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

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• Issues Concerning Loop Corrections to the Primordial Power Spectra
• Infrared-finite graviton two-point function in static de Sitter space
• Negative Energy Cosmology and the Cosmological Constant
• Covariant and infrared-free graviton two-point function in de Sitter spacetime II
• Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections
• Possible Enhancement of High Frequency Gravitational Waves