General relativity (GR) was proven via the direct detection of gravitational waves from mergers binary black holes and neutron stars by advanced LIGO virgo detectors. These detections confirmed prediction GR provided first evidence existence stellar-mass (BHs). However, occurrence singularities at centers BHs suggests that is inapplicable because breakdown equivalence principle singularities. T...

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present ...

Along this review, we focus on the study of several properties of modified gravity theories, in particular on black-hole solutions and its comparison with those solutions in General Relativity, and on Friedmann–Lemaı̂tre–Robertson–Walker metrics. The thermodynamical properties of fourth order gravity theories are also a subject of this investigation with special attention on local and global sta...

We review inflationary cosmology in modified gravity such as R gravity with its extensions in order to generalize the Starobinsky inflation model. In particular, we explore inflation realized by three kinds of effects: modification of gravity, the quantum anomaly, and the R term in loop quantum cosmology. It is explicitly demonstrated that in these inflationary models, the spectral index of sca...

The method and probability of distinguishing between the Λ cold dark matter (ΛCDM) model and modified gravity are studied from future observations for the growth rate of cosmic structure (Euclid redshift survey). We compare the mock observational data to the theoretical cosmic growth rate by modified gravity models, including the extended Dvali–Gabadadze–Porrati (DGP) model, kinetic gravity bra...

Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the Universe. Modified gravity theories have richer observational consequences for large scale structures than conventional dark energy models, in that different observables are not described by a single growth factor even in the linear regime. We examine the relationships betw...