Early dark energy from zero-point quantum fluctuations

Abstract

We examine a cosmological model with a dark energy density of the form $ρ_{DE}(t)=ρ_X(t)+ρ_Z(t)$, where $ρ_X$ is the component that accelerates the Hubble expansion at late times and $ρ_Z(t)$ is an extra contribution proportional to $H^2(t)$. This form of $ρ_Z(t)$ follows from the recent proposal that the contribution of zero-point fluctuations of quantum fields to the total energy density should be computed by subtracting the Minkowski-space result from that computed in the FRW space-time. We discuss theoretical arguments that support this subtraction. By definition, this eliminates the quartic divergence in the vacuum energy density responsible for the cosmological constant problem. We show that the remaining quadratic divergence can be reabsorbed into a redefinition of Newton's constant only under the assumption that the energy-momentum tensor of vacuum fluctuations is conserved in isolation. However, in the presence of an ultra-light scalar field $X$ with $m_X<H_0$, as typical of some dark energy models, the gravity effective action depends both on the gravitational field and on the $X$ field. In this case general covariance only requires the conservation of the total energy-momentum tensor, including both the classical term $T^X_{μν}$ and the vacuum expectation value of T_{μν}. If there is an exchange of energy between these two terms, there are potentially observable consequences. We construct an explicit model with an interaction between $ρ_X$ and $ρ_Z$ and we show that the total dark energy density $ρ_{DE}(t)=ρ_X(t)+ρ_Z(t)$ always remains a finite fraction of the critical density at any time, providing a specific model of early dark energy. We discuss the implication of this result for the coincidence problem and we estimate the model parameters by means of a full likelihood analysis using current CMB, SNe Ia and BAO data.