The H0 trouble: Confronting Non-thermal Dark Matter and Phantom Cosmology with the CMB, BAO, and Type Ia Supernovae data

We have witnessed different values of the Hubble constant being found in the literature in the past years. Albeit, early measurements often result in an $H_0$ much smaller than those from late-time ones, producing a statistically significant discrepancy, and giving rise to the so-called Hubble tension. The trouble with the Hubble constant is often treated as a cosmological problem. However, the Hubble constant can be a laboratory to probe cosmology and particle physics models. In our work, we will investigate if the possibility of explaining the $H_0$ trouble using non-thermal dark matter production aided by phantom-like cosmology is consistent with the Cosmic Background Radiation (CMB) and Baryon Acoustic Oscillation (BAO) data. We performed a full Monte Carlo simulation using CMB and BAO datasets keeping the cosmological parameters ${\mathrm{\Omega }}_b{h}^2$, ${\mathrm{\Omega }}_c{h}^2$, $100\theta$, ${\tau }_{opt}$, and $w$ as priors and concluded that a non-thermal dark matter production aided by phantom-like cosmology yields at most $H_0=70.5$ km s${}^{-1}$Mpc${}^{-1}$ which is consistent with some late-time measurements. However, if $H_0>72$ km s${}^{-1}$ Mpc${}^{-1}$ as many late-time observations indicate, an alternative solution to the Hubble trouble is needed. Lastly, we limited the fraction of relativistic dark matter at the matter-radiation equality to be at most 1%.