On infrared and ultraviolet divergences of cosmological perturbations
arXiv:1102.2206 · doi:10.1103/PhysRevD.83.105017
Abstract
We study a consistent infrared and ultraviolet regularization scheme for the cosmological perturbations. The infrared divergences are cured by assuming that the Universe undergoes a transition between a non-singular pre-inflationary, radiation-dominated phase and a slow-roll inflationary evolution. The ultraviolet divergences are eliminated via adiabatic subtraction. A consistent regularization of the field fluctuations through this transition is obtained by performing a mode matching for both the gauge invariant Mukhanov variable and its adiabatic expansion. We show that these quantities do not generate ultraviolet divergences other than the standard ones, when evolving through the matching time. We also show how the de Witt-Schwinger expansion, which can be used to construct the counter-terms regularizing the ultraviolet divergences, ceases to be valid well before horizon exit of the scales of interest. Thus, such counter-terms should not be used beyond the time of the horizon exit so it is unlikely that the observed power spectrum is modified by adiabatic subtraction as claimed in the literature. However, the infrared regularization might have an impact on the observed spectrum, and we briefly discuss this possibility.
10 pages, 4 plots, revTex. Reference and comment added, matches version published in Phys. Rev. D 83, 105017 (2011)
References in corpus (6)
- Black Hole Remnants in the Early Universe
- On Adiabatic Renormalization of Inflationary Perturbations
- The Creation of Particles in an Expanding Universe
- The Impact of Ultraviolet Regularization on the Spectrum of Curvature Perturbations During Inflation
- Quantum backreaction in evolving FLRW spacetimes
- Back-reaction of Cosmological Fluctuations during Power-Law Inflation
Cited by in corpus (42)
- Cosmology and Fundamental Physics with the Euclid Satellite
- No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation
- Perturbative Quantum Gravity Comes of Age
- Towards a reliable effective field theory of inflation
- Origin of Cosmic Magnetic Fields
- Large fluctuations and Primordial Black Holes
- Particle creation from the quantum stress tensor
- Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of Spectrum and Energy-Momentum Tensor
- On the power spectrum generated during inflation
- Energy-momentum tensor and helicity for gauge fields coupled to a pseudo-scalar inflaton
- Remarks on the renormalization of primordial cosmological perturbations
- Revisiting a pre-inflationary radiation era and its effect on the CMB power spectrum
- Renormalization of the inflationary perturbations revisited
- On inflating magnetic fields, and the backreactions thereof
- Adiabatic regularization with a Yukawa interaction
- Second Order Perturbations During Inflation Beyond Slow-roll
- On the equivalence of Jordan and Einstein frames in scale-invariant gravity
- Evolution of vacuum fluctuations generated during and before inflation
- Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion
- Renormalization in gravitational leptogenesis with pseudo-scalar-tensor coupling
- Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
- Untangling PBH overproduction in -SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
- Adiabatic regularisation of power spectra in -inflation
- Evolution of Vacuum Fluctuations of an Ultra-Light Massive Scalar Field generated during and before Inflation
- Gravitational waves induced by spinor fields
- Adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation
- Scale-Invariant Curvature Fluctuations from an Extended Semiclassical Gravity
- Eliminating infrared divergences in an inflationary cosmology
- Constraints on just enough inflation preceded by a thermal era
- Comment on "Origin of cosmic magnetic fields"
- Bonus Properties of States of Low Energy
- Aspects of Quantum Gravity in Cosmology
- Ultraviolet-regularized power spectrum without infrared distortions in cosmological spacetimes
- Semiclassical predictions regarding a pre-inflationary era and its effects on the power spectrum
- Reply to "Comments on Origin of cosmic magnetic fields"
- Thermal gravitational-wave background in the general pre-inflationary scenario
- The Semiclassical Einstein Equation on Cosmological Spacetimes
- On the adiabatic subtraction of cosmological perturbations
- Physical scale adiabatic regularization in cosmological spacetimes
- Lowering tensor-to-scalar ratio by pre-inflationary dynamics
- Regularization and conformal transformations of the power spectrum in general single field inflation
- On Adiabatic Renormalization with a Physically Motivated Infrared Cut-Off