Vacuum dynamics in the Universe: implications on the cosmological tensions

The possibility that the vacuum energy density (VED) could be time dependent in the expanding Universe is intuitively more reasonable than just a rigid cosmological constant for the entire cosmic history. The framework of the running vacuum model (RVM) is a remarcable example, in which the VED appears as a power series of the Hubble rate, H(t), and its derivatives. The RVM contributes to alleviate the cosmological tensions with the data, and at a more fundamental level it also helps to smooth out certain hardcore aspects of the cosmological constant problem. Finally, a very recent extensions of the RVM, in which the dark energy (DE) is a composite system made of running vacuum energy and an entity X called “phantom matter” (which is radically different from phantom DE, since the former produces positive pressure, like ordinary mattter, rather than the negative one produced by the latter) has proven capable to yield an excellent fit to the cosmological data. Such a fit, in addition, is compatible with the observed quintessence-like behavior around our time (as reported by the DESI Collaboration). In my talk, I will discuss some of these theoretical aspects of the VED and also some successful phenomenological implications. Strong electromagnetic and gravitational field physics: From laboratories to early Universe / 168 Renormalizing the vacuum energy in cosmological spacetime: a new approach to the cosmological constant problem Universitat de Barcelona 2 University of Barcelona Phenomenological studies in the last few years have provided significant support to the idea that the vacuum energy density (VED) is a running quantity with the cosmological evolution. Such a running actually helps in alleviating the cosmological tensions afflicting the ΛCDM. The theoretical studies backing up this approach go under the name of “running vacuum model” (RVM). Using this framework, based on quantum field theory (QFT) in curved spacetime, one can show that the properly renormalized VED in FLRW spacetime can be freed from fine tuning troubles and the vacuum dynamics proves to be a smooth power series of the Hubble rate H and its time derivatives. The calculation is performed using a new version of the adiabatic renormalization procedure, which leads to a cosmic evolution with the value of H, i.e. ρ_vac(H). As a result the “cosmological constant” Λ appears here as the nearly sustained value of 8πG(H)ρ_vac(H) around (any) given epoch H, where G(H) is the gravitational coupling, which runs very mildly (logarithmically). The VED evolution between points H and H_0 of the cosmic history reads δρvac(H)∼ν_eff m_Pl^2(H^2−H_0^2) (where the coefficient |νef|≪1) and m_Pl is the Planck mass. The effective coefficient ν_eff receives contributions from all the quantized matter fields and can be explicitly computed in QFT. Remarkably, there also exist higher powers of H which can trigger inflation in the early universe. Finally, the equation of state (EoS) of the running 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 appear as quintessence, as DESI has reported. But the ultimate source of the dynamics stems from the running QFT vacuum, not from fundamental quintessence fields.