Adiabatic regularization of power spectrum and stress tensor of relic gravitational wave without low-frequency distortion

Abstract

Adiabatic regularization is a method to remove UV divergences in quantum fields in curved spacetime. For relic gravitational wave generated during inflation, regularization on all $k$-modes of the power spectrum to 2nd adiabatic order, and of the energy density and pressure to 4th order, respectively, causes low-frequency distortions. To avoid these, we regularize only the short modes inside the horizon during inflation (corresponding to the present frequencies $f\gtrsim 10^9$Hz), and keep the long modes intact. Doing this does not violate the energy conservation since the $k$-modes of RGW are independent of each other during inflation. The resulting spectra are UV convergent and simultaneously free of low-frequency distortion, and these properties remain in the present spectra after evolution, in contrast to regularization at the present time which has some distortion or irregularities. The spectra generally exhibit quick oscillations in frequency domain, even if the initial spectra during inflation have no oscillations. This pattern is due to the interference between the positive and negative frequency modes developed during cosmic expansion, and may be probed by future RGW detections.

arXiv comment39 pages, 20 figures. Fix a typo in eq.(2.8)

References in corpus (40)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• Seven-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Nine-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Parameter Results
• Efficient Computation of CMB anisotropies in closed FRW models
• A Line of Sight Approach to Cosmic Microwave Background Anisotropies
• Three Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis
• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Inflation
• The Five-Hundred-Meter Aperture Spherical Radio Telescope (FAST) Project
• Detecting a stochastic background of gravitational radiation: Signal processing strategies and sensitivities
• Adiabatic and entropy perturbations from inflation
• Limits on the Stochastic Gravitational Wave Background from the North American Nanohertz Observatory for Gravitational Waves
• The Energy-Momentum Tensor for Cosmological Perturbations
• CBR Anisotropy and the Running of the Scalar Spectral Index
• Placing limits on the stochastic gravitational-wave background using European Pulsar Timing Array data
• Production and detection of relic gravitons in quintessential inflationary models
• Pulsar searches and timing with the SKA
• Electromagnetic response of a Gaussian beam to high-frequency relic gravitational waves in quintessential inflationary models
• Relic Gravitational Waves in the Accelerating Universe
• Analytic approach to the CMB polarizations generated by relic gravitational waves
• A Simple Method for One-Loop Renormalization in Curved Space-Time
• Relic Gravitational Waves and Their Detection
• The Implications of the Microwave Background Anisotropies for Laser-Interferometer-Tested Gravitational Waves
• An exact analytic spectrum of relic gravitational waves in an accelerating universe
• On Adiabatic Renormalization of Inflationary Perturbations
• On infrared and ultraviolet divergences of cosmological perturbations
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Relic Gravitational Waves with Modification due to Neutrino Free-Streaming
• Using polarized maser to detect high-frequency relic gravitational waves
• The Power Spectrum in de Sitter Inflation, Revisited
• Approximate Analytic Spectra of Reionized CMB Anisotropies and Polarization generated by Relic Gravitational Waves
• Dynamical back-reaction of relic gravitons
• Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of Spectrum and Energy-Momentum Tensor
• Energy Momentum Pseudo-Tensor of Relic Gravitational Wave in Expanding Universe
• Renormalization of the inflationary perturbations revisited
• Second-order cosmological perturbations. I. Produced by scalar-scalar coupling in synchronous gauge
• Second-order cosmological perturbations. II. Produced by scalar-tensor and tensor-tensor couplings
• Using pulsar timing arrays and the quantum normalization condition to constrain relic gravitational waves
• Analytic Spectra of CMB Anisotropies and Polarization Generated by Scalar Perturbations in Synchronous Gauge
• Adiabatic regularisation of power spectra in $k$-inflation
• Adiabatic regularization of power spectrum in nonminimally coupled general single-field inflation
• Adiabatic regularisation of power spectra in nonminimally coupled chaotic inflation

Cited by in corpus (12)

• Sound speed resonance of the stochastic gravitational wave background
• Second-order cosmological perturbations. IV. Produced by scalar-tensor and tensor-tensor couplings during the radiation dominated stage
• Adiabatic regularization and Green's function of a scalar field in de Sitter space: Positive energy spectrum and no trace anomaly
• 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
• Second-order cosmological perturbations. III. Produced by scalar-scalar coupling during radiation-dominated stage
• Maxwell field with gauge fixing term in de Sitter space: exact solution and stress tensor
• Second-order cosmological perturbations produced by scalar-scalar coupling during inflation stage
• 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
• The equation and solution of 4-point correlation function of galaxies in Gaussian approximation and its parity-odd part
• The Conserved Effective Stress Tensor of Gravitational Wave