Short Distance Physics and the Consistency Relation for Scalar and Tensor Fluctuations in the Inflationary Universe

TL;DR

The paper investigates whether short-distance (trans-Planckian) physics can alter inflationary fluctuations by adopting a generalized initial vacuum rather than the Bunch-Davies state. It develops a formalism with Bogoliubov-like parameters γ_k^S and γ_k^T that modify the scalar and tensor power spectra, leading to spectral indices n_S and n_T with additional contributions d(ln γ)/d ln k and to a tensor-to-scalar ratio A_T^2/A_S^2 = ε γ_k^T/ γ_k^S. Consequently, the standard single-field consistency relation $A_T^2/A_S^2 = -n_T/2$ is generically violated unless specific conditions on γ_k^S, γ_k^T, and ε hold, and even small vacuum-induced modulations can be observationally relevant. The work highlights the vacuum state as a crucial determinant of inflationary predictions and suggests that tensor-mode measurements could probe high-energy physics via trans-Planckian effects.

Abstract

Recent discussions suggest the possibility that short distance physics can significantly modify the behavior of quantum fluctuations in the inflationary universe, and alter the standard large scale structure predictions. Such modifications can be viewed as due to a different choice of the vacuum state. We show that such changes generally lead to violations of the well-known consistency relation between the scalar to tensor ratio and the tensor spectral index. Vacuum effects can introduce an observable modulation to the usual predictions for the scalar and tensor power spectra.