A Simplified Quantum Gravitational Model of Inflation

Abstract

Inflationary quantum gravity simplifies drastically in the leading logarithm approximation. We show that the only counterterm which contributes in this limit is the 1-loop renormalization of the cosmological constant. We go further to make a simplifying assumption about the operator dynamics at leading logarithm order. This assumption is explicitly implemented at 1- and 2-loop orders, and we describe how it can be implemented nonperturbatively. We also compute the expectation value of an invariant observable designed to quantify the quantum gravitational back-reaction on inflation. Although our dynamical assumption may not prove to be completely correct, it does have the right time dependence, it can naturally produce primordial perturbations of the right strength, and it illustrates how a rigorous application of the leading logarithm approximation might work in quantum gravity. It also serves as a partial test of the "null hypothesis" that there are no significant effects from infrared gravitons.

41 pages, version 2 revised for publication in Classical and Quantum Gravity. The principal change is the discussion in section 3 of concerns about spatial inhomogeneities and the validity of expectation values

References in corpus (11)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• De Sitter Space and Eternity
• Stochastic Inflationary Scalar Electrodynamics
• Classical approximation to quantum cosmological correlations
• Reply to `Can infrared gravitons screen $\Lambda$?'
• Infrared Propagator Corrections for Constant Deceleration
• Can infrared gravitons screen $\Lambda$?
• Quantum radiative corrections to slow-roll inflation
• A Simple Operator Check of the Effective Fermion Mode Function during Inflation
• The Quantum-Corrected Fermion Mode Function during Inflation
• Graviton one-loop effective action and inflationary dynamics