The Coincidence Limit of the Graviton Propagator in de Donder Gauge on de Sitter Background

We explicitly work out the de Sitter breaking contributions to the recent solution for the de Donder gauge graviton propagator on de Sitter. We also provide explicit power series expansions for the two structure functions, which are suitable for implementing dimensional regularization. And we evaluate the coincidence limit of the propagator.Comment: 41 pages, uses LaTeX 2e, version 2 has some typoes correcte

A Completely Regular Quantum Stress Tensor with w<−1w < -1

For many quantum field theory computations in cosmology it is not possible to use the flat space trick of obtaining full, interacting states by evolving free states over infinite times. State wave functionals must be specified at finite times and, although the free states suffice to obtain the lowest order effects, higher order corrections necessarily involve changes of the initial state. Failing to correctly change the initial state can result in effective field equations which diverge on the initial value surface, or which contain tedious sums of terms that redshift like inverse powers of the scale factor. In this paper we verify a conjecture from 2004 that the lowest order initial state correction can indeed absorb the initial value divergences and all the redshifting terms of the two loop expectation value of the stress tensor of a massless, minimally coupled scalar with a quartic self interaction on nondynamical de Sitter background.Comment: 23 pages, 1 figur

Classical approximation to quantum cosmological correlations

We investigate up to which order quantum effects can be neglected in calculating cosmological correlation functions after horizon exit. As a toy model, we study $\phi^3$ theory on a de Sitter background for a massless minimally coupled scalar field $\phi$. We find that for tree level and one loop contributions in the quantum theory, a good classical approximation can be constructed, but for higher loop corrections this is in general not expected to be possible. The reason is that loop corrections get non-negligible contributions from loop momenta with magnitude up to the Hubble scale H, at which scale classical physics is not expected to be a good approximation to the quantum theory. An explicit calculation of the one loop correction to the two point function, supports the argument that contributions from loop momenta of scale $H$ are not negligible. Generalization of the arguments for the toy model to derivative interactions and the curvature perturbation leads to the conclusion that the leading orders of non-Gaussian effects generated after horizon exit, can be approximated quite well by classical methods. Furthermore we compare with a theorem by Weinberg. We find that growing loop corrections after horizon exit are not excluded, even in single field inflation.Comment: 44 pages, 1 figure; v2: corrected errors, added references, conclusions unchanged; v3: added section in which we compare with stochastic approach; this version matches published versio

One-loop corrections to the curvature perturbation from inflation

An estimate of the one-loop correction to the power spectrum of the primordial curvature perturbation is given, assuming it is generated during a phase of single-field, slow-roll inflation. The loop correction splits into two parts, which can be calculated separately: a purely quantum-mechanical contribution which is generated from the interference among quantized field modes around the time when they cross the horizon, and a classical contribution which comes from integrating the effect of field modes which have already passed far beyond the horizon. The loop correction contains logarithms which may invalidate the use of naive perturbation theory for cosmic microwave background (CMB) predictions when the scale associated with the CMB is exponentially different from the scale at which the fundamental theory which governs inflation is formulated.Comment: 28 pages, uses feynmp.sty and ioplatex journal style. v2: supersedes version published in JCAP. Some corrections and refinements to the discussion and conclusions. v3: Corrects misidentification of quantum correction with an IR effect. Improvements to the discussio

One-loop corrections to a scalar field during inflation

The leading quantum correction to the power spectrum of a gravitationally-coupled light scalar field is calculated, assuming that it is generated during a phase of single-field, slow-roll inflation.Comment: 33 pages, uses feynmp.sty and ioplatex journal style. v2: matches version published in JCAP. v3: corrects sign error in Eq. (58). Corrects final coefficient of the logarithm in Eq. (105). Small corrections to discussion of divergences in 1-point function. Minor improvements to discussion of UV behaviour in Sec. 4.