If the sum of the energy density rho and thrice the pressure p is nega
tive, then a Robertson-Walker universe can inflate or even oscillate.
But we show at the one-loop level that in a generic grandly unified th
eory rho + 3p cannot be negative at the absolute minimum of the finite
-temperature effective potential. We discuss the implications of this
result for inflation in two grandly unified theories and speculate on
the effects of gravitational friction and anti-friction.