Running vacuum in QFT in FLRW spacetime: the dynamics of $$\rho _{\textrm{vac}}(H)$$ from the quantized matter fields

Abstract

Phenomenological work in the last few years has provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution and that this running helps to alleviate the cosmological tensions afflicting the $$\Lambda $$ Λ CDM. On the theoretical side, recent devoted studies have shown that the properly renormalized $$\rho _{\textrm{vac}}$$ ρ vac in QFT in FLRW spacetime adopts the ‘running vacuum model’ (RVM) form. While in three previous studies by two of us (CMP and JSP) such computations focused solely on scalar fields non-minimally coupled to gravity, in the present work we compute the spin-1/2 fermionic contributions and combine them both. The calculation is performed using a new version of the adiabatic renormalization procedure based on subtracting the UV divergences at an off-shell renormalization point M. The quantum scaling of $$\rho _{\textrm{vac}}$$ ρ vac with M turns into cosmic evolution with the Hubble rate, H. As a result the ‘cosmological constant’ $$\Lambda $$ Λ appears in our framework as the nearly sustained value of $$8\pi G(H)\rho _{\textrm{vac}}(H)$$ 8 π G ( H ) ρ vac ( H ) around (any) given epoch H, where G(H) is the gravitational coupling, which is also running, although very mildly (logarithmically). We find that the VED evolution at present reads $$\delta \rho _\textrm{vac}(H)\sim \nu _{\textrm{eff}}\, m_{\textrm{Pl}}^2 \left( H^2-H_0^2 \right) \ (|\nu _{\textrm{eff}}|\ll 1)$$ δ ρ vac ( H ) ∼ ν eff m Pl 2 H 2 - H 0 2 ( | ν eff | ≪ 1 ) . The coefficient $$\nu _{\textrm{eff}}$$ ν eff receives contributions from all the quantized fields, bosons and fermions, which we compute here for an arbitrary number of matter fields. Remarkably, there also exist higher powers $$\mathcal{O}(H^{6})$$ O ( H 6 ) which can trigger inflation in the early universe. Finally, the equation of state (EoS) of the vacuum receives also quantum corrections from bosons and fermion fields, shifting its value from − 1. The striking consequence is that the EoS of the quantum vacuum may nowadays effectively appears as quintessence.

Stringy running vacuum model and current tensions in cosmology

“…In this way one may avoid the cosmological constant problem. In this respect, we also mention that similar conclusions can be reached in the QFT approach to RVM in the context of theories involving matter fields in curved (cosmological) spacetimes, whereby the novel renormalization studies of [31][32][33][34] also lead to the avoidance of the appearance of a cosmological constant term in the renormalized effective action, in contrast to conventional approaches.…”

“…Apart from serving as prototypes, where such quantum-graviton corrections can be computed reliably, such supergravities play an important rôle also for the physics of StRVM, providing a microscopic origin of the primordial chiral GWs that lead to the CS condensates which drive the RVM inflationary period [44,45]. We stress that such logarithmic corrections H 2 ln(H) also appear in QFT by integrating out matter quantum fields [31][32][33][34]. In the current work we constrain the StRVM by making use of an updated and rich set of cosmological measurements, and study the potential alleviation of the Hubble tension and the tension with the large-scale structure (LSS) data.…”

“…The RVM framework is also capable of explaining the entropy production and, in general, thermodynamical properties of the Universe as being consequences of the decay of the running vacuum [19,[28][29][30]. More recently, the RVM acquired a more fundamental status, which goes beyond the above phenomenological description, in that the VED advocated in it can be derived within the context of renormalizable QFT in curved spacetime, including the appropriate terms (in fact, emerging as quantum effects derived from the effective QFT action) that can trigger inflation in a dynamical way in the early Universe, as shown in [31][32][33][34]-see also [12] for the essentials. Remarkably, the RVM can arguably provide viable alternatives to the ΛCDM at late epoch, with in-principle observable deviations from it, compatible with the current phenomenology, as well as Big-Bang-Nucleosynthesis (BBN) data [35], which remarkably lead to similar order of magnitude of the RVM parameters with those of current-era phenomenology.…”

“…As pointed out above, the RVM as a successful phenomenological framework can be derived within the context of QFT in Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime [31][32][33][34]. It would, however, be desirable to derive the various coefficients parametrising the RVM energy density also from alternative microscopic descriptions.…”

“…In contrast, in the local QFT approach, gravity is considered as a background, and it is matter which is viewed as quantum and integrated over in a path-integral framework. In the QFT approach, in the context of scalar field theories with non-minimal coupling to space-time curvature, one obtains explicit H 6 and higher powers in the VED [32,34]. So far, the explicit H 4 RVM corrections to the VED have been reproduced explicitly only within the StRVM framework, as well as a one-loop supergravity framework in a de Sitter background [52][53][54][55] 5 .…”