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Using a perturbative approach we solve stellar structure equations for low-density (solar-type) stars whose interior is described with a polytropic equation of state in scenarios involving a subset of modified gravity theories. Rather than focusing on particular theories, we consider a model-independent approach in which deviations from General Relativity are effectively described by a single parameter $xi$. We find that for length scales below those set by stellar General Relativistic radii the modifications introduced by modified gravity can affect the computed values of masses and radii. As a consequence, the stellar luminosity is also affected. We discuss possible further implications for higher density stars and observability of the effects before described.
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We introduce The Novel Probes Project, an initiative to advance the field of astrophysical tests of the dark sector by creating a forum that connects observers and theorists. This review focuses on tests of gravity and is intended to be of use primarily to observers, but also to theorists with interest in the development of experimental tests. It is twinned with a separate review on tests of dark matter self-interactions (Adhikari et al., in prep.). Our focus is on astrophysical probes of gravity in the weak-field regime, ranging from stars to quasilinear cosmological scales. These are complementary to both strong-field tests and background and linear probes in cosmology. In particular, the nonlinear screening mechanisms that are an integral part of viable modified gravity models lead to characteristic signals specifically on astrophysical scales. The constraining power of these signals is not limited by cosmic variance, but comes with the challenge of building robust theoretical models of the nonlinear dynamics of stars, galaxies, clusters and large scale structure. In this review we lay the groundwork for a thorough exploration of the astrophysical regime with an eye to using the current and next generation of observations for tests of gravity. We begin by setting the scene for how theories beyond General Relativity are expected to behave, focusing primarily on screened fifth forces. We describe the analytic and numerical techniques for exploring the pertinent astrophysical systems, as well as the signatures of modified gravity. With these in hand we present a range of observational tests, and discuss prospects for future measurements and theoretical developments.
The phenomenology of modified Newtonian dynamics (MOND) on galaxy scales may point to more fundamental theories of either modified gravity (MG) or modified inertia (MI). In this paper, we test the applicability of the global deep-MOND parameter $Q$ which is predicted to vary at the $10%$ level between MG and MI theories. Using mock-observed analytical models of disk galaxies, we investigate several observational uncertainties, establish a set of quality requirements for actual galaxies, and derive systematic corrections in the determination of $Q$. Implementing our quality requirements to the SPARC database yields $15$ galaxies, which are close enough to the deep-MOND regime as well as having rotation curves that are sufficiently extended and sampled. For these galaxies, the average and median values of $Q$ seem to favor MG theories, albeit both MG and MI predictions are in agreement with the data within $1.5sigma$. Improved precision in the determination of $Q$ can be obtained by measuring extended and finely-sampled rotation curves for a significant sample of extremely low-surface-brightness galaxies.
Verlindes heuristic argument for the interpretation of the standard Newtonian gravitational force as an entropic force is generalized by the introduction of a minimum temperature (or maximum wave length) for the microscopic degrees of freedom on the holographic screen. With the simplest possible setup, the resulting gravitational acceleration felt by a test mass m from a point mass M at a distance R is found to be of the form of the modified Newtonian dynamics (MOND) as suggested by Milgrom. The corresponding MOND-type acceleration constant is proportional to the minimum temperature, which can be interpreted as the Unruh temperature of an emerging de-Sitter space. This provides a possible explanation of the connection between local MOND-type two-body systems and cosmology.
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.
We review the effective field theory of modified gravity in which the Lagrangian involves three dimensional geometric quantities appearing in the 3+1 decomposition of space-time. On the flat isotropic cosmological background we expand a general action up to second order in the perturbations of geometric scalars, by taking into account spatial derivatives higher than two. Our analysis covers a wide range of gravitational theories-- including Horndeski theory/its recent generalizations and the projectable/non-projectab
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