Choice of Quantum Vacuum for Inflation Observables

TL;DR

This paper examines how choosing an $oldsymbol{ ext{alpha}}$-vacuum instead of the Bunch--Davies vacuum affects inflationary observables within the Starobinsky model, finding strong observational constraints on such modifications.

Contribution

It provides a detailed comparison of inflationary predictions from $oldsymbol{ ext{alpha}}$-vacua and the Bunch--Davies vacuum, highlighting the constraints from current data.

Findings

$oldsymbol{ ext{alpha}}$-vacua induce limited corrections to spectral index and its runnings.

Energy scale considerations for $oldsymbol{ ext{alpha}}$-vacua are consistent with current experimental bounds.

Latest Planck data strongly restrict the viability of $oldsymbol{ ext{alpha}}$-vacua as initial states.

Abstract

We investigate the modifications to inflationary observables that arise when adopting an $\alpha$-vacuum instead of the standard Bunch--Davies vacuum for quantum fluctuations during inflation. Within the Starobinsky inflationary model, we compute and compare the scalar spectral index, its running, and the running of the running arising from different choices of the initial vacuum state. We further examine the energy scales associated with $\alpha$-vacua and argue that, for any number of extra spatial dimensions, the relevant scale can be truncated at the Hubble scale, $\sim$$\mathcal{O}(10^{13})\,\mathrm{GeV}$, without conflict with current Cavendish-type experimental bounds on sub-millimeter gravity ($\sim$$250\,\mu\mathrm{m}$). Our analysis demonstrates that the $\alpha$-vacuum is subject to stringent constraints as a viable de~Sitter-invariant alternative to the Euclidean (Bunch--Davies) vacuum, with the corrections that it induces in the inflationary observables being strongly limited by the latest Planck data.