Limits on f ( R , T ) gravity from Earth’s atmosphere

We investigate changes in Earth's atmospheric models coming from the f(R,T) modified theory of gravity, in which the gravitational Lagrangian is given by an arbitrary function of the Ricci scalar and the trace of the stress-energy tensor. We obtain a generic form for the gravitational field equations and derive the hydrostatic equation for Earth's atmosphere for leading order terms f(R,T)=R+2χT. Based on the apparent accuracy of the 1976 U.S. Standard Atmosphere model, which varies no more than 10% from observations, we find limits of −1.6×10−13≲χ≲1.8×10−13.