Inflationary universe from perfect fluid andF(R)gravity and its comparison with observational data

Abstract

We investigate the descriptions for the observables of inflationary models, in particular, the spectral index of curvature perturbations, the tensor-to-scalar ratio, and the running of the spectral index, in the framework of perfect fluid models and F (R) gravity theories through the reconstruction methods. Furthermore, the perfect fluid and F (R) gravity descriptions of inflation are compared with the recent cosmological observations such as the Planck satellite and BICEP2 experiment. It is demonstrated with explicit examples that perfect fluid may lead to the inflationary universe consistent with the Planck data. It is also shown that several F (R) gravity models, especially, a power-law model gives the best fit values compatible with the spectral index and tensor-to-scalar ratio within the allowed ranges suggested by the Planck and BICEP2 results.

Accelerating cosmologies and the phase structure ofF(R)gravity with Lagrange multiplier constraints: A mimetic approach

“…[25] (see also [26]). As was demonstrated in [25], the F (R) gravity can be treated as a perfect fluid, and in effect the observational indices can be expressed in terms of the Hubble rate and its higher derivatives. The same applies in our case so we refrain from going into details, however we need to stress that this formalism is valid if some slow-roll approximation is used, meaning that the slow-roll indices have small values during inflation.…”

“…According to the formalism of Ref. [25], the spectral index of primordial curvature perturbations and the scalar-to-tensor ratio r read,…”

“…We shall employ the formalism for the calculation of the Jordan frame observational indices, which was developed in Ref. [25] (see also [26]). As was demonstrated in [25], the F (R) gravity can be treated as a perfect fluid, and in effect the observational indices can be expressed in terms of the Hubble rate and its higher derivatives.…”

“…[25], the slow-roll indices are written as functions of the e-folding number N , in the following way,…”

Spotting deviations fromR2inflation

“…[24,37,38]) accounting for the dark matter component [39,40], the growth of large-scale structures [41] and to provide a mechanism for cosmological inflation through, for instance, the Starobinsky inflationary model [42,43], which is constructed with an extra term to the Einstein-Hilbert Lagrangian of the form f (R) = R 2 . Other recent proposals have been scrutinised in [44][45][46]. One is then tempted to consider general theories of the Ricci scalar with some kind of coupling to an extra scalar field in order to observe potential effects distinguishable from the standard f (R) counterpart predictions.…”