Observability of the total inflationary expansion

TL;DR

This paper investigates the maximum number of inflationary e-folds observable through CMB measurements, considering fluctuations that violate the null energy condition and lead to black hole formation, thus limiting inflation's observability.

Contribution

It provides a new calculation of the upper bound on observable e-folds during inflation, accounting for NEC violations and black hole formation, refining previous constraints.

Findings

Maximum observable e-folds are around 10^5 in simple inflation models.

The boundary of the fluctuation-dominated regime is precisely defined with a few percent uncertainty.

The upper bound is significantly smaller than the de Sitter entropy after inflation.

Abstract

I consider the question of possible observability of the total number of e-folds accumulated during the epoch of inflation. The total number of observable e-folds has been previously constrained by the de Sitter entropy after inflation, assuming that the null energy condition (NEC) holds. The NEC is violated by upward fluctuations of the local Hubble rate, which occur with high probability in the fluctuation-dominated regime of inflation. These fluctuations lead at late times to the formation of black holes and thus limit the observability of inflationary evolution. I compute the maximum number <Delta N> of e-folds that can be observed in principle through measurements of the CMB at arbitrarily late times (if the dark energy disappears). The calculation also provides a reasonably precise definition of the boundary of the fluctuation-dominated regime, with an uncertainty of a few percent. In simple models of single-field inflation compatible with current CMB observations, I find <Delta N> of order 10^5. This upper bound on the observable e-folds, although model-dependent, is much smaller than the de Sitter entropy after inflation. The method of calculation can be used in other models of single-field inflation.