Variable cosmological constant as a Planck scale effect

Abstract

We construct a semiclassical Friedmann-Lemaître-Robertson-Walker (FLRW) cosmological model assuming a running cosmological constant (CC). It turns out that the CC becomes variable at arbitrarily low energies due to the remnant quantum effects of the heaviest particles, e.g. the Planck scale physics. These effects are universal in the sense that they lead to a low-energy structure common to a large class of high-energy theories. Remarkably, the uncertainty concerning the unknown high-energy dynamics is accumulated into a single parameter ν, such that the model has an essential predictive power. Future Type Ia supernovae experiments (like SNAP) can verify whether this framework is correct. For the flat FLRW case and a moderate value ν ∼ 10 −2 , we predict an increase of 10 − 20% in the value of Ω Λ at redshifts z = 1 − 1.5 perfectly reachable by SNAP.

Density perturbations for a running cosmological constant

“…of having no perturbations associated to entropy exchange) and of having no anisotropic stress contributions, we have derived the complete coupled set of matter density and metric perturbations for this model. The RG running of Λ is based on the assumption of a standard quadratic decoupling law at low energies [29,32] energy density [11]. It is important to emphasize that this does not mean that Λ ∼ H 2 , but rather that the (renormalization group) variation of Λ satisfies δΛ ∼ H 2 , and hence Λ = a + b H 2 -see Eq.…”

“…(4.9), we cannot exclude that |ν| could be higher (mainly in the ν > 0 case) once it will 7 The results of these references were presented in terms of a parameter ǫ, and they concluded that values of ǫ at the level of 10 −1 are allowed. However, ǫ is nothing but 3 times the parameter ν originally defined in [29].…”

“…(ii) Conservation law (following from the Bianchi identity) which regulates the exchange of energy between matter and vacuum, 2) and (iii) the renormalization group equation for the CC density, assuming a soft form of decoupling for the cosmological constant [11,29,31] …”

“…The complete analytic solution of the equations (2.1), (2.2), (2.3) can be found in [29,32]. Here we present only those formulas which are relevant for the perturbations calculus.…”

“…The comparison served to place a bound at the level of 10% on the maximum possible difference between the two derivations of the matter power spectrum [43]. By requiring that the amplification of the density fluctuations of the RG model at the recombination era do not surpass this bound the authors of [40] were able to obtain a corresponding bound on the the RG parameter of [29], specifically ν < 10 −3 . Of course this bound is only approximate as it does not come from a direct calculation of the density perturbations in the RG model.…”