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We forecast constraints on minimal model-independent parametrisations of several Modified Gravity theories using mock Stage-IV cosmic shear data. We include nonlinear effects and screening, which ensures recovery of General Relativity on small scales. We introduce a power spectrum emulator to accelerate our analysis and evaluate the robustness of the growth index parametrisation with respect to two cosmologies: $\Lambda$CDM and the normal branch of the DGP model. We forecast the uncertainties on the growth index $\gamma$ to be of the order $\sim 10\%$. We find that our halo-model based screening approach demonstrates excellent performance, meeting the precision requirements of Stage-IV surveys. However, neglecting the screening transition results in biased predictions for cosmological parameters. We find that the screening transition shows significant degeneracy with baryonic feedback, requiring a much better understanding of baryonic physics for its detection. Massive neutrinos effects are less prominent and challenging to detect solely with cosmic shear data., Comment: 22 pages, 16 figures, 2 tables plus Appendices. Our power spectrum boost emulators for extended cosmologies are publicly available at https://github.com/nebblu/ReACT-emus/tree/main/emulators

To fully exploit the data from next generation surveys, we need an accurate modelling of the matter power spectrum up to non-linear scales. Therefore in this work we present the halo model reaction framework for the Generalized Cubic Covariant Galileon (GCCG) model, a modified gravity model within the Horndeski class of theories which extends the cubic covariant Galileon (G3) by including power laws of the derivatives of the scalar field in the K-essence and cubic terms. We modify the publicly available software ReACT for the GCCG in order to obtain an accurate prediction of the non-linear power spectrum. In the limit of the G3 model we compare the modified ReACT code to $N$-body simulations and we find agreement within 5\% for a wide range of scales and redshifts. We then study the relevant effects of the modifications introduced by the GCCG on the non-linear matter power spectrum. Finally, we provide forecasts from spectroscopic and photometric primary probes by next generation surveys using a Fisher matrix method. We show that future data will be able to constrain at 1$\sigma$ the two additional parameters of the model at the percent level and that considering non-linear corrections to the matter power spectrum beyond the linear regime is crucial to obtain this result., Comment: 17 pages, 7 figures, code available at https://github.com/nebblu/ACTio-ReACTio

The cosmological constant and its phenomenology remain among the greatest puzzles in theoretical physics. We review how modifications of Einstein's general relativity could alleviate the different problems associated with it that result from the interplay of classical gravity and quantum field theory. We introduce a modern and concise language to describe the problems associated with its phenomenology, and inspect no-go theorems and their loopholes to motivate the approaches discussed here. Constrained gravity approaches exploit minimal departures from general relativity; massive gravity introduces mass to the graviton; Horndeski theories lead to the breaking of translational invariance of the vacuum; and models with extra dimensions change the symmetries of the vacuum. We also review screening mechanisms that have to be present in some of these theories if they aim to recover the success of general relativity on small scales as well. Finally, we summarise the statuses of these models in their attempt to solve the different cosmological constant problems while being able to account for current astrophysical and cosmological observations., Comment: 54 pages, 2 figures, 1 table. Invited review for Universe, Special Issue "Cosmological Constant" (https://www.mdpi.com/journal/universe/special_issues/cosmological_constant_problem)

Understanding nonlinear structure formation is crucial for fully exploring the data generated by stage IV surveys, requiring accurate modelling of the power spectrum. This is challenging for deviations from $\Lambda$CDM, but we must ensure that alternatives are well tested, to avoid false detections. We present an extension of the halo model reaction framework for interacting dark energy. We modify the halo model including the additional force present in the Dark Scattering model and implement it into ReACT. The reaction is combined with a pseudo spectrum from EuclidEmulator2 and compared to N-body simulations. Using standard mass function and concentration-mass relation, we find predictions to be 1 % accurate at $z=0$ up to $k=0.8~h/{\rm Mpc}$ for the largest interaction strength tested ($\xi=50$ b/GeV), improving to $2~h/{\rm Mpc}$ at $z=1$. For smaller interaction strength ($10$ b/GeV), we find 1 % agreement at $z=1$ up to scales above $3.5~h/{\rm Mpc}$, being close to $1~h/{\rm Mpc}$ at $z=0$. Finally, we improve our predictions with the inclusion of baryonic feedback and massive neutrinos and study degeneracies between the effects of these contributions and those of the interaction. Limiting the scales to where our modelling is 1 % accurate, we find a degeneracy between the interaction and feedback, but not with massive neutrinos. We expect the degeneracy with feedback to be resolvable by including smaller scales. This work represents the first analytical tool for calculating the nonlinear spectrum for interacting dark energy models., Comment: 11 pages, 4 figures. Version 2: version accepted for publication in MNRAS, including additional explanations and minor corrections. The version of ReACT used in this work is available at https://github.com/PedroCarrilho/ReACT/tree/react_with_interact_baryons

Interacting dark energy models have been proposed as attractive alternatives to $\Lambda$CDM. Forthcoming Stage-IV galaxy clustering surveys will constrain these models, but they require accurate modelling of the galaxy power spectrum multipoles on mildly non-linear scales. In this work we consider a dark scattering model with a simple 1-parameter extension to $w$CDM - adding only $A$, which describes a pure momentum exchange between dark energy and dark matter. We then provide a comprehensive comparison of three approaches of modeling non-linearities, while including the effects of this dark sector coupling. We base our modeling of non-linearities on the two most popular perturbation theory approaches: TNS and EFTofLSS. To test the validity and precision of the modelling, we perform an MCMC analysis using simulated data corresponding to a $\Lambda$CDM fiducial cosmology and Stage-IV surveys specifications in two redshift bins, $z=0.5$ and $z=1$. We find the most complex EFTofLSS-based model studied to be better suited at both, describing the mock data up to smaller scales, and extracting the most information. Using this model, we forecast uncertainties on the dark energy equation of state, $w$, and on the interaction parameter, $A$, finding $\sigma_w=0.06$ and $\sigma_A=1.1$ b/GeV for the analysis at $z=0.5$ and $\sigma_w=0.06$ and $\sigma_A=2.0$ b/GeV for the analysis at $z=1$. In addition, we show that a false detection of exotic dark energy up to 3$\sigma$ would occur should the non-linear modelling be incorrect, demonstrating the importance of the validation stage for accurate interpretation of measurements., Comment: 30 pages, 10 figures. Version accepted for publication in JCAP

In the context of forthcoming galaxy surveys, to ensure unbiased constraints on cosmology and gravity when using non-linear structure information, percent-level accuracy is required when modelling the power spectrum. This calls for frameworks that can accurately capture the relevant physical effects, while allowing for deviations from $\Lambda$CDM. Massive neutrino and baryonic physics are two of the most relevant such effects. We present an integration of the halo model reaction frameworks for massive neutrinos and beyond-$\Lambda$CDM cosmologies. The integrated halo model reaction, combined with a pseudo power spectrum modelled by HMCode2020 is then compared against $N$-body simulations that include both massive neutrinos and an $f(R)$ modification to gravity. We find that the framework is 4% accurate down to at least $k\approx 3 \, h/{\rm Mpc}$ for a modification to gravity of $|f_{\rm R0}|\leq 10^{-5}$ and for the total neutrino mass $M_\nu \equiv \sum m_\nu \leq 0.15$ eV. We also find that the framework is 4% consistent with EuclidEmulator2 as well as the Bacco emulator for \B{most of the considered} $\nu w$CDM cosmologies down to at least $k \approx 3 \, h$/Mpc. Finally, we compare against hydrodynamical simulations employing HMCode2020's baryonic feedback modelling on top of the halo model reaction. For $\nu \Lambda$CDM cosmologies we find 2% accuracy for $M_\nu \leq 0.48$eV down to at least $k\approx 5h$/Mpc. Similar accuracy is found when comparing to $\nu w$CDM hydrodynamical simulations with $M_\nu = 0.06$eV. This offers the first non-linear, theoretically general means of accurately including massive neutrinos for beyond-$\Lambda$CDM cosmologies, and further suggests that baryonic, massive neutrino and dark energy physics can be reliably modelled independently., Comment: 13 pages, 11 figures. MNRAS accepted version. Download ReACT: https://github.com/nebblu/ReACT/tree/react_with_neutrinos

We study the potential of Bayesian Neural Networks (BNNs) to detect new physics in the dark matter power spectrum, concentrating here on evolving dark energy and modifications to General Relativity. After introducing a new technique to quantify classification uncertainty in BNNs, we train two BNNs on mock matter power spectra produced using the publicly available code $\tt{ReACT}$ in the $k$-range $\left(0.01 - 2.5\right) \, h \mathrm{Mpc}^{-1} $ and redshift bins $\left(0.1,0.478,0.783,1.5\right)$ with Euclid-like noise. The first network classifies spectra into five labels including $\Lambda$CDM, $f(R)$, $w$CDM, Dvali-Gabadaze-Porrati (DGP) gravity and a "random" class whereas the second is trained to distinguish $\Lambda$CDM from non-$\Lambda$CDM. Both networks achieve a comparable training, validation and test accuracy of $\sim 95\%$. Each network is also capable of detecting deviations from $\Lambda$CDM that were not included in the training set, demonstrated with spectra generated using the growth-index $\gamma$. We then quantify the constraining power of each network by computing the smallest deviation from $\Lambda$CDM such that the noise-averaged non-$\Lambda$CDM classification probability is at least $2\sigma$, finding these bounds to be $f_{R0} \lesssim 10^{-7}$, $\Omega_{rc} \lesssim 10^{-2} $, $-1.05 \lesssim w_0 \lesssim 0.95 $, $-0.2 \lesssim w_a \lesssim 0.2 $, $0.52 \lesssim \gamma \lesssim 0.59 $. The bounds on $f(R)$ can be improved by training a specialist network to distinguish solely between $\Lambda$CDM and $f(R)$ power spectra which can detect a non-zero $f_{R0}$ at $\mathcal{O}\left(10^{-8}\right)$ with a confidence $>2\sigma$. We expect that further developments, such as the inclusion of smaller length scales or additional extensions to $\Lambda$CDM, will only improve the potential of BNNs to detect new physics using cosmological datasets., Comment: 19+9 pages, 16 figures, code available at https://github.com/Mik3M4n/BaCoN, data available at https://doi.org/10.5281/zenodo.4309918. v2: matches version accepted for publication in PRD. v3: title matches published version

We present constraints on extensions to the flat $\Lambda$CDM cosmological model by varying the spatial curvature $\Omega_K$, the sum of the neutrino masses $\sum m_\nu$, the dark energy equation of state parameter $w$, and the Hu-Sawicki $f(R)$ gravity $f_{R0}$ parameter. With the combined $3\times2$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 (2dFLenS), we find results that are fully consistent with a flat $\Lambda$CDM model with $\Omega_K=0.011^{+0.054}_{-0.057}$, $\sum m_\nu<1.76$ eV (95% CL), and $w=-0.99^{+0.11}_{-0.13}$. The $f_{R0}$ 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 $\Lambda$CDM model or any of the considered extensions. Besides extensions to the flat $\Lambda$CDM parameter space, we also explore restrictions to common subsets of the flat $\Lambda$CDM 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 CMB. Neither the beyond-$\Lambda$CDM models nor the imposed restrictions explored in this analysis are able to resolve the $\sim 3\sigma$ tension in $S_8$ between the $3\times2$pt constraints and Planck, with the exception of $w$CDM, where the $S_8$ tension is resolved. The tension in the $w$CDM case persists, however, when considering the joint $S_8$-$w$ parameter space. The joint flat $\Lambda$CDM CMB lensing and $3\times2$pt analysis is found to yield tight constraints on $\Omega_{\rm m}=0.307^{+0.008}_{-0.013}$, $\sigma_8=0.769^{+0.022}_{-0.010}$, and $S_8=0.779^{+0.013}_{-0.013}$., Comment: 15 pages, 9 figures, 3 tables, accepted in A&A. This paper concludes the KiDS-1000 series of papers: Heymans, Tr\"oster et al. (arXiv:2007.15632), Asgari et al. (arXiv:2007.15633), Hildebrandt et al. (arXiv:2007.15635), Joachimi et al. (arXiv:2007.01844), and Giblin et al. (arXiv:2007.01845). Data products, likelihoods, and posteriors can be found http://kids.strw.leidenuniv.nl/DR4/lensing.php

We examine the extent to which primordial black holes (PBHs) can constitute the observed dark matter while also giving rise to the measured matter-antimatter asymmetry and account for the observed baryon abundance through asymmetric Hawking radiation generated by a derivative coupling of curvature to the baryon-lepton current. We consider both broad and monochromatic mass spectra for this purpose. For the monochromatic spectrum we find that the correct dark matter and baryon energy densities are recovered for peak masses of the spectrum of $M_{\rm pk} \geq 10^{12}$ kg whereas for the broad case the observed energy densities can be reproduced regardless of peak mass. Adopting some simplifications for the early-time expansion history as a first approximation, we also find that the measured baryon asymmetry can be recovered within an order of magnitude. We argue furthermore that the correct value of the baryon-lepton yield can in principle be retrieved for scenarios where a significant amount of the radiation is produced by PBH decay during or after reheating, as is expected when the decaying PBHs also cause reheating, or when an early matter-dominated phase is considered. We conclude from this first analysis that the model merits further investigation., Comment: 26 pages, 6 figures, 2 tables

Despite the great observational success of the standard cosmological model some discrepancies in the inferred parameter constraints have manifested among a number of cosmological data sets. These include a tension between the expansion rate of our Cosmos as inferred from the cosmic microwave background (CMB) and as found from local measurements, the preference for an enhanced amplitude of CMB lensing, a somewhat low quadrupole moment of the CMB fluctuations as well as a preference for a lower amplitude of matter fluctuations in large-scale structure surveys than inferred from the CMB. We analyse these observational tensions under the addition of spatial curvature and a free CMB background temperature that may deviate from its locally measured value. With inclusion of these parameters, we observe a trend in the parameter constraints from CMB and baryon acoustic oscillation data towards an open and hotter universe with larger current expansion rate, standard CMB lensing amplitudes, lower amplitude of matter fluctuations, and marginally lower CMB quadrupole moment, consistently reducing the individual tensions among the cosmological data sets. Combining this data with local distance measurements, we find a preference for an open and hotter universe beyond the 99.7% confidence level. Finally, we briefly discuss a local void as a possible source for a deviation of the locally measured CMB temperature from its background value and as mimic of negative spatial curvature for CMB photons. This interpretation implies a $\sim$20% underdensity in our local neighbourhood of $\sim$10-100 Mpc in diameter, which is well within cosmic variance., Comment: 5 pages, 2 figures. Updated discussion on local void interpretation

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 $\Lambda$CDM for current and ongoing surveys. With further improvement, particularly in terms of the accuracy of the non-linear $\Lambda$CDM power spectrum, ReACT can, in principle, meet the accuracy requirements for future surveys such as Euclid and LSST., Comment: 14 pages, 5 figures, MNRAS accepted version. ReACT code available here: https://github.com/nebblu/ReACT

Constraints on gravity and cosmology will greatly benefit from performing joint clustering and weak lensing analyses on large-scale structure data sets. Utilising non-linear information coming from small physical scales can greatly enhance these constraints. At the heart of these analyses is the matter power spectrum. Here we employ a simple method, dubbed "Hybrid $P_\ell(k)$", based on the Gaussian Streaming Model (GSM), to calculate the quasi non-linear redshift space matter power spectrum multipoles. This employs a fully non-linear and theoretically general prescription for the matter power spectrum. We test this approach against comoving Lagrangian acceleration simulation measurements performed in GR, DGP and $f(R)$ gravity and find that our method performs comparably or better to the dark matter TNS redshift space power spectrum model for dark matter. When comparing the redshift space multipoles for halos, we find that the Gaussian approximation of the GSM with a linear bias and a free stochastic term, $N$, is competitive to the TNS model. Our approach offers many avenues for improvement in accuracy as well as further unification under the halo model., Comment: 34 pages, 16 figures, JCAP accepted version. HyPk code available at: https://github.com/nebblu/HyPk

Future large-scale structure surveys will measure three-point statistics with high statistical significance. This will offer significant improvements on our understanding of gravity, provided we can model these statistics accurately. We assess the performance of several schemes for theoretical modelling of the matter bispectrum, including halo-model based approaches and fitting formulae. We compare the model predictions against N-body simulations, considering scales up to $k_{\rm max} = 4 h/{\rm Mpc}$, well into non-linear regime of structure formation. Focusing on the equilateral configuration, we conduct this analysis for three theories of gravity: general relativity, $f(R)$ gravity, and the DGP braneworld model. Additionally, we compute the lensing convergence bispectrum for these models. We find that all current modelling prescriptions in modified gravity, in particular for theories with scale-dependent linear growth, fail to attain the accuracy required by the precision of the Stage IV surveys such as \emph{Euclid}. Among these models, we find that a halo-model corrected fitting formula achieves the best overall performance., Comment: 44 pages, 16 figures, 4 tables. JCAP accepted version

Future galaxy clustering surveys will probe small scales where non-linearities become important. Since the number of modes accessible on intermediate to small scales is very high, having a precise model at these scales is important especially in the context of discriminating alternative cosmological models from the standard one. In the mildly non-linear regime, such models typically differ from each other, and galaxy clustering data will become very precise on these scales in the near future. As the observable quantity is the angular power spectrum in redshift space, it is important to study the effects of non-linear density and redshift space distortion (RSD) in the angular power spectrum. We compute non-linear contributions to the angular power spectrum using a flat-sky approximation that we introduce in this work, and compare the results of different perturbative approaches with $N$-body simulations. We find that the TNS perturbative approach is significantly closer to the $N$-body result than Eulerian or Lagrangian 1-loop approximations, effective field theory of large scale structure or a halofit-inspired model. However, none of these prescriptions is accurate enough to model the angular power spectrum well into the non-linear regime. In addition, for narrow redshift bins, $\Delta z \lesssim 0.01$, the angular power spectrum acquires non-linear contributions on all scales, right down to $\ell=2$, and is hence not a reliable tool at this time. To overcome this problem, we need to model non-linear RSD terms, for example as TNS does, but for a matter power spectrum that remains reasonably accurate well into the deeply non-linear regime, such as halofit., Comment: 30 pages, 15 figures

Accurate modelling of non-linear scales in galaxy clustering will be crucial for data analysis of Stage IV galaxy surveys. A selection of competing non-linear models must be made based on validation studies. We provide a comprehensive set of forecasts of two different models for the halo redshift space power spectrum, namely the commonly applied TNS model and an effective field theory of large scale structure (EFTofLSS) inspired model. Using simulation data and a least-$\chi^2$ analysis, we determine ranges of validity for the models. We then conduct an exploratory Fisher analysis using the full anisotropic power spectrum to investigate parameter degeneracies. We proceed to perform an MCMC analysis utilising the monopole, quadrupole, and hexadecapole spectra, with a restricted range of scales for the latter in order to avoid biasing our growth rate, $f$, constraint. We find that the TNS model with a Lorentzian damping and standard Eulerian perturbative modelling outperforms other variants of the TNS model. Our MCMC analysis finds that the EFTofLSS-based model may provide tighter marginalised constraints on $f$ at $z=0.5$ and $z=1$ than the TNS model, despite having additional nuisance parameters. However this depends on the range of scales used as well as the fiducial values and priors on the EFT nuisance parameters. Finally, we extend previous work to provide a consistent comparison between the Fisher matrix and MCMC forecasts using the multipole expansion formalism, and find good agreement between them., Comment: 23 pages, 21 figures, MNRAS accepted version

We provide in depth MCMC comparisons of two different models for the halo redshift space power spectrum, namely a variant of the commonly applied Taruya-Nishimichi-Saito (TNS) model and an effective field theory of large scale structure (EFTofLSS) inspired model. Using many simulation realisations and Stage IV survey-like specifications for the covariance matrix, we check each model's range of validity by testing for bias in the recovery of the fiducial growth rate of structure formation. The robustness of the determined range of validity is then tested by performing additional MCMC analyses using higher order multipoles, a larger survey volume and a more highly biased tracer catalogue. We find that under all tests, the TNS model's range of validity remains robust and is found to be much higher than previous estimates. The EFTofLSS model fails to capture the spectra for highly biased tracers as well as becoming biased at higher wavenumbers when considering a very large survey volume. Further, we find that the marginalised constraints on $f$ for all analyses are stronger when using the TNS model., Comment: 25 pages, 19 figures. Accepted version for publication in JCAP

We assess the performance of the Taruya, Nishimichi and Saito (TNS) model for the halo redshift space power spectrum, focusing on utilising mildly non-linear scales to constrain the growth rate of structure f. Using simulations with volume and number density typical of forthcoming Stage IV galaxy surveys, we determine ranges of validity for the model at redshifts z = 0.5 and z = 1. We proceed to perform a Bayesian MCMC analysis utilising the monopole, quadrupole, and hexadecapole spectra, followed by an exploratory Fisher matrix analysis. As previously noted in other forecasts as well as in real data analyses, we find that including the hexadecapole can significantly improve the constraints. However, a restricted range of scales is required for the hexadecapole in order for the growth parameter estimation to remain unbiased, limiting the improvement. We consistently quantify these effects by employing the multipole expansion formalism in both our Fisher and MCMC forecasts., Comment: 12 pages, 7 figures, 2 tables, accepted in OJA

Cosmic microwave background (CMB) lensing is an integrated effect whose kernel is greater than half the peak value in the range $1

Gravity-induced non-Gaussianity in the large-scale structure of the Universe, characterised by higher-order statistics such as the bispectrum (three-point cumulant), is expected to contain rich cosmological information. A measurement of the bispectrum will not only improve the cosmological constraints, but also give us the possibility to probe gravity on cosmological scales. In this paper, we present a framework to numerically calculate the one-loop matter bispectrum based on standard perturbation theory (SPT). This approach allows general modifications to the standard $\Lambda$CDM model to be easily implemented. We demonstrate the performance of the bispectrum calculation in three representative cases, namely the Vainshtein-screened Dvali-Gabadadze-Porrati (DGP) model, the chameleon-screened Hu-Sawicki $f(R)$ model and the phenomenological dark scattering (DS) momentum-exchange model. The predicted bispectra are then compared with measured results from a set of cosmological $N$-body simulations, and the impact of possible systematics arising from simplified or approximate treatments in the perturbative calculation is studied in detail. We find that the one-loop bispectrum calculation offers significantly more information on general screening and momentum exchange effects than the leading-order bispectrum calculation. Further, the accuracy of the one-loop prediction is shown to be comparable to non-linear fitting formulas over a wide range of wavenumbers ($k\lesssim0.3\,h$$\mbox{Mpc}^{-1}$) even at lower redshifts, $z\lesssim 1$., Comment: 25 pages, 10 figures. Accepted version; minor text typos corrected, 3 references added

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 $\Lambda$CDM and nDGP at each redshift. At one-loop at $z = 0$, the reach of the EFTofLSS is $k_{\rm reach}\approx 0.14 \, h { \rm Mpc^{-1}}$ for both $\Lambda$CDM 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 $\Lambda$CDM and nDGP, and verify that this is proportional to the modification of the linear coupling constant of the Poisson equation., Comment: 34 pages, 12 figures; v2: JCAP published version, small improvements and additions

Modifications to gravity can provide attractive alternatives to the dark components of the standard model of cosmology. These modifications to general relativity (GR) must be hidden at small scales where theory is well tested, and so one naturally looks to the large scales in order to detect any deviations from GR. One particularly promising avenue in testing gravity at cosmological scales is within the anisotropy of galaxy clustering in redshift space. This thesis presents a framework for consistently constructing large scale structure observables in redshift space for gravitational theories that include an additional scalar degree of freedom, specifically, the Horndeski class of theories with a generalized potential term. The relevance of such a framework in the context of next generation spectroscopic surveys is then investigated using N-body simulations. The thesis concludes with ongoing and recently completed extensions to this framework, including interacting dark energy models and the effective field theory of large scale structure., Comment: Ph.D. thesis, University of Portsmouth January 2018. 230 pages, 59 figures

We investigate the capabilities of perturbation theory in capturing non-linear effects of dark energy. We test constant and evolving $\omega$ models, as well as models involving momentum exchange between dark energy and dark matter. Specifically, we compare perturbative predictions at 1-loop level against N-body results for four non-standard equations of state as well as varying degrees of momentum exchange between dark energy and dark matter. The interaction is modelled phenomenologically using a time dependent drag term in the Euler equation. We make comparisons at the level of the matter power spectrum and the redshift space monopole and quadrupole. The multipoles are modelled using the Taruya, Nishimichi and Saito (TNS) redshift space spectrum. We find perturbation theory does very well in capturing non-linear effects coming from dark sector interaction. We isolate and quantify the 1-loop contribution coming from the interaction and from the non-standard equation of state. We find the interaction parameter $\xi$ amplifies scale dependent signatures in the range of scales considered. Non-standard equations of state also give scale dependent signatures within this same regime. In redshift space the match with N-body is improved at smaller scales by the addition of the TNS free parameter $\sigma_v$. To quantify the importance of modelling the interaction, we create mock data sets for varying values of $\xi$ using perturbation theory. This data is given errors typical of Stage IV surveys. We then perform a likelihood analysis using the first two multipoles on these sets and a $\xi=0$ modelling, ignoring the interaction. We find the fiducial growth parameter $f$ is generally recovered even for very large values of $\xi$ both at $z=0.5$ and $z=1$. The $\xi=0$ modelling is most biased in its estimation of $f$ for the phantom $\omega=-1.1$ case., Comment: 22 pages, 15 figures. Added text elucidating method and results. Included new Fig. 12. Accepted for publication in JCAP

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 $\leq 6\%$ deviations in the first two correlation function multipoles for all models for separations in $50$Mpc$/h \leq s \leq 180$Mpc/$h$. 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., Comment: 21 pages, 8 figures, accepted for publication in JCAP

We use a set of N-body simulations employing a modified gravity (MG) model with Vainshtein screening to study matter and halo hierarchical clustering. As test-case scenarios we consider two normal branch Dvali-Gabadadze-Porrati (nDGP) gravity models with mild and strong growth rate enhancement. We study higher-order correlation functions $\xi_n(R)$ up to $n=9$ and associated hierarchical amplitudes $S_n(R)\equiv\xi_n(R)/\sigma(R)^{2n-2}$. We find that the matter PDFs are strongly affected by the fifth-force on scales up to $50h^{-1}$Mpc, and the deviations from GR are maximised at $z=0$. For reduced cumulants $S_n$, we find that at small scales $R\leq10h^{-1}$Mpc the MG is characterised by lower values, with the deviation growing from $7\%$ in the reduced skewness up to even $40\%$ in $S_5$. To study the halo clustering we use a simple abundance matching and divide haloes into thee fixed number density samples. The halo two-point functions are weakly affected, with a relative boost of the order of a few percent appearing only at the smallest pair separations ($r\leq 5h^{-1}$Mpc). In contrast, we find a strong MG signal in $S_n(R)$'s, which are enhanced compared to GR. The strong model exhibits a $>3\sigma$ level signal at various scales for all halo samples and in all cumulants. In this context, we find that the reduced kurtosis to be an especially promising cosmological probe of MG. Even the mild nDGP model leaves a $3\sigma$ imprint at small scales $R\leq3h^{-1}$Mpc, while the stronger model deviates from a GR-signature at nearly all scales with a significance of $>5\sigma$. Since the signal is persistent in all halo samples and over a range of scales, we advocate that the reduced kurtosis estimated from galaxy catalogues can potentially constitute a strong MG-model discriminatory as well as GR self-consistency test., Comment: 19 pages, 11 figures, comments are welcome

We elucidate the importance of the consistent treatment of gravity-model specific non-linearities when estimating the growth of cosmological structures from redshift space distortions (RSD). Within the context of standard perturbation theory (SPT), we compare the predictions of two theoretical templates with redshift space data from COLA (COmoving Lagrangian Acceleration) simulations in the normal branch of DGP gravity (nDGP) and General Relativity (GR). Using COLA for these comparisons is validated using a suite of full N-body simulations for the same theories. The two theoretical templates correspond to the standard general relativistic perturbation equations and those same equations modelled within nDGP. Gravitational clustering non-linear effects are accounted for by modelling the power spectrum up to one loop order and redshift space clustering anisotropy is modelled using the Taruya, Nishimichi and Saito (TNS) RSD model. Using this approach, we attempt to recover the simulation's fiducial logarithmic growth parameter $f$. By assigning the simulation data with errors representing an idealised survey with a volume of $10\mbox{Gpc}^3/h^3$, we find the GR template is unable to recover fiducial $f$ to within 1$\sigma$ at $z=1$ when we match the data up to $k_{\rm max}=0.195h$/Mpc. On the other hand, the DGP template recovers the fiducial value within $1\sigma$. Further, we conduct the same analysis for sets of mock data generated for generalised models of modified gravity using SPT, where again we analyse the GR template's ability to recover the fiducial value. We find that for models with enhanced gravitational non-linearity, the theoretical bias of the GR template becomes significant for stage IV surveys. Thus, we show that for the future large data volume galaxy surveys, the self-consistent modelling of non-GR gravity scenarios will be crucial in constraining theory parameters., Comment: 27 pages, 19 figures. Improved analysis using 20 x 1Gpc^3/h^3 MG-PICOLA simulations for nDGP and GR cosmologies. New appendix validating use of MG-PICOLA in the analysis and hence validating our conclusions. 3 new figures in main text (4,5,12) illustrating non-linearity. New Tables. I,II,III summarizing template performances. Cosmetic changes made to accommodate new data and analysis

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. 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 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 it's application within the light of upcoming high precision RSD data., Comment: 23 pages, 23 figures, accepted for publication in JCAP