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 $f(R,T) = R + 2\chi T.$ 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 $-1.6\times 10^{-13} \lesssim \chi \lesssim 1.8\times 10^{-13}$.