Abstract
We analyse several saddle point inflationary scenarios based on power-law f(R) models. We investigate inflation resulting from f(R)=R+αnM2(1−n)Rn+αn+1M−2nRn+1 and f(R)=∑nlαnM2(1−n)Rn as well as l→∞ limit of the latter. In all cases we have found relation between αn coefficients and checked consistency with the PLANCK data as well as constraints coming from the stability of the models in question. Each of the models provides solutions which are both stable and consistent with PLANCK data, however only in parts of the parameter space where inflation starts on the plateau of the potential, some distance from the saddle. And thus all the correct solutions bear some resemblance to the Starobinsky model.
Highlights
Cosmic inflation [1,2,3] is a theory of the early universe which predicts cosmic acceleration and generation of seeds of the large scale structure of the present universe
In this paper we considered several f (R) theories with saddle point in the Einstein frame potential
Term R, Starobinsky term α2 R2 and higher order terms which are the source of the saddle point
Summary
Cosmic inflation [1,2,3] is a theory of the early universe which predicts cosmic acceleration and generation of seeds of the large scale structure of the present universe. In order to obtain small r one needs a low-scale inflation, which may be provided by a potential with a saddle point. In order to obtain quasi de Sitter evolution of space–time one needs a range of energies for which the R2 M−2 term dominates the Lagrangian density This would require all higher order corrections (such as R3, R4, etc.) [21] to be suppressed by a mass scale much bigger than M. One naturally expects all higher order correction to GR to appear at the same energy scale if one wants to avoid the fine-tuning of coefficients of all higher order terms From this perspective it would be better to generate inflation in f (R) theory without the Starobinsky plateau, which in principle could be obtained in the saddle point inflation. In the low scale inflation one obtains gives 1 − ns 2|η|
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