Unifying the study of background dynamics and perturbations in $f(R)$-gravity

Abstract

In this paper we show how the covariant gauge invariant equations for the evolution of scalar, vector and tensor perturbations for a generic f (R)-gravity theory can be recast in order to exploit the power of dynamical system methodology. In this way, recent results describing the dynamics of the background FRW model can be easily combined with these equations to reveal important details pertaining to the evolution of cosmological models in fourth order gravity.

Axial dissipative dust as a source of gravitational radiation in f(R) gravity

“…where F = df dR and = ∇ ν ∇ ν . The density (ρ (D) ), pressure (p (D) ) and energy flux (q (D) α ) associated with the dark source are given by [29]…”

Cosmological dynamics of fourth order gravity: A compact view

“…In the non -compact analysis developed in [26], non of these boundary points appear. Furthermore, even though N ± is not a boundary point, it doesn't appear in [26], because of it's special location in the phase space -it lies exactly on the intersection of the plane x = 0 and the surface z = y = 1 − (Q + x) 2 .…”

“…In the non -compact analysis developed in [26], non of these boundary points appear. Furthermore, even though N ± is not a boundary point, it doesn't appear in [26], because of it's special location in the phase space -it lies exactly on the intersection of the plane x = 0 and the surface z = y = 1 − (Q + x) 2 . In this case one has to take the limit of Γ carefully as one approaches this point and the standard techniques of finding fixed points breaks down for this case.…”

Cosmological dynamics of fourth order gravity

“…The solutions obtained in this way have to be considered particular solutions of the cosmological equations which are found by using a specific ansatz (i.e. the fixed point condition [25]). For this reason it is important to stress that only direct substitution of the results derived from this approach in the cosmological equations can ensure that the solution is physical (i.e.…”