Back Reaction of Cosmological Perturbations and the Cosmological Constant Problem

TL;DR

This paper investigates how cosmological fluctuations influence the universe's background, suggesting that infrared modes may dynamically cancel the cosmological constant, with implications for understanding dark energy.

Contribution

It compares two methods of quantifying back-reaction effects and proposes a potential mechanism for the dynamical cancellation of the cosmological constant.

Findings

Infrared modes contribute a negative effective energy-momentum tensor.

Back-reaction effects can be large despite small fluctuation amplitudes.

Infrared mode effects cancel in single-field inflation but may be significant in multi-field models.

Abstract

The presence of cosmological fluctuations influences the background cosmology in which the perturbations evolve. This back-reaction arises as a second order effect in the cosmological perturbation expansion. The effect is cumulative in the sense that all fluctuation modes contribute to the change in the background geometry, and as a consequence the back-reaction effect can be large even if the amplitude of the fluctuation spectrum is small. We review two approaches used to quantify back-reaction. In the first approach, the effect of the fluctuations on the background is expressed in terms of an effective energy-momentum tensor. We show that in the context of an inflationary background cosmology, the long wavelength contributions to the effective energy-momentum tensor take the form of a negative cosmological constant, whose absolute value increases as a function of time since the phase space of infrared modes is increasing. This then leads to the speculation that gravitational back-reaction may lead to a dynamical cancellation mechanism for a bare cosmological constant, and yield a scaling fixed point in the asymptotic future in which the remnant cosmological constant satisfies $\Omega_{\Lambda} \sim 1$. We then discuss how infrared modes effect local observables (as opposed to mathematical background quantities) and find that the leading infrared back-reaction contributions cancel in single field inflationary models. However, we expect non-trivial back-reaction of infrared modes in models with more than one matter field.