Explaining JWST star formation history at $z \sim 17$ by modifying $\Lambda$CDM

Recent cosmological observations indicate a $5\sigma$ discrepancy between the values of the Hubble constant $H_0$ derived from late and early universe probes. A further possible tension at the $\sim 3\sigma$ level arises from different measurements of $\sigma_8$. These measurements suggest the existence of new physics. Here, we explore several theories of modified gravity that may help to resolve these cosmological tensions. These include a family of phenomenological modified theories, where only Newton's gravitational constant and the Einstein-Boltzmann equations are affected. We consider one particular class of these theories: cosmologies with varying growth index $\gamma$ and varying dark energy Equation of State (EoS) $w_\Lambda$. We also consider the normal branch of the Dvali-Gabadadze-Porrati (nDGP) model as well as $k$-mouflage gravity, which involves a non-trivially coupled scalar field. Our main aim is to narrow down the modified gravity landscape by constraining each model using high-redshift JWST data. Several probes are considered in this work: Stellar Mass Function (SMF), Stellar Mass Density (SMD), Star Formation Rate Density (SFRD) and Ultra-Violet Luminosity Function (UVLF) along with the Epoch of Reionization (EoR). We find that generally, the choice of $r_c\gtrsim 10^{3.5}$ Mpc is preferred for nDGP, while $\beta\sim0.1$, $K_0\gtrsim 0.9$ is favored for $k$-mouflage. Moreover, in the context of phenomenological gravity, phantom-like dark energy EoS $w_\Lambda\lesssim -1$ is preferred over the quintessence.