One loop back reaction on chaotic inflation - art. no. 044010

We extend, for the case of a general scalar potential, the inflaton-gravito n Feynman rules recently developed by Iliopoulos et al. [Nucl. Phys. B534, 419 (1998)]. As an application we compute the leading term, for late comovi ng times, of the one loop back reaction on the expansion rate for V(phi) = 1/2m(2)phi(2). This is expressed as the logarithmic time derivative of the scale factor in the coordinate system for which the expectation value of th e metric has the form [O\g(mu nu)((t) over bar,(x) over right arrow)\0]dx(m u)dx(nu) = -d (t) over bar(2) + a(2)((t) over bar)d (x) over right arrow.(d ) over right arrow x. This quantity should be a gauge-independent observabl e. Our result for it agrees exactly with that inferred from the effect prev iously computed by Mukhanov and co-workers [Phys. Rev. Lett. 78, 1624 (1997 ); Phys. Rev. D 56, 3248 (1997)] using canonical quantization. It is signif icant that the two calculations were made with completely different schemes for fixing the gauge, and that our computation was done using the standard formalism of covariant quantization. This should settle some of the issues recently raised by Unruh (astro-ph/9802323). [S0556-2821(99)04814-6].