Improved Calculation of the Primordial Gravitational Wave Spectrum in the Standard Model

Abstract

We show that the energy density spectrum of the primordial gravitational waves has characteristic features due to the successive changes in the relativistic degrees of freedom during the radiation era. These changes make the evolution of radiation energy density deviate from the conventional adiabatic evolution, ρ_r~ a^{-4}, and thus cause the expansion rate of the universe to change suddenly at each transition which, in turn, modifies the spectrum of primordial gravitational waves. We take into account all the particles in the Standard Model of elementary particles. In addition, free-streaming of neutrinos damps the amplitude of gravitational waves, leaving characteristic features in the energy density spectrum. Our calculations are solely based on the standard model of cosmology and particle physics, and therefore these features must exist. Our calculations significantly improve the previous ones which ignored these effects and predicted a smooth, featureless spectrum.

25 papes, 11 figures, submitted to PRD

References in corpus (1)

• An exact analytic spectrum of relic gravitational waves in an accelerating universe

Cited by in corpus (147)

• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Gravitational Wave Spectrum Induced by Primordial Scalar Perturbations
• The cosmological gravitational wave background from primordial density perturbations
• Cosmology with the Laser Interferometer Space Antenna
• New Horizons for Fundamental Physics with LISA
• Gravitational Wave Production At The End Of Inflation
• The First Three Seconds: a Review of Possible Expansion Histories of the Early Universe
• Inflationary interpretation of the stochastic gravitational wave background signal detected by pulsar timing array experiments
• Probing reheating temperature of the universe with gravitational wave background
• New physics from the polarised light of the cosmic microwave background
• Primordial gravitational waves from NANOGrav: a broken power-law approach
• Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak
• Precision calculations of the gravitational wave background spectrum from inflation
• Sensitivity to a Frequency-Dependent Circular Polarization in an Isotropic Stochastic Gravitational Wave Background
• Blue-tilted Tensor Spectrum and Thermal History of the Universe
• Stochastic gravitational waves from cosmic string loops in scaling
• Relic gravitational waves and their detection
• Resonant multiple peaks in the induced gravitational waves
• Space laser interferometers can determine the thermal history of the early Universe
• Measuring the spectrum of primordial gravitational waves with CMB, PTA and Laser Interferometers
• Gravitational Wave and CMB Probes of Axion Kination
• Imprints of Relic Gravitational Waves in Cosmic Microwave Background Radiation
• Decoding the phases of early and late time reheating through imprints on primordial gravitational waves
• Causal gravitational waves as a probe of free streaming particles and the expansion of the Universe
• Blue-tilted inflationary tensor spectrum and reheating in the light of NANOGrav results
• Thermal History of the Early Universe and Primordial Gravitational Waves from Induced Scalar Perturbations
• Spectrum of Primordial Gravitational Waves in Modified Gravities: A Short Overview
• The Imprint of Relativistic Particles on the Anisotropies of the Stochastic Gravitational-Wave Background
• Confronting sound speed resonance with pulsar timing arrays
• Primordial Gravitational Wave Signals in Modified Cosmologies
• The impact of cosmic neutrinos on the gravitational-wave background
• Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy
• Dark Holograms and Gravitational Waves
• Multi-wavelength constraints on the inflationary consistency relation
• Damping of gravitational waves by matter
• Primordial Gravitational Waves Predictions for GW170817-compatible Einstein-Gauss-Bonnet Theory
• Pion condensation in the early Universe at nonvanishing lepton flavor asymmetry and its gravitational wave signatures
• Relic Gravitational Waves with A Running Spectral Index and Its Constraints at High Frequencies
• Bridging the gap: spectral distortions meet gravitational waves
• Prospects of discovering sub-solar primordial black holes using the stochastic gravitational wave background from third-generation detectors
• Exploring the NANOGrav Signal and Planet-mass Primordial Black Holes through Higgs Inflation
• Spectral distortions from the dissipation of tensor perturbations
• Testing the Early Universe with Anisotropies of the Gravitational Wave Background
• Inferring the lensing rate of LIGO-Virgo sources from the stochastic gravitational wave background
• Implications of the B-mode Polarization Measurement for Direct Detection of Inflationary Gravitational Waves
• Chirality of Gravitational Waves in Chern-Simons $f(R)$ Gravity Cosmology
• Probing the speed of scalar-induced gravitational waves with pulsar timing arrays
• Gravitational waves induced by scalar-tensor mixing
• Detecting relic gravitational waves in the CMB: Optimal parameters and their constraints
• Towards a reliable calculation of relic radiation from primordial gravitational waves
• Fingerprint of GeV scale right-handed neutrinos on inflationary gravitational waves and PTA data
• All-sky, all-frequency directional search for persistent gravitational-waves from Advanced LIGO's and Advanced Virgo's first three observing runs
• Impact of anisotropic stress of free-streaming particles on gravitational waves induced by cosmological density perturbations
• WMAP-normalized Inflationary Model Predictions and the Search for Primordial Gravitational Waves with Direct Detection Experiments
• Gravitational wave background from vacuum and thermal fluctuations during axion-like inflation
• Measuring Inflaton Couplings via Primordial Gravitational Waves
• Imprints of Barrow-Tsallis Cosmology in Primordial Gravitational Waves
• Constraint on the early Universe by relic gravitational waves: From pulsar timing observations
• 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
• Impact of high-scale Seesaw and Leptogenesis on inflationary tensor perturbations as detectable gravitational waves
• Signatures of Non-thermal Dark Matter with Kination and Early Matter Domination: Gravitational Waves versus Laboratory Searches
• Precision Early Universe Cosmology from Stochastic Gravitational Waves
• Microphysical manifestations of viscosity and consequences for anisotropies in the very early universe
• Secondary graviton spectra and waterfall-like fields
• Probing neutrino interactions and dark radiation with gravitational waves
• Improved Predictions on Higgs-Starobinsky Inflation and Reheating with ACT DR6 and Primordial Gravitational Waves
• Constraints upon the spectral indices of relic gravitational waves by LIGO S5
• Gravitational Waves-Tomography of Low-Scale-Leptogenesis
• Amplification of the Primordial Gravitational Waves Energy Spectrum by a Kinetic Scalar in $F(R)$ Gravity
• Non-Markovian open quantum system approach to the early universe: I. Damping of gravitational waves by matter
• Cosmological consequences of classical flavor-space locked gauge field radiation
• The paradigm of warm quintessential inflation and spontaneous baryogenesis
• Clarifying transfer function approximations for the large-scale gravitational wave background in $\Lambda$CDM
• Chiral Imprint of a Cosmic Gauge Field on Primordial Gravitational Waves
• Lectures on Reheating after Inflation
• Comparison of delensing methodologies and assessment of the delensing capabilities of future experiments
• Avoided Deconfinement in Randall-Sundrum Models
• Impact of the free-streaming neutrinos to the second order induced gravitational waves
• Explicit spacetime-symmetry breaking and the dynamics of primordial fields
• Effects of the QCD Equation of State and Lepton Asymmetry on Primordial Gravitational Waves
• Precision cosmology with primordial GW backgrounds in presence of astrophysical foregrounds
• Detecting relic gravitational waves in the CMB: Comparison of different methods
• Amplification of Primordial Gravitational Waves by a Geometrically Driven non-canonical Reheating Era
• A Brief History of Curvature
• $f(R)$-Gravity Generated Post-inflationary Eras and their Effect on Primordial Gravitational Waves
• Primordial gravitational waves amplification from causal fluids
• No evidence for the blue-tilted power spectrum of relic gravitational waves
• Lepton asymmetry in the primordial gravitational wave spectrum
• Stochastic gravitational-wave background searches and constraints on neutron-star ellipticity
• Impact of memory-burdened black holes on primordial gravitational waves in light of Pulsar Timing Array
• What is needed of a scalar field if it is to unify inflation and late time acceleration ?
• Relativistic viscous effects on the primordial gravitational waves spectrum
• Effects of a Pre-inflationary de Sitter Bounce on the Primordial Gravitational Waves in $f(R)$ Gravity Theories
• Detecting Relic Gravitational Waves in the CMB: Comparison of Planck and Ground-based Experiments
• DESI constraints on $\alpha$-attractor inflationary models
• Observable Gravitational Waves from Hyperkination in Palatini Gravity and Beyond
• Relic Gravitational Waves And CMB Polarization In The Accelerating Universe
• Generalized Uncertainty Principle mimicking dynamical Dark Energy: matter perturbations and gravitational wave data analysis
• Cosmic backgrounds of relic gravitons and their absolute normalization
• Tomography of flavoured leptogenesis with primordial blue gravitational waves
• Waterfall stiff period can generate observable primordial gravitational waves
• Gravitational waves detectable in laser interferometers from axion-SU(2) inflation
• Probing parity-odd bispectra with anisotropies of GW $V$ modes
• Gravitational-wave background in bouncing models from semi-classical, quantum and string gravity
• Role of spatial curvature in the primordial gravitational wave power spectrum
• The rise of the primordial tensor spectrum from an early scalar-tensor epoch
• The History of Inflation from Microwave Background Polarimetry and Laser Interferometry
• Effective Search Templates for a Primordial Stochastic Gravitational Wave Background
• Cosmology from String T-duality and zero-point length
• An Analytical Study of the Primordial Gravitational-Wave-Induced Contribution to the Large-Scale Structure of the Universe
• Analytic formula for the dynamics around inflation end and implications on primordial gravitational waves
• Scalar-Induced Gravitational Waves in a $\Lambda$CDM Cosmology
• Scalar-Induced Gravitational Waves in Modified Gravity
• Relic Cosmological Vector Fields and Inflationary Gravitational Waves
• Probing PeV scale SUSY-breaking with Satellite Galaxies and Primordial Gravitational Waves
• Damping of gravitational waves in f(R) gravity
• Gauge-dependence of Scalar Induced Gravitational Waves
• Interferences in the Stochastic Gravitational Wave Background
• Dark Universe inspired by the Kaluza-Klein gravity and impact on Primordial Gravitational Waves
• Primordial gravitational waves from spontaneous Lorentz symmetry breaking
• Search for an emission line of a gravitational wave background
• Can the NANOGrav observations constrain the geometry of the universe?
• Testing quantum gravity with primordial gravitational waves
• Non-Gaussianity of Tensor Induced Density Perturbations
• Search for a Gravitational-Wave Background from Sound Speed Resonance from Advanced LIGO and Advanced Virgo's First Three Observing Runs
• Implications of pulsar timing arrays for Gauss-Bonnet Inflation
• Neutrinos as a probe of curvature
• Modified cosmology through generalized mass-to-horizon entropy: implications for structure growth and primordial gravitational waves
• Flat spectra of cosmic gravitons in the nHz and audio bands
• Gravitational Waves with Dark Energy
• Damping of cosmological tensor modes in Horndeski theories after GW170817
• Bias in the tensor-to-scalar ratio from self-interacting dark radiation
• Antipodal Angular Correlations of Inflationary Stochastic Gravitational Wave Background
• ACT DR6 Insights on the Inflationary Attractor models and Reheating
• Spontaneous baryogenesis and generation of gravitational waves in a new model of quintessential $\alpha$-attractor
• Primordial observables of explicit diffeomorphism violation in gravity
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity
• Accelerating Airy tensor modes of cosmological gravitational waves
• Gravitational wave production after inflation for a hybrid inflationary model
• Primordial gravitational waves spectrum in the interacting Bose-Einstein gas model
• $e^{+}{e}^{-}$ annihilation on the stochastic background of primordial gravitational waves with BKP18
• Insights for Early Dark Energy with Big Bang Nucleosynthesis
• Signatures of Primordial Gravitational Waves on the Large-Scale Structure of the Universe
• The gauge invariant cosmological Jacobi map from weak lensing at leading order
• Interaction of exact gravitational waves with matter
• Hamilton-Jacobi analysis of noncanonical inflation in $f(R,T)$ gravity: Constraints from Planck/ACT data, and theoretical bounds