THE PHYSICAL BASIS FOR INFRARED DIVERGENCES IN INFLATIONARY QUANTUM-GRAVITY

We consider tree-order graviton scattering amplitudes on a (3 + 1)-dimensional de Sitter background in conformally flat coordinates. Infra-red divergences which cannot be absorbed using conventional techniques are shown to arise because conformal factors from the vertices are not compensated either by propagators or by external wavefunctions. The physical problem at tree order is therefore late interaction times rather than small spatial coordinate momenta, despite a mathematical problem at small momenta in the naive mode expansion of the propagator. Even in loops, concern over small spatial momenta is physically irrelevant because the chaotic conditions likely to prevail after the Big Bang could not have resulted in the simultaneous onset of inflation over a patch extending much beyond the Hubble radius. This motivates our proposal for a propagator which can be used to compute expectation values well inside the de Sitter patch of a plausible initial state.