Gravitational polarization tensor of thermal λφ4theory

The low-momentum structure of the gravitational polarization tensor of an ultrarelativistic plasma of scalar particles with \ensuremath{\lambda}${\mathrm{\ensuremath{\varphi}}}^{4}$ interactions is evaluated in a two-loop calculation up to and including order ${\ensuremath{\lambda}}^{3/2}$. 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. \textcopyright{} 1996 The American Physical Society.