2025A&A...699A..59S

Recent cosmological observations indicate a 5σ discrepancy between the values of the Hubble constant H₀ derived from late and early Universe probes, and a further possible tension at the ∼3σ level has arisen from different measurements of σ₈. These measurements suggest the existence of new physics. In this work, we explore several theories of modified gravity that may help 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 considered one particular class of these theories: cosmologies with a varying growth index γ and a varying dark energy equation of state (EoS) w_Λ. We also considered the normal branch of the Dvali-Gabadadze-Porrati (nDGP) model and 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: the stellar mass function (SMF), stellar mass density (SMD), star formation rate density (SFRD), and ultraviolet luminosity function (UVLF) along with the Epoch of Reionisation (EoR). The theories we considered are parameterised using r_c (the scale length on which five-dimensional gravity transitions to four dimensions, for nDGP), β (associated with the Weyl re-scaling of the metric tensor), and K₀ (quantifying aspects of the scalar field, for k-mouflage). The analysis carried out in this paper provides new constraints on these parameters. Generally, we find that the choice of r_c≳10^3.5 Mpc is preferred for nDGP, while β∼0.1, K₀≳0.9 is favoured for k-mouflage. Moreover, in the context of phenomenological gravity, phantom-like and ΛCDM cosmology with w_Λ≲-1 is preferred over the quintessence.