Cosmological long wavelength perturbations

TL;DR

This paper derives exact solutions for long wavelength scalar perturbations in cosmology, clarifies their local effects, and discusses implications for the cosmological constant and inflationary perturbation strength.

Contribution

It provides an exact solution framework for scalar long wavelength perturbations and analyzes their physical implications, addressing recent debates in cosmology.

Findings

Long wavelength perturbations are coordinate transformations locally.

Local observers cannot detect the effect of perturbations driving the cosmological constant to zero.

Initial conditions are crucial in understanding the strength of perturbations after inflation.

Abstract

This paper presents an exact solution to the long wavelength perturbations for the scalar modes and for a scalar field theory with arbitrary potential. Locally these modes are coordinate transformations of the homogeneous background solutions (although non-locally they are not). These solutions are then used to discuss a couple of recent papers in which such perturbations play a role. Abramo, Brandenberger, and Mukhanov have recently argued that long wavelength perturbations have the effect of driving the cosmological constant to zero if the higher order perturbation equation are examined. I argue that this effect is invisible to any local observer, and thus does not constitute a relaxation of the cosmological constant in the normal sense of the term. Grishchuk has argued that the standard lore on the strength of the perturbations at the end of inflation is wrong. I discuss the disagreement in light of the exact long wavelength solutions, and emphasize the importance of the initial conditions in resolving the disagreement.