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 (67)

• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• General relativity as an effective field theory: The leading quantum corrections
• Quantum Contributions to Cosmological Correlations
• Equilibrium State of a Massless Self-Interacting Scalar Field in the De Sitter Background
• Leading Quantum Correction to the Newtonian Potential
• Quantum effects can render w<-1 on cosmological scales
• Super-Acceleration from Massless, Minimally Coupled ${\varphi }^4$
• On the Back Reaction Problem for Gravitational Perturbations
• The Energy-Momentum Tensor for Cosmological Perturbations
• De Sitter Space and Eternity
• The Quantum Gravitational Back-Reaction On Inflation
• Quantum Contributions to Cosmological Correlations II: Can These Corrections Become Large?
• Quantum Gravity Slows Inflation
• Stochastic Quantum Gravitational Inflation
• Stochastic Inflationary Scalar Electrodynamics
• On the one loop corrections to inflation and the CMB anisotropies
• Two Loop Scalar Self-Mass during Inflation
• Back Reaction And Local Cosmological Expansion Rate
• Complementarity of the Maldacena and Randall-Sundrum Pictures
• Leading Log Solution for Inflationary Yukawa
• On the Quantum Corrections to the Newtonian Potential
• Improved Estimates of Cosmological Perturbations
• Photon mass from inflation
• One Loop Vaccum Polarization in a Locally de Sitter Background
• Stationary Universe
• Quantum Stability of a w < - 1 Phase of Cosmic Acceleration
• Cosmological Dark Energy: Prospects for a Dynamical Theory
• Quantum corrections to slow roll inflation and new scaling of superhorizon fluctuations
• The Fermion Self-Energy during Inflation
• Quantum power correction to the Newton law
• One Loop Graviton Self-Energy In A Locally De Sitter Background
• Classical approximation to quantum cosmological correlations
• Reply to `Can infrared gravitons screen $\Lambda$?'
• Gravitons Enhance Fermions during Inflation
• Long Range Forces in Quantum Gravity
• Production of Massless Fermions during Inflation
• Quantum corrections to the inflaton potential and the power spectra from superhorizon modes and trace anomalies
• Infrared Propagator Corrections for Constant Deceleration
• A Leading Logarithm Approximation for Inflationary Quantum Field Theory
• No One Loop Back_Reaction In Chaotic Inflation
• Two Loop Scalar Bilinears for Inflationary SQED
• Dynamics of super-horizon photons during inflation with vacuum polarization
• Can infrared gravitons screen $\Lambda$?
• Non-Perturbative Models For The Quantum Gravitational Back-Reaction On Inflation
• Fermion Mass Generation in de Sitter Space
• Quantum radiative corrections to slow-roll inflation
• Long Range Forces from Two Neutrino Exchange Revisited
• A Scalar Measure Of The Local Expansion Rate
• Cosmological long wavelength perturbations
• Dimensionally Regulated Graviton 1-Point Function in de Sitter
• One Loop Back Reaction On Chaotic Inflation
• A Simple Operator Check of the Effective Fermion Mode Function during Inflation
• Photon mass generation during inflation: de Sitter invariant case
• Quantum long-range interactions in general relativity
• Quantum Cosmological Correlations in an Inflating Universe: Can fermion and gauge fields loops give a scale free spectrum?
• Adiabatic regularization of the graviton stress-energy tensor in de Sitter space-time
• Back-Reaction Is For Real
• A Measure of Cosmological Acceleration
• Matter Contributions to the Expansion Rate of the Universe
• A new diagrammatic representation for correlation functions in the in-in formalism
• A graviton propagator for inflation
• Plane waves in a general Robertson-Walker background
• The Quantum-Corrected Fermion Mode Function during Inflation
• General plane wave mode functions for scalar-driven cosmology
• Graviton one-loop effective action and inflationary dynamics
• A Newtonian Model for the Quantum Gravitational Back-Reaction on Inflation

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• Light propagation in statistically homogeneous and isotropic universes with general matter content
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• A Completely Regular Quantum Stress Tensor with $w<-1$
• One-loop effective action for non-local modified Gauss-Bonnet gravity in de Sitter space
• The Graviton Propagator in de Donder Gauge on de Sitter Background
• A Phenomenological Model for the Early Universe
• Issues Concerning Loop Corrections to the Primordial Power Spectra
• Mode-sum construction of the covariant graviton two-point function in the Poincaré patch of de Sitter space
• The Hubble Effective Potential
• Constructing Infrared Finite Propagators in Inflating Space-time
• Infrared Behavior of Quantum Fields in Inflationary Cosmology -- Issues and Approaches: an overview
• Infrared-finite graviton two-point function in static de Sitter space
• Negative Energy Cosmology and the Cosmological Constant
• Primordial Density Perturbations and Reheating from Gravity
• Covariant and infrared-free graviton two-point function in de Sitter spacetime II
• Stochastic Samples versus Vacuum Expectation Values in Cosmology
• Removing the Faddeev-Popov zero modes from Yang-Mills theory in spacetimes with compact spatial sections
• The Volume of the Past Light-Cone and the Paneitz Operator
• Primordial Gravitational Waves Enhancement
• Possible Enhancement of High Frequency Gravitational Waves