Zero-point quantum fluctuations in cosmology

Abstract

We reexamine the classic problem of the renormalization of zero-point quantum fluctuations in a Friedmann-Robertson-Walker background. We discuss a number of issues that arise when regularizing the theory with a momentum-space cutoff, and show explicitly how introducing noncovariant counterterms allows to obtain covariant results for the renormalized vacuum energy-momentum tensor. We clarify some confusion in the literature concerning the equation of state of vacuum fluctuations. Further, we point out that the general structure of the effective action becomes richer if the theory contains a scalar field ϕ with mass m smaller than the Hubble parameter H(t). Such an ultralight particle cannot be integrated out completely to get the effective action. Apart from the volume term and the Einstein-Hilbert term, that are reabsorbed into renormalizations of the cosmological constant and Newton’s constant, the effective action in general also has a term proportional to F(ϕ)R, for some function F(ϕ). As a result, vacuum fluctuations of ultralight scalar fields naturally lead to models where the dark energy density has the form ρDE(t) =ρx(t) + ρz(t), where ρX is the component that accelerates the Hubble expansion at late times and ρz(t)is an extra contribution proportional to H2(t). We perform a detailed comparison of such models with CMB, SNIa and BAO dat

Infrared Non-local Modifications of General Relativity

“…As a matter of fact, had we started with a regularization that preserves covariance, such as dimensional regularization, this is the result we would have obtained. Thus, the apparent 1/3 ratio is an artefact of our regularization scheme, and the physics cannot depend on it [11][12][13].…”

“…Indeed, an important remark is that this is merely a "naturalness" argument, not a prediction [11][12][13]16]. In QFT the parameters of the Lagrangian cannot be predicted, only their dependence on the probing scale can, i.e.…”

“…without having considered any limit and non-perturbatively [44,45], 13 . Another advantage is that in the presence of a heavy source with mass M S , the corresponding Vainshtein radius r V ∼ m −2 M −2 M S 1/3 is now larger than the distance at which the effective theory breaks down, so that there exists a region where GR is recovered [31,32,47].…”

“…But even if the phenomenology privileges one of these metrics, we would still be left with a "God-given" non-dynamical field. One way to 13 Note however that this does not necessarily imply that the Minkowski solution is stable in the fully non-linear theory. Indeed, it is already a remarkably difficult task to demonstrate this in the case of GR [46].…”

Can dark energy emerge from quantum effects in a compact extra dimension?

“…Nevertheless, this procedure introduces two flaws: i) the energy density scales as k d+1 c , which leads to a catastrophic value compared to the observed energy density in our universe for any scale k c related to high-energy physics scales; ii) this cutoff in momentum explicitly violates Lorentz-invariance and leads to a vacuum expectation value of the energy-momentum tensor, which is not proportional to g µν and therefore cannot be accepted as such for a description of vacuum. The inclusion of non-Lorentz invariant counter terms can restore the symmetry and lead to the correct equation of state (Hollenstein et al 2012). Another convenient approach is to use a covariant regularization, such as the dimensional regularization in which the number of dimensions d is written as d = D + , with D an integer and → 0.…”