Limits on <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo>,</mml:mo><mml:mi>T</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> 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 $f(R,T)=R+2\ensuremath{\chi}T$. 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 $\ensuremath{-}1.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}\ensuremath{\lesssim}\ensuremath{\chi}\ensuremath{\lesssim}1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}13}$.

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