Eur. Phys. J. Plus (2013) 128: 155
https://doi.org/10.1140/epjp/i2013-13155-4

Regular Article

Cosmological implications of a viable non-analytical f(R) model

¹ Dipartimento di Fisica, Università di Napoli “Federico II” and INFN, Napoli, Italy
² Dipartimento di Fisica, Università di Roma “Sapienza”, Rome, Italy
³ Dipartimento di Fisica e Scienze della Terra, Università di Ferrara and INFN, Rome, Italy
⁴ ENEA - C.R. Frascati (Rome), UTFUS-MAG, Rome, Italy

^* e-mail: giovanni.montani@frascati.enea.it

Received: 18 November 2013
Revised: 25 November 2013
Accepted: 27 November 2013
Published online: 16 December 2013

Abstract

Power-law corrections (having the exponent strictly between 2 and 3) to the Einstein-Hilbert action yield an extended theory of gravity which is consistent with Solar-System tests and properly reproduces the main phases of the Universe thermal history. We find two distinct constraints for the characteristic length scale of the model: a lower bound from the Solar-System test and an upper bound by requiring the existence of the matter-dominated era. We also show how the extended framework can accommodate the existence of an early de Sitter phase. Within the allowed range of characteristic length scales, the relation between the expansion rate and the energy scale of inflation is modified, yielding a value of the rate several orders of magnitude smaller than in the standard picture. The observational implication of this fact is that a tiny value of the tensor-to-scalar ratio is expected in the extended framework. The suppression of primordial tensor modes also implies that the inflationary scale can be made arbitrarily close to the Planck one according to the current limits. Finally, an analysis of the propagation of gravitational waves on a Robertson-Walker background is addressed.