Estimating power-law exponents from observations in electromagnetic non-minimal Maxwell-Gauss-Bonnet coupling cosmology

We discuss a generalized non-minimal Maxwell-Gauss-Bonnet power-law cosmological model characterized by the presence of electromagnetic field and variable cosmological and gravitational constant. We analyze the late-time dynamics characterized by power-law solutions. The model is constrained with local gravitational acceleration measurements, the SH0ES project which estimate the Hubble parameter, Planck TT, TE, EE + low E +lensing +SNe+ BAO data which estimate the EoS parameter and data coming from distant supernovae type Ia, the Hubble function $H\left(z\right)$ measurements and information coming from the Alcock-Paczynski test which estimate the numerical range of the non-minimal coupling parameter. By adopting a variable cosmological and gravitational constants, it was found that the universe is acceleratedly expanding with time and dominated by dark/phantom energy and an electromagnetic field comparable to the cosmological lambda. The variations of the gravitational constant time agree with several phenomenological theories including the entropic and holographic principle. The final fate of an asymptotically static universe was found also to be a plausible scenario in the model discussed.