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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 summarize the statuses of these models in their attempts to solve the different cosmological constant problems while being able to account for current astrophysical and cosmological observations. [ABSTRACT FROM AUTHOR]

In the context of forthcoming galaxy surveys, to ensure unbiased constraints on cosmology and gravity when using non-linear structure information, per cent-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 cold dark matter (ΛCDM). 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 ΛCDM 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 per cent accurate down to at least |$k\approx 3 \, h\, {\rm Mpc}^{-1}$| for a modification to gravity of | f R0| ≤ 10−5 and for the total neutrino mass M ν ≡ ∑ m ν ≤ 0.15 eV. We also find that the framework is 4 per cent consistent with EuclidEmulator2 as well as the Bacco emulator for most of the considered ν w CDM cosmologies down to at least |$k \approx 3 \, h$|  Mpc−1. Finally, we compare against hydrodynamical simulations employing HMCode2020 's baryonic feedback modelling on top of the halo model reaction. For νΛCDM cosmologies, we find 2 per cent accuracy for M ν ≤ 0.48 eV down to at least k ≈ 5 h  Mpc−1. Similar accuracy is found when comparing to ν w CDM hydrodynamical simulations with M ν = 0.06 eV. This offers the first non-linear, theoretically general means of accurately including massive neutrinos for beyond-ΛCDM cosmologies, and further suggests that baryonic, massive neutrino, and dark energy physics can be reliably modelled independently. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

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-χ2 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 utilizing 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 marginalized 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. [ABSTRACT FROM AUTHOR]

Neutron star models are studied in the context of scalar-tensor theories of gravity in the presence of a conformally coupled scalar field, using two different numerical equations of state (EoS) representing different degrees of stiffness. In both cases we obtain a complete solution by matching the interior numerical solution of the coupled Einstein-scalar field hydrostatic equations, with an exact metric on the surface of the star. These are then used to find the effect of the scalar field and its coupling to geometry, on the neutron star structure, particularly the maximum neutron star mass and radius. We show that in the presence of a conformally coupled scalar field, neutron stars are less dense and have smaller masses and radii than their counterparts in the minimally coupled case, and the effect increases with the magnitude of the scalar field at the center of the star. [ABSTRACT FROM AUTHOR]

Understanding non-linear 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 Λ cold dark matter, 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 per cent accurate at z  = 0 up to k  = 0.8  h  Mpc−1 for the largest interaction strength tested (ξ = 50 b GeV−1), improving to 2  h  Mpc−1 at z  = 1. For smaller interaction strength (10 b GeV−1), we find 1 per cent agreement at z  = 1 up to scales above 3.5  h  Mpc−1, being close to 1  h  Mpc−1 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 per cent 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 non-linear spectrum for interacting dark energy models. [ABSTRACT FROM AUTHOR]