Constraints on just enough inflation preceded by a thermal era

TL;DR

This paper explores constraints on 'just enough' inflation models that are preceded by a thermal era, revealing conflicts with observational bounds unless an extremely large number of relativistic degrees of freedom is assumed.

Contribution

It provides new bounds on the Hubble parameter and thermal conditions for pre-inflationary eras in minimal inflation models, highlighting significant theoretical challenges.

Findings

Upper bound on inflaton temperature from CMB data

Lower bound on Hubble parameter conflicts with tensor constraints

Requires an unrealistically large number of relativistic degrees of freedom

Abstract

If the inflationary era is preceded by a radiation dominated era in which the inflaton too was in thermal equilibrium at some very early time then the CMB data places an upper bound on the comoving temperature of the (decoupled) inflaton quanta. In addition, if one considers models of "just enough" inflation, where the number of e-foldings of inflation is just enough to solve the horizon and flatness problems, then we get a lower bound on the Hubble parameter during inflation, $H_{\rm inf}$, which is in severe conflict with the upper bound from tensor perturbations. Alternatively, imposing the upper bound on $H_{\rm inf}$ implies that such scenarios are compatible with the data only if the number of relativistic degrees of freedom in the thermal bath in the pre-inflationary Universe is extremely large (greater than $10^9$ or $10^{11})$. We are not aware of scenarios in which this can be satisfied.