Cosmological Backgrounds of Gravitational Waves

Abstract

Gravitational waves (GWs) have a great potential to probe cosmology. We review early universe sources that can lead to cosmological backgrounds of GWs. We begin by presenting definitions of GWs in flat space-time and in a cosmological setting, and discussing the reasons why GW backgrounds from the early universe are of a stochastic nature. We recap current observational constraints on stochastic backgrounds, and discuss some of the characteristics of present and future GW detectors including advanced LIGO, advanced Virgo, the Einstein Telescope, KAGRA, LISA. We then review in detail early universe GW generation mechanisms proposed in the literature, as well as the properties of the GW backgrounds they give rise to. We classify the backgrounds in five categories: GWs from quantum vacuum fluctuations during standard slow-roll inflation, GWs from processes that operate within extensions of the standard inflationary paradigm, GWs from post-inflationary preheating and related non-perturbative phenomena, GWs from first order phase transitions (related or not to the electroweak symmetry breaking), and GWs from topological defects, in particular from cosmic strings. The phenomenology of early universe processes that can generate a stochastic background of GWs is extremely rich, and some backgrounds are within the reach of near-future GW detectors. A future detection of any of these backgrounds will provide crucial information on the underlying high energy theory describing the early universe, probing energy scales well beyond the reach of particle accelerators.

third version, corrected typos and the section about the transfer function, acknowledgements added

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• Gravitational wave production from preheating with trilinear interactions
• Detecting the stochastic gravitational wave background with the TianQin detector
• Multi-wavelength observations of cosmological phase transitions using LISA and Cosmic Explorer
• Searching for High Frequency Gravitational Waves with Phonons
• Probing a stationary non-Gaussian background of stochastic gravitational waves with pulsar timing arrays
• Oscillating scalar dissipating in a medium
• Clarifying transfer function approximations for the large-scale gravitational wave background in $\Lambda$CDM
• Impact of a Midband Gravitational Wave Experiment On Detectability of Cosmological Stochastic Gravitational Wave Backgrounds
• Comparison of delensing methodologies and assessment of the delensing capabilities of future experiments
• Probing the inflationary background of gravitational waves from large to small scales
• The scalar, vector, and tensor modes in gravitational wave turbulence simulations
• Parity Violating Non-Gaussianity from Axion-Gauge Field Dynamics
• Gravitational waves in warped compactifications
• Hunting WIMPs with LISA: Correlating dark matter and gravitational wave signals
• Analytic study of dark photon and gravitational wave production from axion
• Gravitational waves from breaking of an extra $U(1)$ in $SO(10)$ grand unification
• Impact of LIGO-Virgo black hole binaries on gravitational wave background searches
• Induced gravitational waves: the effect of first order tensor perturbations
• Astrophysical neutrino oscillations after pulsar timing array analyses
• Precision cosmology with primordial GW backgrounds in presence of astrophysical foregrounds
• Slaying Axion-Like Particles via Gravitational Waves and Primordial Black Holes from Supercooled Phase Transition
• Amplification of Primordial Gravitational Waves by a Geometrically Driven non-canonical Reheating Era
• Detecting circular polarisation in the stochastic gravitational-wave background from a first-order cosmological phase transition
• What is the amplitude of the Gravitational Waves background expected in the Starobinsky model ?
• Phase decoherence of gravitational wave backgrounds
• Effects of the QCD Equation of State and Lepton Asymmetry on Primordial Gravitational Waves
• Targeted search for the kinematic dipole of the gravitational-wave background
• Nonperturbative structure in coupled axion sectors and implications for direct detection
• Unraveling Cosmological Anisotropies within Stochastic Gravitational Wave Backgrounds
• Tracking the Multifield Dynamics with Cosmological Data: A Monte Carlo approach
• $f(R)$-Gravity Generated Post-inflationary Eras and their Effect on Primordial Gravitational Waves
• Sensitivity to Dark Sector Scales from Gravitational Wave Signatures
• Induced Gravitational Waves from Multi-Sound Speed Resonances during Cosmological Inflation
• Improving the detection sensitivity to primordial stochastic gravitational waves with reduced astrophysical foregrounds
• Axion Poltergeist
• Stochastic Gravitational Waves from Post-inflationary Structure Formation
• What is needed of a scalar field if it is to unify inflation and late time acceleration ?
• LIGO as a probe of Dark Sectors
• Relativistic viscous effects on the primordial gravitational waves spectrum
• LiteBIRD and CMB-S4 Sensitivities to Reheating in Plateau Models of Inflation
• Fully developed relativistic turbulence
• Detection of high-frequency gravitational waves using high-energy pulsed lasers
• Gravitational waves from bubble collisions in FLRW spacetime
• PeV-Scale SUSY and Cosmic Strings from F-term Hybrid Inflation
• Effects of a Pre-inflationary de Sitter Bounce on the Primordial Gravitational Waves in $f(R)$ Gravity Theories
• Primordial Magnetogenesis in a Bouncing Universe
• Double-graviton production from Standard Model plasma
• Probing the reheating phase through primordial magnetic field and CMB
• Lepton Flavour Violation Tests of Type II Seesaw Leptogenesis
• Scalar induced gravitational waves from Chern-Simons gravity during inflation era
• Open Quantum System Approach to the Gravitational Decoherence of Spin-1/2 Particles
• Self Consistent Thermal Resummation: A Case Study of the Phase Transition in 2HDM
• "Stairway to Heaven" -- Spectroscopy of Particle Couplings with Gravitational Waves
• Big Bang Nucleosynthesis Limits and Relic Gravitational Waves Detection Prospects
• Simulating relic gravitational waves from inflationary magnetogenesis
• Gravitational-wave signatures from reheating
• Observable Gravitational Waves from Hyperkination in Palatini Gravity and Beyond
• Gravitational wave and particle emission from a cosmic string loop: local case
• Angular Resolution of the Search for Anisotropic Stochastic Gravitational-Wave Background with Terrestrial Gravitational-Wave Detectors
• The Probability Distribution of Astrophysical Gravitational-Wave Background Fluctuations
• Primordial Black Holes and Scalar-induced Gravitational Waves in Radiative Hybrid Inflation
• Linearized dispersion relations in viscous relativistic hydrodynamics
• Charting the Nanohertz Gravitational Wave Sky with Pulsar Timing Arrays
• Gravitational waves in ultra-slow-roll and their anisotropy at two loops
• Measuring kinematic anisotropies with pulsar timing arrays
• Curvature Perturbations From Stochastic Particle Production During Inflation
• Linearized propagation equations for metric fluctuations in a general (non-vacuum) background geometry
• Warp factor and the gravitational wave spectrum
• Nonlinear gravitational-wave memory from cusps and kinks on cosmic strings
• The Muon Smasher's Guide
• Measuring the Energy Scale of Inflation with Large Scale Structures
• Measuring the primordial gravitational wave background in the presence of other stochastic signals
• Search for high-frequency gravitational waves with Rydberg atoms
• Probing parity-odd bispectra with anisotropies of GW $V$ modes
• Gravitational waves from low-scale cosmic strings
• Strongly Magnetized Hot QCD Matter and Stochastic Gravitational Wave Background
• On the gauge dependence of scalar induced secondary gravitational waves during radiation and matter domination eras
• Search for a gravitational wave background from primordial black hole binaries using data from the first three LIGO-Virgo-KAGRA observing runs
• On Particle Production from Phase Transition Bubbles
• Nonlinear Fluctuations in Relativistic Causal Fluids
• Gravitational Absorption Lines
• Constraining the history of reheating with the NANOGrav 15-year data
• Model-independent features of gravitational waves from bubble collisions
• Fast Likelihood-free Reconstruction of Gravitational Wave Backgrounds
• Primordial acoustic turbulence: three-dimensional simulations and gravitational wave predictions
• Templated Anisotropic Analyses of the LISA Galactic Foreground
• Gravitational Wave Symphony from Oscillating Spectator Scalar Fields
• Stochastic gravitational waves from long cosmic strings
• Gravitational Waves from Phase Transitions
• Connecting Cosmic Inflation to Particle Physics with LiteBIRD, CMB-S4, EUCLID and SKA
• An Étude on the Regularization and Renormalization of Divergences in Primordial Observables
• Cosmic (super)strings with a time-varying tension
• Functors of actions
• Low frequency tail of gravitational wave spectra from hydromagnetic turbulence
• Imprint of Early Dark Energy in Stochastic Gravitational Wave Background
• On the response of the Einstein Telescope to Doppler anisotropies
• Jointly setting upper limits on multiple components of an anisotropic stochastic gravitational-wave background
• White dwarf binary modulation can help stochastic gravitational wave background search
• Sub-GeV dark matter and nano-Hertz gravitational waves from a classically conformal dark sector
• Primordial Black Holes (as Dark Matter) from the Supercooled Phase Transitions with Radiative Symmetry Breaking
• Gravitational effects on fluid dynamics in cosmological first-order phase transitions
• Present and future of CosmoLattice
• Constraints on Non-Gaussian primordial curvature perturbation from the LIGO-Virgo-KAGRA third observing run
• Constraining the stochastic gravitational wave background using the future lunar seismometers
• Scalar induced gravitational waves review
• Modern Cosmology, an Amuse-Gueule
• Muffled Murmurs: Environmental effects in the LISA stochastic signal from stellar-mass black hole binaries
• Characteristics of interaction between Gravitons and Photons
• Scalar induced gravitational waves in chiral scalar-tensor theory of gravity
• Fundamental Physics and Cosmology with TianQin
• Spectator dark matter in non-standard cosmologies
• A universal bound on the duration of a kination era
• Toward a test of Gaussianity of a gravitational wave background
• The effect of quantum decoherence on inflationary gravitational waves
• Host Galaxy Demographics Of Individually Detectable Supermassive Black-hole Binaries with Pulsar Timing Arrays
• Anisotropies of cosmological gravitational wave backgrounds in non-flat spacetime
• Quasinormal ringing of thick braneworlds with a finite extra dimension
• Perspectives and Outlook from HEP Window on the Universe
• Probing Reheating Phase via Non-Helical Magnetogenesis and Secondary Gravitational Waves
• Left-Right Symmetry Breaking and Gravitational Waves : A Tale of Two Phase Transitions
• On the Expected Production of Gravitational Waves During Preheating
• Stochastic gravitational waves from spin-3/2 fields -- Hunting SUSY in the sky
• Future targets for light gauge bosons from cosmic strings
• Chromo-natural inflation supported by enhanced friction from Horndeski gravity
• Effects of a Late Gravitational Transition on Gravitational Waves and Anticipated Constraints
• Untargeted Bayesian search of anisotropic gravitational-wave backgrounds through the analytical marginalization of the posterior
• Observational prospects for phase transitions at LISA: Fisher matrix analysis
• Assessing the Impact of Unequal Noises and Foreground Modeling on SGWB Reconstruction with LISA
• Non-thermal production of heavy vector dark matter from relativistic bubble walls
• Searching for double-peak and doubly broken gravitational-wave spectra from Advanced LIGO-Virgo's first three observing runs
• Model-independent search for anisotropies in stochastic gravitational-wave backgrounds and application to LIGO-Virgo's first three observing Runs
• Thermal Emission of Gravitational Waves from Weak to Strong Coupling
• Gravitational waves from first-order electroweak phase transition in a model with light sgoldstinos
• Real-Time Nucleation and Off-Equilibrium Effects in High-Temperature Quantum Field Theories
• Triple Higgs boson production and electroweak phase transition in the two-real-singlet model
• Measuring the anisotropies in astrophysical and cosmological gravitational-wave backgrounds with Taiji and LISA networks
• Gravitational tests of electroweak relaxation
• Bubble-wall speed with loop corrections
• Alternative LISA-TAIJI networks: Detectability of the Parity Violation in Stochastic Gravitational Wave Background
• Astrometry meets Pulsar Timing Arrays: Synergies for Gravitational Wave Detection
• Scalar-Induced Gravitational Waves in Modified Gravity
• Detectability of the chiral gravitational wave background from audible axions with the LISA-Taiji network
• Cosmic superstrings in large volume compactifications: PTAs, LISA and time-varying tension
• Scalar-Induced Gravitational Waves in a $\Lambda$CDM Cosmology
• Gravitational wave stochastic background in reduced Horndeski theories
• The LISA forecast on a smooth crossover beyond the Standard Model through the scalar-induced gravitational waves
• Corrections to the gravitational wave phasing
• Non-linear corrections of overlap reduction functions for pulsar timing arrays
• Gravitational-wave searches in the era of Advanced LIGO and Virgo
• Will Gravitational Waves Discover the First Extra-Galactic Planetary System?
• Gauge-dependence of Scalar Induced Gravitational Waves
• Multi-messenger FIMP
• A Covariant Approach for Particle Creation in Non-flat Background
• Unbiased estimation of gravitational-wave anisotropies from noisy data
• Improving the detection sensitivity to primordial stochastic gravitational waves with reduced astrophysical foregrounds. II. Subthreshold binary neutron stars
• Impact of the observation frequency coverage on the significance of a gravitational wave background detection in PTA data
• Next-generation global gravitational-wave detector network: Impact of detector orientation on compact binary coalescence and stochastic gravitational-wave background searches
• Probing intermediate scale Froggatt-Nielsen models at future gravitational wave observatories
• Primordial Gravitational Waves in Generalized Palatini Gravity
• Dissecting the nanohertz gravitational wave sky: Frequency-correlated anisotropy induced by eccentric supermassive black hole binaries
• Interferences in the Stochastic Gravitational Wave Background
• Gravitational waves in a cyclic Universe: resilience through cycles and vacuum state
• Frequency-Domain Distribution of Astrophysical Gravitational-Wave Backgrounds
• Modified propagation of gravitational waves from the early radiation era
• Gravitational waves generation in turbulent hypermagnetic fields before the electroweak phase transition
• Characterization of Extragalactic Point-Sources on E- and B-mode Maps of the CMB Polarization
• Pulsar timing and polarimetry: results and perspectives
• Gravitational wave background from primordial black holes in globular clusters
• On the anisotropies of the cosmological gravitational-wave background from pulsar timing array observations
• Magnetism in the Early Universe
• Searching for Anisotropy in the Gravitational Wave Background Using the Parkes Pulsar Timing Array
• Multimodality in the Search for New Physics in Pulsar Timing Data and the Case of Kination-amplified Gravitational-wave Background from Inflation
• Graviscalar quasinormal modes and asymptotic tails of a thick brane
• Impact of hypermagnetic fields on relic gravitational waves, neutrino oscillations and baryon asymmetry
• Gravitational Waves sourced by Gauge Fields during Inflation
• Gravitational waves from axion inflation in the gradient expansion formalism. Part I. Pure axion inflation
• Thermal evolution of dark matter and gravitational-wave production in the early universe from a symplectic glueball model
• Primary gravitational waves at high frequencies I: Origin of suppression in the power spectrum
• Rapid Construction of Joint Pulsar Timing Array Datasets: The Lite Method
• Unified laboratory-frame analysis of atomic gravitational-wave sensors
• An Upper Limit on the Initial Temperature of the Radiation-Dominated Universe
• An SZ-Like Effect on Cosmological Gravitational Wave Backgrounds
• Connecting Inflation to the NANOGrav 15-year Data Set via Massive Gravity
• Effects of calibration uncertainties on the detection and parameter estimation of isotropic gravitational-wave backgrounds
• Bounds from multi-messenger astronomy on the Super Heavy Dark Matter
• Gravitational wave induced baryon acoustic oscillations
• Self-consistent interaction of linear gravitational and electromagnetic waves in non-magnetized plasma
• Gravitational waves in minimal Maxwell $f(R)$ gravity
• Perturbations in $\mathbf{O}(D,D)$ string cosmology from double field theory
• Probing high-frequency gravitational waves with entangled vibrational qubits in linear Paul traps
• Impact of Population III stars on the astrophysical gravitational-wave background
• Chiral gravitational waves from thermalized neutrinos in the early Universe
• Search for a Gravitational-Wave Background from Sound Speed Resonance from Advanced LIGO and Advanced Virgo's First Three Observing Runs
• A weakly-modeled search for compact binary coalescences in Einstein Telescope
• Potential Surge Preheating: enhanced resonance from potential features
• Scalar-induced gravitational wave from domain wall perturbation
• Gauge-invariant gravitational waves in matter beyond linearized gravity
• Theoretical Radio Signals from Radio-Band Gravitational Waves Converted from the Neutron Star Magnetic Field
• Breaking the degeneracy of non-canonical quartic inflation by reheating considerations
• VSL-Gravity in light of PSR B1913+16 Full Data Set: Upper limits on graviton mass and its theoretical consequences
• Non-Gaussianity of Tensor Induced Density Perturbations
• Probing supermassive black hole scalarization with Pulsar Timing Arrays
• The constraints on the stochastic gravitational wave background from cosmic strings by an electromagnetic resonance system
• Gravitational waves from low-scale cosmic strings without scaling
• Lorentz Violation with Gravitational Waves: Constraints from NANOGrav and IPTA Data
• A density-responsive scalar-field framework for singularity regularization and dynamical dark energy
• Gravitational wave signal from primordial magnetic fields in the Pulsar Timing Array frequency band
• Dark Matter and Electroweak Baryogenesis with Spontaneous $CP$ Violation in the Early Universe
• Gravitational waves from axion inflation in the gradient expansion formalism. Part II. Fermionic axion inflation
• Scalar-induced gravitational waves including isocurvature perturbations with lattice simulations
• Finite Populations & Finite Time: The Non-Gaussianity of a Gravitational Wave Background
• Revisiting PBH accretion, evaporation and their cosmological consequences
• Prospects for observing supermassive black hole binaries with the space-ground interferometer
• Circularly Polarized Gravitational Wave Background Search with a Network of Space-borne Triangular Detectors
• Observable CMB B-modes from Cosmological Phase Transitions
• Emission of Nambu-Goldstone bosons from the semilocal string network
• Prospects for joint multiband detection of intermediate-mass black holes by LGWA and the Einstein Telescope
• SageNet: Fast Neural Network Emulation of the Stiff-amplified Gravitational Waves from Inflation
• Dynamical backreaction of a mass-acquiring scalar field on first-order phase transitions
• Probing Leptophobic Dark Sectors via Gravitational Wave Signatures
• Probing leptogenesis and the minimal neutrino seesaw mechanism through gravitational waves
• Astrophysical and Cosmological Relevance of the High-Frequency Features in the Stochastic Gravitational-Wave Background
• Supercooled Audible Axions
• Probing cosmic strings via gravitational-wave lensing
• Superradiant dark matter production from primordial black holes: Impact of multiple modes and gravitational wave emission
• Search for high-frequency gravitational waves via re-analysis of cavity axion data
• Observable Gravitational Wave Strain at Second Order
• Searching for continuous gravitational waves from highly deformed compact objects with DECIGO
• First-post-Newtonian generation of gravitational waves in Einstein-Cartan theory
• Complementary signatures of $\alpha -$attractor inflation in CMB and cosmic string Gravitational Waves
• Constraints on High-Frequency Gravitational Waves from Graviton-Photon Conversion in the M87 Galaxy
• Collapsing domain walls with ${\mathbb{Z}}_2$-violating coupling to thermalized fermions and their impact on gravitational wave detections
• Smearing of primordial gravitational waves
• Gravitational wave energy spectral density properties from BPASS Galactic binary population in the Milky Way galaxy
• LISA and $\gamma$-ray telescopes as multi-messenger probes of a first-order cosmological phase transition
• Estimating the gravitational wave background anisotropy: a Bayesian approach boosted by cross-correlation angular power spectrum
• Antipodal Angular Correlations of Inflationary Stochastic Gravitational Wave Background
• Overlap reduction function for gravitational wave detectors in an expanding Universe
• About the measure of the bare cosmological constant
• The Effect of Mission Duration on LISA Science Objectives
• ACT DR6 Insights on the Inflationary Attractor models and Reheating
• Insights for Early Dark Energy with Big Bang Nucleosynthesis
• The role of longitudinal polarizations in Horndeski and macroscopic gravity: Introducing gravitational plasmas
• Primordial gravitational waves from excited states
• Constraints and detection capabilities of GW polarizations with space-based detectors in different TDI combinations
• Cosmic Collider Gravitational Waves sourced by Right-handed Neutrino production from Bubbles: Testing Seesaw, Leptogenesis and Dark Matter
• Constraining the inflaton potential with gravitational waves from oscillons
• Probing Bose-enhanced Inflaton Decay with Gravitational Waves
• Very-High-Frequency Gravitational Waves from Multi-Monodromy Inflation
• Linear perturbations of an exact gravitational wave in the Bianchi IV universe
• London-like tensor modes of gravitational waves in cosmic string cosmology
• High Sensitivity Methodologies to Detect Radio Band Gravitational Waves
• Inflationary phase transitions in the early Universe: A Bayesian study with space-based gravitational-wave detectors
• Gravitational Waves from Gauge Quanta Produced during Inflation
• Secondary gravitational waves against a strong gravitational wave in the Bianchi VI universe
• Stochastic gravitational wave background from the collisions of dark matter halos
• Detecting stochastic gravitational wave background from cosmic strings with next-generation detector networks: Component separation based on a multi-source astrophysical foreground noise model
• Torsion-Induced Modification to Friedmann Equations in $AdS{L}_4$ Gauged Gravity
• Constraints on typical relic gravitational waves based on data of LIGO
• Stochastic gravitational wave background due to core collapse resulting in neutron stars
• Detection of the stochastic gravitational wave background with the space-borne gravitational-wave detector network
• New LISA dynamics feedback control scheme: Common-mode isolation of test mass control and probes of test-mass acceleration
• One-Dimensional Primordial Gravitational Waves In Pure Quadratic Gravity
• Time-dependent deflection reconstruction: new technique to search for gravitational waves with the cosmic microwave background
• Spatial Correlation between Pulsars from Interfering Gravitational-Wave Sources in Massive Gravity
• Test of the Statistical Isotropy of the Universe using Gravitational Waves
• How gravitational waves change photon orbital angular momentum quantum states
• Decay of acoustic turbulence in two dimensions and implications for cosmological gravitational waves
• Bubble Correlation in First-Order Phase Transitions
• Accelerating Airy tensor modes of cosmological gravitational waves
• Gravitational Waves from Hyperbolic Encounters of Primordial Black Holes in Dwarf Galaxies
• Gravitational wave complementarity and impact of NANOGrav data on gravitational leptogenesis: cosmic strings
• Mutated hilltop inflation in light of Planck/ACT observations
• Graph-based Summary Statistics for Revealing the Stochastic Gravitational Wave Background in Pulsar Timing Arrays
• Hamilton-Jacobi analysis of noncanonical inflation in $f(R,T)$ gravity: Constraints from Planck/ACT data, and theoretical bounds
• Model-agnostic gravitational-wave background characterization algorithm
• Uncertainty in predicting the stochastic gravitational wave background from compact binary coalescences
• Gravitational wave production after inflation for a hybrid inflationary model
• Comparison of maximum likelihood mapping methods for gravitational-wave backgrounds
• Testing No slip model with pulsar timing arrays: NANOGrav and IPTA
• AliCPT Sensitivity to Cosmic Reheating
• Dark Matter Freeze-in from a $Z^{\prime }$ Reheaton
• Efficient Search for Detection Candidates Using a Peak Finder Strategy for All-Sky-All-Frequency Gravitational Wave Radiometer
• Correlation of Gravitational Wave Background Noises and Statistical Loss for Angular Averaged Sensitivity Curves
• Scalar-Induced Gravitational Waves in Palatini $f(R)$ Gravity