Addressing the $H_0$ tension through matter with pressure and no early dark energy

Abstract: We propose that the Hubble tension arises due to an unaccounted additional component, that behaves as \emph{matter with pressure}. We demonstrate that this fluid remains subdominant compared to both dust and radiation throughout nearly the entire universe expansion history. Specifically, the additional fluid satisfies the Zel'dovic limit with a constant equation of state, $\omega_s > 0$, and a quite small normalized energy density, $\Omega_s$. Accordingly, this component modifies both the sound horizon and the background expansion rate, \emph{acting quite differently from early dark energy models}, without significantly affecting the other cosmological parameters. To show this, we perform a Monte Carlo Markov chain analysis of our model, hereafter dubbed $\Lambda_{\omega_s}$CDM paradigm, using the publicly available \texttt{CLASS} Boltzmann code. Our results confirm the presence of this fluid, with properties that closely resemble those of radiation. We find best-fit values that satisfy $\omega_s \lesssim \omega_\gamma$ and a relative energy density $\Omega_s / \Omega_\gamma = 0.45$, with $\omega_r$ and $\Omega_r$ the equation of state and density of photons, respectively. The effective fluid may be associated with generalized K-essence models or, alternatively, with Proca-type vector fields, albeit we do not exclude \emph{a priori} more exotic possibilities, i.e., dark radiation, axions, and so on. Physical implications of our results are analyzed in detail, indicating a statistical preference for the $\Lambda_{\omega_s}$CDM scenario over the conventional $\Lambda$CDM background.