An extension of the cosmological standard model with a bounded Hubble expansion rate

Abstract

The possibility of having an extension of the cosmological standard model with a Hubble expansion rate H constrained to a finite interval is considered. Two periods of accelerated expansion arise naturally when the Hubble expansion rate approaches to the two limiting values. The new description of the history of the universe is confronted with cosmological data and with several theoretical ideas going beyond the standard cosmological model.

Linearized treatment of scalar perturbations in the Asymptotic Cosmological Model

“…In our previous work [13] we found that given an expansion history parameterized by a modified Friedman equation in a universe filled by a given component, it was always possible to find a biparametric family of f (R) theories (see Ref. [27] for a review) which had the same homogeneous evolution as a solution of their equations of motion.…”

“…The solution of the system of equations (45), (46) together with the equation of state of the dominant component of the stress-energy tensor, defines R (0) and its derivatives as functions of the Hubble parameter H [13]. If we expand (44) in powers of the scalar perturbations of the FRW metric (11), the first order term gives the linearized equations for the perturbations.…”

“…The set of equations coming from G µ i;µ = 0 define the terms proportional to e mn and f mn in (15) as a function of the terms in (14). The set of equations coming from G µ 0;µ define the rest of the terms in (15) as a function of the terms in (14) and (13). Therefore, the only freedom, for what concerns linearized perturbations, is that of choosing the set of functions {a nm , b nm , c nm , d nm }, with some of them fixed by the homogeneous dynamics (1).…”

“…[13]. In this model the universe is filled with photons and neutrinos (massless particles), baryons (electrically charged massive particles) and Dark Matter (electrically neutral massive particles), but General Relativity (GR) is only a good approximation to the gravitational interaction in a certain range of the Hubble rate H, between but far from its two bounds, H − and H + .…”

“…The Asymptotic Cosmological Model (ACM) was presented [13] as a strictly phenomenological generalization of the Standard Cosmological Model including a past and a future epoch of accelerated expansion. It follows from the assumptions that GR is not a fundamental theory, but only a good approximation when the Hubble rate H is between but far away from two fundamental scales H − and H + , which act as bounds on H. A general covariant metric theory of gravity without spatial curvature is assumed.…”