Choice of Quantum Vacuum for Inflation Observables

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.

14 pages, 4 figures

References in corpus (18)

• Planck 2018 results. X. Constraints on inflation
• String Theory Dynamics In Various Dimensions
• Planck 2013 results. XXII. Constraints on inflation
• DESI 2024 VI: Cosmological Constraints from the Measurements of Baryon Acoustic Oscillations
• Sub-millimeter Tests of the Gravitational Inverse-square Law
• Hawking Radiation and Black Hole Thermodynamics
• A note on inflation and transplanckian physics
• Infinitely Large New Dimensions
• DESI 2024 III: Baryon Acoustic Oscillations from Galaxies and Quasars
• Inflation in Models with Large Extra Dimensions Driven by a Bulk Scalar Field
• Inflation with General Initial Conditions for Scalar Perturbations
• Dynamics of a large extra dimension inspired hybrid inflation model
• $\alpha$-vacuum and inflationary bispectrum
• Mukhanov-Sasaki equation in manifestly gauge-invariant linearized cosmological perturbation theory with dust reference fields
• Large extra dimensions from higher-dimensional inflation
• Corrections to $n_s$ and $n_t$ from high scale physics
• The Effect of $\alpha$-Vacua on the Scalar and Tensor Spectral Indices: Slow-Roll Approximation
• Alpha-Vacua, Black Holes, and AdS/CFT