Abstract
We derive the evolution equation for the density matrix of a UV- and IR- limited band of comoving momentum modes of the canonically normalized scalar degree of freedom in two examples of nearly de Sitter universes. Including the effects of a cubic interaction term from the gravitational action and tracing out a set of longer wavelength modes, we find that the evolution of the system is non-Hamiltonian and non-Markovian. We find linear dissipation terms for a few modes with wavelength near the boundary between system and bath and nonlinear dissipation terms for all modes. The non-Hamiltonian terms persist to late times when the scalar field dynamics is such that the curvature perturbation continues to evolve on super-Hubble scales.
Highlights
In cosmological models for the primordial universe, the unavoidable quantum fluctuations of matter and of the linearized gravitational field are the original source of the rich structure of late-time inhomogeneities observed today as variations in the temperature of the cosmic microwave background (CMB) [1] and the distribution of galaxies [2]
The fact that our cosmological observations today are limited to a finite volume of space, leaving sufficiently long wavelength modes fundamentally unobservable, leads to an interesting conundrum for studies of inflationary particle physics via postinflation statistics: if fluctuations with wavelengths observable to us can be coupled to fluctuations on unobservable scales, there is additional non-Gaussian sample variance [3,4,5,6,7,8,9,10,11,12] that affects the precision with which inferences can be made from the data
The relative qualitative time-dependence of the two cases is not affected by this choice: As the figure shows, both the linear and nonlinear dissipation terms decay with time in the slowroll case, but increase in the nonattractor case, when bath modes are summed over, as η → 0−
Summary
In cosmological models for the primordial universe, the unavoidable quantum fluctuations of matter and of the linearized gravitational field are the original source of the rich structure of late-time inhomogeneities observed today as variations in the temperature of the cosmic microwave background (CMB) [1] and the distribution of galaxies [2]. The fact that our cosmological observations today are limited to a finite volume of space, leaving sufficiently long wavelength modes fundamentally unobservable, leads to an interesting conundrum for studies of inflationary particle physics via postinflation statistics: if fluctuations with wavelengths observable to us can be coupled to fluctuations on unobservable scales, there is additional non-Gaussian sample variance [3,4,5,6,7,8,9,10,11,12] that affects the precision with which inferences can be made from the data. We use the fact of IR-limited observational cosmology and the associated issue of classical non-Gaussian cosmic variance, as motivation to investigate the quantum evolution equations of a system of cosmological modes coupled to a bath of these long wavelength modes, during an inflationary era.
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