Steepest Growth in the Primordial Power Spectrum from Excited States at a Sudden Transition

TL;DR

This paper investigates how different initial quantum states during inflation, especially excited states, influence the steepest possible growth of the primordial power spectrum following a sudden transition, affecting small-scale density perturbations.

Contribution

It demonstrates that the growth rate of the primordial power spectrum after a transition depends on the initial quantum state, with $k^6$ growth possible for certain excited states, extending previous understanding.

Findings

$k^6$ growth possible for $ ext{α}>0$

$k^4$ growth for $ ext{α}\leq0$ including Bunch-Davies

Enhanced small-scale power spectrum sensitive to initial quantum state

Abstract

Sudden phase transitions during inflation can give rise to strongly enhanced primordial density perturbations on scales much smaller than those directly probed by cosmic microwave background anisotropies. In this paper, we study the effect of the incoming quantum state on the steepest growth found in the primordial power spectrum using a simple model of an instantaneous transition during single-field inflation. We consider the case of a general de Sitter-invariant initial state for the inflaton field (the $\alpha$-vacuum), and also an incoming state perturbed by a preceding transition. For the $\alpha$-vacua we find that $k^6$ growth is possible for $\alpha>0$, while $k^4$ growth is seen for $\alpha\leq0$, including the standard case of an initial Bunch-Davies vacuum state. The features of an enhanced primordial power spectrum on small scales are thus sensitive to the initial quantum state during inflation. We calculate the scalar-induced gravitational wave power spectrum for each case.