Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy

Abstract

We include the effect of neutrino free streaming into the spectrum of relic gravitational waves (RGWs) in the currently accelerating universe. For the realistic case of a varying fractional neutrino energy density and a non-vanishing derivative of mode function at the neutrino decoupling, the integro-differential equation of RGWs is solved by a perturbation method for the period from the neutrino decoupling to the matter-dominant stage. Incorporating it to the analytic solution of the whole history of expansion of the universe, the analytic solution of GRWs is obtained, evolving from the inflation up to the current acceleration. The resulting spectrum of GRWs covers the whole range of frequency $(10^{-19}\sim 10^{10})$Hz, and improves the previous results. It is found that the neutrino free-streaming causes a reduction of the spectral amplitude by $\sim 20$ in the range $(10^{-16}\sim 10^{-10})$ Hz, and leaves the other portion of the spectrum almost unchanged. This agrees with the earlier numerical calculations. Examination is made on the difference between the accelerating and non-accelerating models, and our analysis shows that the ratio of the spectral amplitude in accelerating $\Lambda$CDM model over that in CDM model is $\sim 0.7$, and within the various accelerating models of ${\Omega }_{\Lambda }>{\Omega }_m$ the spectral amplitude is proportional to ${\Omega }_m/{\Omega }_{\Lambda }$ for the whole range of frequency. Comparison with LIGO S5 Runs Sensitivity shows that RGWs are not yet detectable by the present LIGO, and in the future LISA may be able to detect RGWs in some inflationary models.

22 pages,12 figures, accepeted by PRD

References in corpus (43)

• First Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Determination of Cosmological Parameters
• An All-Sky Analysis of Polarization in the Microwave Background
• Gravitational Wave Experiments and Early Universe Cosmology
• Statistics of Cosmic Microwave Background Polarization
• Signature of Gravity Waves in Polarization of the Microwave Background
• Cosmological parameters from combining the Lyman-alpha forest with CMB, galaxy clustering and SN constraints
• CMB Anisotropies: Total Angular Momentum Method
• New BBN limits on Physics Beyond the Standard Model from He4
• Updated Nucleosynthesis Constraints on Unstable Relic Particles
• Improved Calculation of the Primordial Gravitational Wave Spectrum in the Standard Model
• Damping of Tensor Modes in Cosmology
• Cosmic Microwave Background Polarization
• A new cosmic microwave background constraint to primordial gravitational waves
• Quintom models with an equation of state crossing -1
• Cosmic Microwave Background Fluctuations from Gravitational Waves: An Analytic Approach
• Analytic approach to the polarization of the cosmic microwave background in flat and open universes
• Gravitational Wave Astronomy: in Anticipation of First Sources to be Detected
• Challenges for scaling cosmologies
• Reheating After Quintessential Inflation and Gravitational Waves
• Quintessence and Gravitational Waves
• Electromagnetic response of a Gaussian beam to high-frequency relic gravitational waves in quintessential inflationary models
• Two-Field Quintom Models in the w-w' Plane
• Polarization of the Microwave Background due to Primordial Gravitational Waves
• Relic gravitational waves and their detection
• Relic Gravitational Waves in the Accelerating Universe
• Comment on "Damping of Tensor Modes in Cosmology"
• Large Angular Scale Polarization of the Cosmic Microwave Background and the Feasibility of its Detection
• Imprints of Relic Gravitational Waves in Cosmic Microwave Background Radiation
• Crossing $w=-1$ by a single scalar on a Dvali-Gabadadze-Porrati brane
• Critical comments on the paper "Crossing $\omega =-1$ by a single scalar field on a Dvali-Gabadadze-Porrati brane" by H Zhang and Z-H Zhu [Phys.Rev.D75,023510(2007)]
• Reconstruction of Hessence Dark Energy and the Latest Type Ia Supernovae Gold Dataset
• Relic Gravitational Waves and Limits on Inflation
• Analytic approach to the CMB polarizations generated by relic gravitational waves
• Relic Gravitational Waves and Their Detection
• Features in Dark Energy Equation of State and Modulations in the Hubble Diagram
• 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
• Polarization of the Microwave Background in Inflationary Cosmology
• Coincidence Problem in YM Field Dark Energy Model
• Gravitational Waves and the Polarisation of the Cosmic Microwave Background
• The Stochastic Gravitational-Wave Background and the Inflation to Radiation Transition in the Early Universe
• Large-scale Polarization of the Cosmic Microwave Background Radiation
• Numeric Spectrum of Relic Gravitational Waves in Accelerating Universe

Cited by in corpus (41)

• Dark Energy
• Perturbative Photon Fluxes Generated by High-Frequency Gravitational Waves and Their Physical Effects
• Detecting Relic Gravitational Waves by Pulsar Timing Arrays: Effects of Cosmic Phase Transitions and Relativistic Free-Streaming Gases
• Relic Gravitational Waves with A Running Spectral Index and Its Constraints at High Frequencies
• Probing Decoupling in Dark Sectors with the Cosmic Microwave Background
• 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
• Damping of Primordial Gravitational Waves from Generalized Sources
• Cosmic Microwave Background Acoustic Peak Locations
• Approximate Analytic Spectra of Reionized CMB Anisotropies and Polarization generated by Relic Gravitational Waves
• Modifications by QCD transition and $e^{+}{e}^{-}$ annihilation on analytic spectrum of relic gravitational waves in accelerating universe
• Vacuum and Gravitons of Relic Gravitational Waves, and Regularization of Spectrum and Energy-Momentum Tensor
• Constraints upon the spectral indices of relic gravitational waves by LIGO S5
• Energy Momentum Pseudo-Tensor of Relic Gravitational Wave in Expanding Universe
• Detecting very-high-frequency relic gravitational waves by electromagnetic wave polarizations in a waveguide
• Relic gravitons and high-frequency detectors
• New Primordial-Magnetic-Field Limit from The Latest LIGO S5 data
• New method to constrain the relativistic free-streaming gas in the Universe
• 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
• Relic Gravitational Waves And CMB Polarization In The Accelerating Universe
• 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
• Relic gravitational waves in the frame of slow-roll inflation with a power-law potential and the detection
• Revisit relic gravitational waves based on the latest CMB observations
• Resonance of Gaussian electromagnetic field to the high frequency gravitational waves
• 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
• Damping of gravitational waves in f(R) gravity
• Signal photon flux generated by high-frequency relic gravitational waves
• Relic gravitons and non-stationary processes
• Imprints of relic gravitational waves on pulsar timing
• Flat spectra of cosmic gravitons in the nHz and audio bands
• The investigation of detectability of the relic gravitational waves based on the WMAP-9 and Planck
• Initial Condition of Relic Gravitational Waves Constrained by LIGO S6 and Multiple Interferometers
• Plane Gravitational Radiation from Neutrinos Source with Kalb-Ramond Coupling
• The Conserved Effective Stress Tensor of Gravitational Wave
• Relic gravitons at intermediate frequencies and the expansion history of the Universe
• Constraints on typical relic gravitational waves based on data of LIGO