Disformal map and Petrov classification in modified gravity

Nonderivative modified gravity: a classification

We analyze the theories of gravity modified by a generic nonderivative potential built from the metric, under the minimal requirement of unbroken spatial rotations. Using the canonical analysis, we classify the potentials V according to the number of degrees of freedom (DoF) that propagate at the nonperturbative level. We then compare the nonperturbative results with the perturbative DoF propag...

Riemannian Curvature and the Petrov Classification

Let M be a Lorentzian space-time manifold. If p G 31, let TV(M) denote the tangent space to M at p and let I e Tp (M ) be a null vector. Because of the identification of radiation in General Relativity with null geodesic congruences of curves in M, one is led to study the geometrical properties of the wave surfaces of I. These are the two dimensional subspaces of TP(M), each member of which is ...

Disformal Inflation

We show how short inflation naturally arises in a non-minimal gravity theory with a scalar field without any potential terms. This field drives inflation solely by its derivatives, which couple to the matter only through the combination ḡμν = gμν − 1 m4∂μφ∂νφ. The theory is free of instabilities around the usual Minkowski vacuum. Inflation lasts as long as φ̇ > m, and terminates gracefully once ...

Modified gravity and cosmology

Viscosity in Modified Gravity

A bulk viscosity is introduced in the formalism of modified gravity. It is shown that, based on a natural scaling law for the viscosity, a simple solution can be found for quantities such as the Hubble parameter and the energy density. These solutions may incorporate a viscosity-induced Big Rip singularity. By introducing a phase transition in the cosmic fluid, the future singularity can nevert...