Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of Spectrum and Energy-Momentum Tensor

Abstract

The spectrum of relic gravitational wave (RGW) contains high-frequency divergences, which should be removed. We present a systematic study of the issue, based on the exact RGW solution that covers the five stages, from inflation to the acceleration, each being a power law expansion. We show that the present RGW consists of vacuum dominating at $f>10^{11}$Hz and graviton dominating at $f<10^{11}$Hz, respectively. The gravitons are produced by the four cosmic transitions, mostly by the inflation-reheating one. We perform adiabatic regularization to remove vacuum divergences in three schemes: at present, at the end of inflation, and at horizon-exit, to the 2-nd adiabatic order for the spectrum, and the 4-th order for energy density and pressure. In the first scheme a cutoff is needed to remove graviton divergences. We find that all three schemes yield the spectra of a similar profile, and the primordial spectrum defined far outside horizon during inflation is practically unaffected. We also regularize the gauge-invariant perturbed inflaton and the scalar curvature perturbation by the last two schemes, and find that the scalar spectra, the tensor-to-scalar ratio, and the consistency relation remain unchanged.

30 pages, 13 figures, accepted by Phys. Rev. D

References in corpus (20)

• BICEP2 I: Detection Of B-mode Polarization at Degree Angular Scales
• A Joint Analysis of BICEP2/Keck Array and Planck Data
• The transition temperature in QCD
• Improved Calculation of the Primordial Gravitational Wave Spectrum in the Standard Model
• A joint analysis of Planck and BICEP2 B modes including dust polarization uncertainty
• Relic Gravitational Waves in the Accelerating Universe
• Perturbative Quantum Gravity Comes of Age
• Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy
• An exact analytic spectrum of relic gravitational waves in an accelerating universe
• On Adiabatic Renormalization of Inflationary Perturbations
• Using polarized maser to detect high-frequency relic gravitational waves
• Small Angular Scale Measurements of the CMB Temperature Power Spectrum from QUaD
• Amplitude of Perturbations from Inflation
• Effects of Quantized Scalar Fields in Cosmological Spacetimes with Big Rip Singularities
• Modifications by QCD transition and $e^{+}{e}^{-}$ annihilation on analytic spectrum of relic gravitational waves in accelerating universe
• Approximate Analytic Spectra of Reionized CMB Anisotropies and Polarization generated by Relic Gravitational Waves
• The Impact of Ultraviolet Regularization on the Spectrum of Curvature Perturbations During Inflation
• Second Order Gauge-Invariant Perturbations during Inflation
• Constraints upon the spectral indices of relic gravitational waves by LIGO S5
• Study of the Spectrum of Inflaton Perturbations

Cited by in corpus (21)

• No-go for the formation of heavy mass Primordial Black Holes in Single Field Inflation
• Large fluctuations and Primordial Black Holes
• Adiabatic regularization with a Yukawa interaction
• Quantum principle of sensing gravitational waves: From the zero-point fluctuations to the cosmological stochastic background of spacetime
• Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion
• Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge
• Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage
• Regularized-Renormalized-Resummed loop corrected power spectrum of non-singular bounce with Primordial Black Hole formation
• Second-order cosmological perturbations. II. Produced by scalar-tensor and tensor-tensor couplings
• Untangling PBH overproduction in $w$-SIGWs generated by Pulsar Timing Arrays for MST-EFT of single field inflation
• A massless scalar field in Robertson-Walker spacetimes: Adiabatic regularization and Green's function
• Point-splitting regularization of the stress tensor of a coupling scalar field in de Sitter space
• Maxwell field with gauge fixing term in de Sitter space: exact solution and stress tensor
• Second-order cosmological perturbations. III. Produced by scalar-scalar coupling during radiation-dominated stage
• Estimation of spectrum and parameters of relic gravitational waves using space-borne interferometers
• Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
• Primary gravitational waves at high frequencies I: Origin of suppression in the power spectrum
• Regularized stress tensor of vector fields in de Sitter space
• Maxwell field with gauge fixing term in the radiation- and matter-dominant stages: exact solution and stress tensor
• Semiclassical approach to atomic decoherence by gravitational waves
• The Conserved Effective Stress Tensor of Gravitational Wave