Back Reaction of Cosmological Perturbations and the Cosmological Constant Problem

TL;DR

The paper investigates how cosmological perturbations back-react on the background and on local observables, focusing on infrared scalar modes in inflation. It introduces two approaches: an effective energy-momentum tensor $\tau_{\mu\nu}$ describing back-reaction, which for IR modes acts like a negative cosmological constant whose magnitude grows with time, and a local observable analysis of the expansion rate $\Theta$, which shows leading IR effects cancel in single-field models but may persist in multi-field setups. The key finding is that infrared back-reaction can dynamically attenuate the bare cosmological constant, potentially yielding a late-time state with $\Omega_{\Lambda} \sim 1$, though this relies on extrapolations beyond linear perturbation theory and on multi-field dynamics. The work highlights both the intriguing possibility of a dynamical relaxation mechanism for $\Lambda$ and the significant unresolved issues regarding covariance, observability, and nonperturbative validity, pointing to further theoretical development especially in multi-field contexts. $\Lambda_{\mathrm{eff}}(t) = \Lambda_0 + 8\pi G\rho_{br}(t)$ plays a central role in the speculative mechanism, with the IR phase space growth driving the evolution toward a potential scaling regime with $\Lambda_{\mathrm{eff}}$ comparable to the matter density.

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 $Ω_Λ \sim 1$. 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.