The gravitational polarization tensor of thermal $\lambda\phi^4$ theory

The low-momentum structure of the gravitational polarization tensor of an ultrarelativistic plasma of scalar particles with $\lambda\phi^4$ interactions is evaluated in a two-loop calculation up to and including order $\lambda^{3/2}$. This turns out to require an improved perturbation theory which resums a local thermal mass term as well as nonlocal hard-thermal-loop vertices of scalar and gravitational fields.