The Hubble Tension in Light of the Symmetry of Scale Invariance

Abstract: When the expansion rate of the Universe at recombination is used to infer the present expansion rate $H_0$, the value derived in the $Λ$CDM model, $H_0=67.4$ km/s/mpc, is about in 6$\, σ$ tension with the value measured locally, $H_0=74$ km/s/mpc. In this work, we consider instead the expansion history in the context of the symmetry of scale-invariant vacuum (SIV model). We first perform two major cosmological tests: the Hubble diagram for type-Ia supernovae and the fundamental relation between $H_0$, the age of the Universe, and the total density of matter, $Ω_m$. This allows us to constrain $Ω_m$ in SIV, with both tests giving the best agreement for $Ω_m \simeq 0.20$. We then study the physical connections of the dynamical and thermal states of the Universe at recombination with the present Hubble constant, $H_0$, and the present temperature, $T$, in the $Λ$CDM and SIV contexts. We find that, in SIV, the properties at recombination may be conveyed to the present ones ($T=2.726$ and $H_0$ at $z=0$) without any tension, indicating $H_0=74$ km/s/mpc in spite of the anchoring on the CMB. This is due to the slightly different expansion and temperature histories of the two cosmological models. Importantly, this happens to occur for $Ω_m \simeq 0.20$, as constrained in SIV with supernovae and cosmic age. This suggests that the Hubble tension currently found between $H_0$ values in the early and late Universe may simply be the result of $ΛCDM$ ignoring the small but still measurable effects of scale invariance.