One loop back reaction on power law inflation - art. no. 044011

We consider quantum-mechanical corrections to a homogeneous, isotropic, and spatially flat geometry whose scale factor expands classically as a genera l power of the comoving time. The effects of both gravitons and the scalar inflaton are computed at one loop using the manifestly causal formalism of Schwinger [J. Math. Phys. 2, 407 (1961); Particles, Sources and Fields (Add ison, Wesley, Reading, MA, 1970)] with the Feynman rules recently developed by Iliopoulos ef al. [Nucl. Phys. B 534, 419 (1998)]. We find no significa nt effect, in marked contrast to the result obtained by Mukhanov and co-wor kers [Phys. Rev. Lett. 78, 1624 (1998); Phys. Rev. D 56, 3248 (1997)] for c haotic inflation based on a quadratic potential. By applying the canonical technique of Mukhanov and co-workers to the exponential potentials of power law inflation, we show that the two methods produce the same results, with in the approximations employed, for these backgrounds. We therefore conclud e that the shape of the inflaton potential can have an enormous impact on t he one loop back reaction. [S0556-2821(99)04914-0].