Constraint on minimal exponential measure (MEMe) modified gravity model on earth's atmosphere

We investigate how much the Newtonian-scale gravity within alternative coupling theory agrees with our understanding of Earth's atmosphere. We compare the atmospheric pressure structure predicted by the Minimal Exponential Measure (MEMe) model with one from US Standard Atmosphere 1976 model which deviates less than 10% from observation. By using Bayesian analysis via Markov-chain Monte Carlo, we found that, to be able to consistently reproduce our current understanding of Earth's atmosphere structure, the parameter q should yield |q| < 3.06 × 10^-14 m³J^-1 in 2σ credibility, comparable to the constraint from GW170817 standard siren. We also compare this value with bounds from Eddington-inspired Born-Infeld gravity, which share a similar Poisson equation in Newtonian-scale.