Constraints on just enough inflation preceded by a thermal era

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, $H_{\inf }$, which is in severe conflict with the upper bound from tensor perturbations. Alternatively, imposing the upper bound on $H_{\inf }$ 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.

Clearer presentation, agrees with published version

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• Warm bounce in loop quantum cosmology and the prediction for the duration of inflation
• Thermal gravitational-wave background in the general pre-inflationary scenario
• Semiclassical predictions regarding a pre-inflationary era and its effects on the power spectrum
• A solution to the initial condition problems of inflation : NATON
• Lowering tensor-to-scalar ratio by pre-inflationary dynamics
• A plausible solution to the problem of initial conditions for inflation