Non-Unitary Evolution in the General Extended EFT of Inflation & Excited Initial States

TL;DR

This paper explores non-unitary evolution in the extended EFT of inflation, showing how certain solutions lead to excited initial states and finite power spectra, with implications for UV physics and initial conditions.

Contribution

It introduces a detailed analysis of the time-dependent dispersion relations in gEEFToI, revealing conditions for excited initial states and finite power spectra through solutions of the Confluent Heun equation.

Findings

Non-unitary evolution leads to excited initial states.

Finite power spectra require specific eigensolutions of the CH equation.

Loss of unitarity at small wavelengths influences initial state choices.

Abstract

I study the "general" case that arises in the Extended Effective Field Theory of Inflation (gEEFToI), in which the coefficients of the sixth order polynomial dispersion relation depend on the physical wavelength of the fluctuation mode, hence they are time-dependent. At arbitrarily short wavelengths the unitarity is lost for each mode. Depending on the values of the gEEFToI parameters in the unitary gauge action, two scenarios can arise: in one, the coefficients of the polynomial become singular, flip signs at some physical wavelength and asymptote to a constant value as the wavelength of the mode is stretched to infinity. Starting from the WKB vacuum, the two-point function is essentially singular in the infinite IR limit. In the other case, the coefficients of the dispersion relation evolve monotonically from zero to a constant value in the infinite IR. In order to have a finite power spectrum starting from the vacuum in this case, the mode function has to be an eigensolution of the Confluent Heun (CH) equation, which leads to a very confined parameter space for gEEFToI. Finally, I look at a solution of the CH equation which is regular in the infinite IR limit and yields a finite power spectrum in either scenario. I demonstrate that this solution asymptotes to an excited state in past infinity in both cases. The result is interpreted in the light of the loss of unitarity for very small wavelengths. The outcome of such a non-unitary phase evolution should prepare each mode in the excited initial state that yields a finite two-point function for all the parameter space. This will be constraining of the new physics that UV completes such scenarios.