Large Blue Spectral Isocurvature Spectral Index Signals Time-Dependent Mass

TL;DR

This paper demonstrates that a constant-mass isocurvature dark matter field limits the measurable spectral index to about 2.4, suggesting that higher observed indices imply time-dependent masses during inflation.

Contribution

It establishes a theoretical upper bound on the isocurvature spectral index for constant-mass fields, linking measurements to the dynamics of inflationary degrees of freedom.

Findings

Maximum spectral index for constant-mass fields is about 2.4.

Future measurements exceeding this index indicate time-dependent masses.

Bound is robust against reheating details and improves with better tensor-to-scalar ratio constraints.

Abstract

We show that if a spectator linear isocurvature dark matter field degree of freedom has a constant mass through its entire evolution history, the maximum measurable isocurvature spectral index that is consistent with the current tensor-to-scalar ratio bound is about 2.4, even if experiments can be sensitive to a $10^{-6}$ contamination of the predominantly adiabatic power spectrum with an isocurvature power spectrum at the shortest observable length scales. Hence, any foreseeable future measurement of a blue isocurvature spectral index larger than about 2.4 may provide nontrivial evidence for dynamical degrees of freedom with time-dependent masses during inflation. The bound is not sensitive to the details of the reheating scenario and can be made mildly smaller if the tensor-to-scalar ratio is better constrained in the future.