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We have witnessed different values of the Hubble constant being found in theliterature in the past years. Albeit, early measurements often result in an$H_0$ much smaller than those from late-time ones, producing a statisticallysignificant discrepancy, and giving rise to the so-called Hubble tension. Thetrouble with the Hubble constant is often treated as a cosmological problem.However, the Hubble constant can be a laboratory to probe cosmology andparticle physics models. In our work, we will investigate if the possibility ofexplaining the $H_0$ trouble using non-thermal dark matter production aided byphantom-like cosmology is consistent with the Cosmic Background Radiation (CMB)and Baryon Acoustic Oscillation (BAO) data. We performed a full Monte Carlosimulation using CMB and BAO datasets keeping the cosmological parameters$\Omega_b h^2$, $\Omega_c h^2$, $100\theta$, $\tau_{opt}$, and $w$ as priorsand concluded that a non-thermal dark matter production aided by phantom-likecosmology yields at most $H_0=70.5$ km s$^{-1}$Mpc$^{-1}$ which is consistentwith 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 Hubbletrouble is needed. Lastly, we limited the fraction of relativistic dark matterat the matter-radiation equality to be at most 1\%.

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