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Recent studies of QFT in cosmological spacetime indicate that the speeding up of the present universe may not just be associated with a rigid cosmological term but with a running one that evolves with the expansion rate $\Lambda =\Lambda \left(H\right)$. This running is inherited from the cosmic evolution of the vacuum energy density (VED), ${\rho }_{\mathrm{vac}}$, which is sensitive to quantum effects in curved spacetime that ultimately trigger that running. The VED is a function of the Hubble rate and its time derivatives ${\rho }_{\mathrm{vac}}={\rho }_{\mathrm{vac}}(H,\dot{H},\ddot{H},\dots )$. Two nearby points of cosmic evolution during the FLRW epoch are smoothly related as $\delta {\rho }_{\mathrm{vac}}\sim \mathcal{O}\left(H^2\right)$. In the very early universe, in contrast, the higher powers of the Hubble rate take over and bring about a period of fast inflation. They originate from quantum effects on the effective action of a vacuum, which we compute. Herein, we focus on the lowest possible power for inflation to occur: $H^4$. During the inflationary phase, H remains approximately constant and very large. Subsequently, the universe enters the usual FLRW radiation epoch. This new mechanism (‘RVM inflation’) is not based on any supplementary ‘inflaton’ field; it is fueled by pure QFT effects on the dynamical background and is different from Starobinsky’s inflation, in which H is never constant. Full article

A substantial body of phenomenological and theoretical work over the last few years strengthens the possibility that the vacuum energy density (VED) of the universe is dynamical, and in particular that it adopts the ‘running vacuum model’ (RVM) form, in which the VED evolves mildly as $\delta {\rho }_{\mathrm{vac}}\left(H\right)\sim {\nu }_{\mathrm{eff}}{m}_{\mathrm{Pl}}^2\mathcal{O}\left(H^2\right)$, where H is the Hubble rate and ${\nu }_{\mathrm{eff}}$ is a (small) free parameter. This dynamical scenario is grounded on recent studies of quantum field theory (QFT) in curved spacetime and also on string theory. It turns out that what we call the ‘cosmological constant’, $\mathsf{\Lambda }$, is no longer a rigid parameter but the nearly sustained value of $8\pi G\left(H\right){\rho }_{\mathrm{vac}}\left(H\right)$ around any given epoch $H\left(t\right)$, where $G\left(H\right)$ is the gravitational coupling, which can also be very mildly running (logarithmically). Of particular interest is the possibility suggested in past works that such a running may help to cure the cosmological tensions afflicting the $\mathsf{\Lambda }$CDM. In the current study, we reanalyze the RVM in full and we find it becomes further buttressed. Using modern cosmological data, namely a compilation of the latest SNIa+BAO+$H\left(z\right)$+LSS+CMB observations, we probe to what extent the RVM provides a quality fit better than the concordance $\mathsf{\Lambda }$CDM model, with particular emphasis on its impact on the ${\sigma }_8$ and $H_0$ tensions. We utilize the Einstein–Boltzmann system solver CLASS and the Monte Carlo sampler MontePython for the statistical analysis, as well as the statistical DIC criterion to compare the running vacuum against the rigid vacuum (${\nu }_{\mathrm{eff}}=0$). On fundamental grounds, ${\nu }_{\mathrm{eff}}$ receives contributions from all the quantized matter fields in FLRW spacetime. We show that with a tiny amount of vacuum dynamics (${\nu }_{\mathrm{eff}}\ll 1$) the global fit can improve significantly with respect to the $\mathsf{\Lambda }$CDM and the mentioned tensions may subside to inconspicuous levels. Full article

We elaborate further on the compatibility of the “vacuumon potential” that characterises the inflationary phase of the running vacuum model (RVM) with the swampland criteria. The work is motivated by the fact that, as demonstrated recently by the authors, the RVM framework can be derived as an effective gravitational field theory stemming from underlying microscopic (critical) string theory models with gravitational anomalies, involving condensation of primordial gravitational waves. Although believed to be a classical scalar field description, not representing a fully fledged quantum field, we show here that the vacuumon potential satisfies certain swampland criteria for the relevant regime of parameters and field range. We link the criteria to the Gibbons–Hawking entropy that has been argued to characterise the RVM during the de Sitter phase. These results imply that the vacuumon may, after all, admit under certain conditions, a rôle as a quantum field during the inflationary (almost de Sitter) phase of the running vacuum. The conventional slow-roll interpretation of this field, however, fails just because it satisfies the swampland criteria. The RVM effective theory derived from the low-energy effective action of string theory does, however, successfully describe inflation thanks to the $\sim H^4$ terms induced by the gravitational anomalous condensates. In addition, the stringy version of the RVM involves the Kalb–Ramond (KR) axion field, which, in contrast to the vacuumon, does perfectly satisfy the slow-roll condition. We conclude that the vacuumon description is not fully equivalent to the stringy formulation of the RVM. Our study provides a particularly interesting example of a successful phenomenological theory beyond the $\Lambda$CDM, such as the RVM, in which the fulfilment of the swampland criteria by the associated scalar field potential, along with its compatibility with (an appropriate form of) the weak gravity conjecture, prove to be insufficient conditions for warranting consistency of the scalar vacuum field representation as a faithful ultraviolet complete representation of the RVM at the quantum gravity level. Full article