Model independent results for the inflationary epoch and the breaking of the degeneracy of models of inflation

Abstract

We address the problem of determining inflationary characteristics in a model independent way. We start from a recently proposed equation which allows to accurately calculate the value of the inflaton at horizon crossing ${\varphi }_k$. We then use an equivalent form of this equation to write a formula that relates the number of e-folds from horizon crossing to the pivot scale $N_{ke}+N_{ep}$ with the tensor-to-scalar index $r$, hence a general bound for $N_{ke}+N_{ep}$ follows. $N_{ke}$ is the number of e-folds from the scale factor $a_k$ during inflation to the end of inflation at $a_e$ and $N_{ep}$ is the number of e-folds from $a_e$ to the pivot scale factor $a_p$. In particular, at present $r<0.063$ implies $N_{ke}+N_{ep}<112.5$ e-folds at $k=k_p$ and 128.1 e-folds at the present scale with wavenumber mode $k_0$. We also give a lower bound to the size of the universe during the inflationary epoch that gave rise to the current observable universe. We also discussed the problem of degeneracy of inflationary models and argue that this degeneration can only be resolved by studying model predictions from the reheating epoch.

13 pages, four tables, three figures. Accepted for publication in JCAP. Small changes to match the accepted version

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Cited by in corpus (8)

• Curing inflationary degeneracies using reheating predictions and relic gravitational waves
• Reheating in Models with Non-minimal Coupling in metric and Palatini formalisms
• Model independent bounds for the number of $e$-folds during the evolution of the universe
• Issues in Palatini ${\mathcal{R}}^2$ inflation: Bounds on the Reheating Temperature
• Power spectrum of density fluctuations, halo abundances and clustering with primordial black holes
• GEO-FPT: a model of the galaxy bispectrum at mildly non-linear scales
• Constraints for the running index independent of the parameters of the model
• Breaking the degeneracy of non-canonical quartic inflation by reheating considerations