, however, when considering the joint S8 − w parameter space. The joint flat ΛCDM CMB lensing and 3 × 2 pt analysis is found to yield tight constraints on Ωm = 0.307−0.013+0.008, σ8 = 0.769−0.010+0.022, and S8 = 0.779−0.013+0.013.

We compare analytical computations with numerical simulations for dark-matter clustering, in general relativity and in the normal branch of DGP gravity (nDGP). Our analytical frameword is the Effective Field Theory of Large-Scale Structure (EFTofLSS), which we use to compute the one-loop dark-matter power spectrum, including the resummation of infrared bulk displacement effects. We compare this to a set of 20 COLA simulations at redshifts z = 0, z = 0.5, and z = 1, and fit the free parameter of the EFTofLSS, called the speed of sound, in both ΛCDM and nDGP at each redshift. At one-loop at z = 0, the reach of the EFTofLSS is k reach ≈ 0.14 hMpc −1 for both ΛCDM and nDGP. Along the way, we compare two different infrared resummation schemes and two different treatments of the time dependence of the perturbative expansion, concluding that they agree to approximately 1% over the scales of interest. Finally, we use the ratio of the COLA power spectra to make a precision measurement of the difference between the speeds of sound in ΛCDM and nDGP, and verify that this is proportional to the modification of the linear coupling constant of the Poisson equation.Despite the success of the ΛCDM model, alternatives, coming in the form of modifications to gravity or to the energy components of the universe, are currently under active investigation (see [1] for a review). Generically, modified gravity theories predict a fifth force sourced by additional degrees of freedom. To overcome strong local experimental constraints on gravity, all largely consistent with GR, modified gravity theories must employ screening mechanisms. These mechanisms filter out fifth force effects at small scales (see [2][3][4] for reviews) so that the theory does not violate the strong experimental tests. These short-scales constraints have pushed searches for deviations from GR to the large-scale structure of the universe [5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. On the observational side, this field will soon enter an exciting new era with the commencement of the largest and most precise astronomical surveys to date, including EUCLID 1 [20], WFIRST 2 [21], DESI 3 [22], and LSST 4 [23].One widely used quantity in survey data analyses is the matter power spectrum, used both in lensing and in clustering experiments [24][25][26][27][28][29][30][31][32]. Currently, perturbative templates are widely used to compute this quantity (see [33,34] for early reviews of relevant theory). In order to make the most of the upcoming data sets, such approaches must improve on two fronts. Firstly, because most information is concentrated at short scales, one would like to be able to accurately describe the mildly non-linear regime. Secondly, as the sizes of the surveys increase, the statistical errors are pushed into the percent and sub-percent regime: this calls for precise control over theoretical errors and for common approximations used in theoretical templates to be quantified and, if necessary, improved.The first of these problems has recently been tac...

To effectively exploit large-scale structure surveys, we depend on accurate and reliable predictions of non-linear cosmological structure formation. Tools for efficient and comprehensive computational modelling are therefore essential to perform cosmological parameter inference analyses. We present the public software package ReACT, demonstrating its capability for the fast and accurate calculation of non-linear power spectra from non-standard physics. We showcase ReACT through a series of analyses on the DGP and f(R) gravity models, adopting LSST-like cosmic shear power spectra. Accurate non-linear modelling with ReACT has the potential to more than double LSST’s constraining power on the f(R) parameter, in contrast to an analysis that is limited to the quasi-linear regime. We find that ReACT is sufficiently robust for the inference of consistent constraints on theories beyond ΛCDM for current and ongoing surveys. With further improvement, particularly in terms of the accuracy of the non-linear ΛCDM power spectrum, ReACT can, in principle, meet the accuracy requirements for future surveys such as Euclid and LSST.

We extend our previous redshift space power spectrum code to the redshift space correlation function. Here we focus on the Gaussian Streaming Model (GSM). Again, the code accommodates a wide range of modified gravity and dark energy models. For the non-linear real space correlation function used in the GSM we use the Fourier transform of the RegPT 1-loop matter power spectrum. We compare predictions of the GSM for a Vainshtein screened and Chameleon screened model as well as GR. These predictions are compared to the Fourier transform of the Taruya, Nishimichi and Saito (TNS) redshift space power spectrum model which is fit to N-body data. We find very good agreement between the Fourier transform of the TNS model and the GSM predictions, with ≤ 6% deviations in the first two correlation function multipoles for all models for redshift space separations in 50Mpc/h ≤ s ≤ 180Mpc/h. Excellent agreement is found in the differences between the modified gravity and GR multipole predictions for both approaches to the redshift space correlation function, highlighting their matched ability in picking up deviations from GR. We elucidate the timeliness of such non-standard templates at the dawn of stage-IV surveys and discuss necessary preparations and extensions needed for upcoming high quality data.