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We link observational parameters such as the deceleration parameter, the jerk, the kerk (snap) and higher-order derivatives of the scale factor, called statefinders, to the conditions which allow to develop sudden future singularities of pressure with finite energy density. In this context, and within the framework of Friedmann cosmology, we also propose higher-order energy conditions which relate time derivatives of the energy density and pressure which may be useful in general relativity.
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-Lemaitre-Robertson-Walker metrics. The
The effects of a running gravitational coupling and the entropic force on future singularities are considered. Although it is expected that the quantum corrections remove the future singularities or change the singularity type, treating the running g
We study a metric cubic gravity theory considering odd-parity modes of linear inhomogeneous perturbations on a spatially homogeneous Bianchi type I manifold close to the isotropic de Sitter spacetime. We show that in the regime of small anisotropy, t
The models of cyclic universes and cyclic multiverses based on the alternative gravity theories of varying constants are considered.
Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven toward a drastic end known as the `Big Rip singularity where al