Cosmological Gravitational Wave Background Research Articles

Induced gravitational waves: the effect of first order tensor perturbations

Scalar induced gravitational waves contribute to the cosmological gravitational wave background. They can be related to the primordial density power spectrum produced towards the end of inflation and therefore are a convenient new tool to constrain models of inflation. These waves are sourced by terms quadratic in perturbations and hence appear at second order in cosmological perturbation theory. While the focus of research so far was on purely scalar source terms we also study the effect of including first order tensor perturbations as an additional source. This gives rise to two additional source terms: a term quadratic in the tensor perturbations and a cross term involving mixed scalar and tensor perturbations. We present full analytical expressions for the spectral density of these new source terms and discuss their general behaviour. To illustrate the generation mechanism we study two toy models containing a peak on small scales. For these models we show that the scalar-tensor contribution becomes non-negligible compared to the scalar-scalar contribution on smaller scales. We also consider implications for future gravitational wave surveys.

Inflationary initial conditions for the cosmological gravitational wave background

The initial conditions on the anisotropies of the stochastic gravitational-wave background of cosmological origin (CGWB) largely depend on the mechanism that generates the gravitational waves. Since the CGWB is expected to be non-thermal, the computation of the initial conditions could be more challenging w.r.t. the Cosmic Microwave Background (CMB), whose interactions with other particles in the early Universe lead to a blackbody spectrum. In this paper, we show that the initial conditions for the cosmological background generated by quantum fluctuations of the metric during inflation deviate from adiabaticity. These primordial gravitational waves are indeed generated by quantum fluctuations of two independent degrees of freedom (the two polarization states of the gravitons). Furthermore, the CGWB plays a negligible role in the Einstein's equations, because its energy density is subdominant w.r.t. ordinary matter. Therefore, the only possible way to compute the initial conditions for inflationary gravitons is to perturb the energy-momentum tensor of the gravitational field defined in term of the small-scale tensor perturbation of the metric. This new and self-consistent approach shows that a large, non-adiabatic initial condition is present even during the single-field inflation. Such a contribution enhances the total angular power spectrum of the CGWB compared to the standard adiabatic case, increasing also the sensitivity of the anisotropies to the presence of relativistic and decoupled particles in the early Universe. In this work we have also proved that our findings are quite general and apply to both single-field inflation and other scenarios in which the CGWB is generated by the quantum fluctuations of the metric, like the curvaton.

Impact of the noise knowledge uncertainty for the science exploitation of cosmological and astrophysical stochastic gravitational wave background with LISA

Impact of the noise knowledge uncertainty for the science exploitation of cosmological and astrophysical stochastic gravitational wave background with LISA

On the anisotropies of the cosmological gravitational-wave background from pulsar timing array observations

Significant evidence for a stochastic gravitational-wave background has recently been reported by several Pulsar Timing Array observations. These studies have shown that, in addition to astrophysical explanations based on supermassive black hole binaries (SMBHBs), cosmological origins are considered equally important sources for these signals. To further explore these cosmological sources, in this study, we discuss the anisotropies in the cosmological gravitational wave background (CGWB) in a model-independent way. Taking the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) 15-year dataset as a benchmark, we estimate the angular power spectra of the CGWB and their cross-correlations with cosmic microwave background (CMB) fluctuations and weak gravitational lensing. We find that the NANOGrav 15-year data implies suppressed Sachs-Wolf (SW) effects in the CGBW spectrum, leading to a marginally negative cross-correlation with the CMB at large scales. This procedure is applicable to signals introduced by different early universe processes and is potentially useful for identifying unique features about anisotropies of CGWB from future space-based interferometers and astrometric measurements.

Elastic scattering of cosmological gravitational wave backgrounds: primordial black holes and stellar objects

Primordial black holes (PBHs) are plausible dark matter candidates that formed from the gravitational collapse of primordial density fluctuations. Current observational constraints allow asteroid-mass PBHs to account for all of the cosmological dark matter. We show that elastic scattering of a cosmological gravitational wave background, these black holes generate spectral distortions on the background of 0.3% for cosmologically relevant frequencies without considering coherent scattering and 5% when the coherent enhancement is included. Scattering from stellar objects induce much smaller distortions. Detectability of this signal depends on our ultimate understanding of the unperturbed background spectrum.

Erratum: Detecting cosmological gravitational wave background after removal of compact binary coalescences in future gravitational wave detectors [Phys. Rev. D 107 , 064048 (2023)

Erratum: Detecting cosmological gravitational wave background after removal of compact binary coalescences in future gravitational wave detectors [Phys. Rev. D <b>107</b> , 064048 (2023)

GW_CLASS: Cosmological Gravitational Wave Background in the cosmic linear anisotropy solving system

The anisotropies of the Cosmological Gravitational Wave Background (CGWB) retain information about the primordial mechanisms that source the gravitational waves and about the geometry and the particle content of the universe at early times. In this work, we discuss in detail the computation of the angular power spectra of CGWB anisotropies and of their cross correlation with Cosmic Microwave Background (CMB) anisotropies, assuming different processes for the generation of these primordial signals. We present an efficient implementation of our results in a modified version of CLASS which will be publicly available. By combining our new code GW_CLASS with MontePython, we forecast the combined sensitivity of future gravitational wave interferometers and CMB experiments to the cosmological parameters that characterize the cosmological gravitational wave background.

Unraveling the CMB lack-of-correlation anomaly with the cosmological gravitational wave background

Since the very first observations, the Cosmic Microwave Background (CMB) has revealed on large-scales unexpected features known as anomalies, which challenge the standard Λ cold dark matter (ΛCDM) cosmological model. One such anomaly is the “lack-of-correlation”, where the measured two-point angular correlation function of CMB temperature anisotropies is compatible with zero, differently from the predictions of the standard model. This anomaly could indicate a deviation from the standard model, unknown systematics, or simply a rare realization of the model itself. In this study, we explore the possibility that the lack-of-correlation anomaly is a consequence of living in a rare realization of the standard model, by leveraging the potential information provided by the cosmological gravitational wave background (CGWB) detectable by future gravitational wave (GW) interferometers. We analyze both constrained and unconstrained realizations of the CGWB to investigate the extent of information that GWs can offer. To quantify the impact of the CGWB on the lack-of-correlation anomaly, we employ established estimators and introduce a new estimator that addresses the “look-elsewhere” effect. Additionally, we consider three different maximum multipoles, denoted as ℓ max, to account for the anticipated capabilities of future GW detectors (ℓ max = 4, 6, 10). Summarizing our findings for the case of ℓ max = 4, we identify the angular range [63∘ - 180∘] as the region where future observations of the CGWB maximize the probability of rejecting the standard model. Furthermore, we calculate the expected significance of this observation, demonstrating that 98.81% (81.67%) of the constrained GW realizations enhance the current significance of the anomaly when considering the full-sky (masked) Planck SMICA map as our CMB sky.

Confronting sound speed resonance with pulsar timing arrays

The stochastic signal detected by pulsar timing arrays (PTAs) has raised great interest in understanding its physical origin. Assuming the signal is a cosmological gravitational-wave background produced by overly large primordial curvature perturbations, we investigate the sound speed resonance effect with an oscillatory behavior using the combined PTA data from NANOGrav 15-yr data set, PPTA DR3, and EPTA DR2.We find that the stochastic signal can be explained by the induced gravitational waves sourced by the sound speed resonance mechanism, with the oscillation frequency f * ∈ [1.51, 4.90] × 10-7Hz and the start time of oscillation |τ 0| ∈ [2.05, 106] × 107s.

New universal property of cosmological gravitational wave anisotropies

The anisotropies of the stochastic gravitational wave background, as produced in the early phases of cosmological evolution, can act as a key probe of the primordial universe particle content. We point out a new universal property of gravitational wave anisotropies of cosmological origin: for adiabatic initial conditions, their angular power spectrum is insensitive to the equation of state of the cosmic fluid driving the expansion before big-bang nucleosynthesis. Any deviation from this universal behaviour points to the presence of non-adiabatic sources of primordial fluctuations. Such scenarios can be tested by gravitational wave detectors operating at a frequency range which is fully complementary to CMB experiments. In this work we prove this general result, and we illustrate its consequences for a representative realisation of initial conditions based on the curvaton scenario. In the case of the simplest curvaton setup, we also find a significant cross-correlation between gravitational wave anisotropies and the CMB temperature fluctuations. There is a fourfold enhancement vis-\`{a}-vis the purely adiabatic scenario. We discuss the implications of our findings for identifying the origin of the (cosmological) gravitational wave background when, as is often the case, this cannot be determined solely on the basis of its spectral shape.

Detecting cosmological gravitational wave background after removal of compact binary coalescences in future gravitational wave detectors

The improved sensitivity of third generation gravitational wave detectors opens the possibility of detecting the primordial cosmological stochastic gravitational wave background (SGWB). Detection of the cosmological SGWB is facing a novel challenge: it will likely be masked by the foreground generated by a large number of coalescences of compact binary systems consisting of black holes and/or neutron stars. In this paper, we investigate the possibility of reducing this foreground by removing (notching) the individually resolved compact binary signals in time-frequency space. We establish that such an approach could be used to reach the SGWB sensitivity floor defined by the unresolved part of the compact binaries foreground, which we find to be between ${\mathrm{\ensuremath{\Omega}}}_{\mathrm{GW}}\ensuremath{\sim}(9.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}--8.6\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}11})$ for a frequency independent energy density spectrum and depending on the rate of coalescing binary neutron star systems. Since third-generation gravitational wave detectors will not be able to resolve all compact binaries, the unresolvable component of the compact binaries foreground may limit the SGWB searches with these detectors.

Probing neutrino interactions and dark radiation with gravitational waves

After their generation, cosmological backgrounds of gravitational waves propagate nearly freely but for the expansion of the Universe and the anisotropic stress of free-streaming particles. Primordial signals — both that from inflation and the infrared spectrum associated to subhorizon production mechanisms — would carry clean information about the cosmological history of these effects. We study the modulation of the standard damping of gravitational waves by free-streaming radiation due to the decoupling (or recoupling) of interactions. We focus on nonstandard neutrino interactions in effect after the decoupling of weak interactions as well as more general scenarios in the early Universe involving other light relics. We develop semianalytic results in fully free-streaming scenarios to provide intuition for numerical results that incorporate interaction rates with a variety of temperature dependencies. Finally, we compute the imprint of neutrino interactions on the B-mode polarization of the cosmic microwave background, and we comment on other means to infer the presence of such effects at higher frequencies.

Covariant transverse-traceless projection for secondary gravitational waves

Second-order tensor modes induced by nonlinear gravity are a key component of the cosmological background of gravitational waves. A detection of this background would allow us to probe the primordial power spectrum at otherwise inaccessible scales. Usually, the energy density of these gravitational waves is studied within perturbation theory in a particular gauge -- a connection between our physical spacetime and a fictitious background. It is a widely recognized issue that the second-order, scalar-induced gravitational waves are gauge dependent. This issue arises because they are not well-defined as tensors in the physical spacetime at second-order and are thus unphysical. In this paper, we propose the covariant transverse-traceless projection of the extrinsic curvature to study cosmological gravitational waves on a spatial hypersurface. We define a new energy density which is based purely on spacetime tensors, independent of perturbation theory, and thus is gauge invariant by definition. We show that, in the context of second-order perturbation theory, this new energy density contains only propagating modes in the constant-time hypersurface in the Newtonian gauge. We further show that we can recover the same gravitational waves after a transformation to the synchronous gauge, so long as we correctly identify the Newtonian hypersurface.

Test of the statistical isotropy of the universe using gravitational waves

Since WMAP and Planck some anomalous features appeared in the Cosmic Microwave Background (CMB) large-angle anisotropy, the so-called anomalies. One of these is the hemispherical power asymmetry, i.e. a difference in the average power on the two hemispheres centered around (l,b) = (221, -20), which shows a relatively high level of significance. Such an anomaly could be the signature of a departure from statistical isotropy on large scales. Here we investigate the physical origin of this anomaly using the Cosmological Gravitational Wave Background (CGWB) detectable by future GW detectors. Indeed, the CGWB offers a unique window to explore the early universe and we show that it can be used in combination with CMB data to shed light on the statistical isotropy of our universe. Specifically, we study the evolution of gravitons in the presence of a modulating field in the scalar gravitational potentials accounting for the hemispherical power asymmetry and we infer the amplitude of this modulating field through a minimal variance estimator exploiting both constrained and unconstrained realizations of the CGWB. We show that the addition of the CGWB will allow an improvement in the assessment of the physical origin of the CMB power asymmetry. Accounting for the expected performances of LISA and BBO, we also show that the latter is expected to be signal-dominated on large-scales, proving that the CGWB could be the keystone to assess the significance of this anomaly.

Measuring parity violation in the Stochastic Gravitational Wave Background with the LISA-Taiji network

Parity violation is a powerful observable to distinguish a cosmological background of Gravitational Waves (GWs) from an astrophysical one. Planar single GW interferometers, both on ground and in space, are unable to measure the net circular polarization of an isotropic Stochastic Gravitational Wave Background (SGWB). In this paper, we explore the possibility of detecting circular polarization of an isotropic SGWB by cross-correlating two space-based detectors planned to be launched around 2034: LISA and Taiji. We compute the response of such a network to chirality and we perform a Fisher forecast analysis on the I and V Stokes parameters for the SGWB. We find that a clear measurement of chirality can be claimed for a maximally chiral flat signal with amplitude h 2 ΩGW ≃ 10−12 at the frequency scales of LISA and Taiji.

Searching for cosmological gravitational-wave backgrounds with third-generation detectors in the presence of an astrophysical foreground

The stochastic cosmological gravitational-wave background (CGWB) provides a direct window to study early universe phenomena and fundamental physics. With the proposed third-generation ground-based gravitational wave detectors, Einstein Telescope (ET) and Cosmic Explorer (CE), we might be able to detect evidence of a CGWB. However, to dig out these prime signals would be a difficult quest as the dominance of the astrophysical foreground from compact-binary coalescence (CBC) will mask this CGWB. In this paper, we study a subtraction-noise projection method, making it possible to reduce the residuals left after subtraction of the astrophysical foreground of CBCs, greatly improving our chances to detect a cosmological background. We carried out our analysis based on simulations of ET and CE and using posterior sampling for the parameter estimation of binary black-hole mergers. We demonstrate the sensitivity improvement of stochastic gravitational-wave searches and conclude that the ultimate sensitivity of these searches will not be limited by residuals left when subtracting the estimated BBH foreground, but by the fraction of the astrophysical foreground that cannot be detected even with third-generation instruments, or possibly by other signals not included in our analysis. We also resolve previous misconceptions of residual noise in the context of Gaussian parameter estimation.

General solutions of the leakage in integral transforms and applications to the EB-leakage and detection of the cosmological gravitational wave background

For an orthogonal integral transform with complete dataset, any two components are linearly independent; however, when some data points are missing, there is going to be leakage from one component to another, which is referred to as the “leakage in integral transforms” in this work. A special case of this kind of leakage is the EB-leakage in detection of the cosmological gravitational wave background (CGWB). I first give the general solutions for all integral transforms, prove that they are the best solutions, and then apply them to the case of EB-leakage and detection of the CGWB. In the upcoming decade, most likely, new cosmic microwave background (CMB) data are from ground/balloon experiments, so they provide only partial sky coverage. Even in a fullsky mission, due to the Galactic foreground, part of the sky is still unusable. Within this context, the EB-leakage becomes inevitable. I show how to use the general solutions to achieve the minimal error bars of the EB-leakage, and use it to find out the maximum ability to detect the CGWB through CMB. The results show that, when focusing on the tensor-to-scalar ratio r (at a pivot scale of 0.05 Mpc−1), 1% sky coverage (fsky=1%) is enough for a 5σ-detection of r≥ 10−2, but is barely enough for r=10−3. If the target is to detect r∼ 10−4 or 10−5, then fsky≥ 10% is strongly recommended to enable a 5σ-detection and to reserve some room for other errors.

Gravitational Casimir effect, the Lifshitz theory, and the existence of gravitons

It has been predicted that, if gravitational wave reflectors exist, two such parallel plane gravitational mirrors separated by an empty gap will interact not only via the well-known Casimir effect of quantum electrodynamics but also because of an analogous gravitational Casimir force. It has been further claimed that this phenomenon would demonstrate the existence of gravitons. In this note, we discuss epistemological pitfalls of such a conclusion connected to the logical structure of the Lifshitz theory and we show such an experiment cannot prove gravity quantization. We also expose interpretative challenges of any future data due to extreme uncertainties on the spectrum of the predicted stochastic astrophysical and cosmological gravitational wave background.

Updated constraints and forecasts on primordial tensor modes

We present new, tight, constraints on the cosmological background of gravitational waves (GWs) using the latest measurements of CMB temperature and polarization anisotropies provided by the Planck, BICEP2 and Keck Array experiments. These constraints are further improved when the GW contribution $N^{\rm GW}_{\rm eff}$ to the effective number of relativistic degrees of freedom $N_{\rm eff}$ is also considered. Parametrizing the tensor spectrum as a power law with tensor-to-scalar ratio $r$, tilt $n_\mathrm{t}$ and pivot $0.01\,\mathrm{Mpc}^{-1}$, and assuming a minimum value of $r=0.001$, we find $r < 0.089$, $n_\mathrm{t} = 1.7^{+2.1}_{-2.0}$ ($95\%\,\mathrm{CL}$, no $N^{\rm GW}_{\rm eff}$) and $r < 0.082$, $n_\mathrm{t} = -0.05^{+0.58}_{-0.87}$ ($95\%\,\mathrm{CL}$, with $N^{\rm GW}_{\rm eff}$). When the recently released $95\,\mathrm{GHz}$ data from Keck Array are added to the analysis, the constraints on $r$ are improved to $r < 0.067$ ($95\%\,\mathrm{CL}$, no $N^{\rm GW}_{\rm eff}$), $r < 0.061$ ($95\%\,\mathrm{CL}$, with $N^{\rm GW}_{\rm eff}$). We discuss the limits coming from direct detection experiments such as LIGO-Virgo, pulsar timing (European Pulsar Timing Array) and CMB spectral distortions (FIRAS). Finally, we show future constraints achievable from a COrE-like mission: if the tensor-to-scalar ratio is of order $10^{-2}$ and the inflationary consistency relation $n_\mathrm{t} = -r/8$ holds, COrE will be able to constrain $n_\mathrm{t}$ with an error of $0.16$ at $95\%\,\mathrm{CL}$. In the case that lensing $B$-modes can be subtracted to $10\%$ of their power, a feasible goal for COrE, these limits will be improved to $0.11$ at $95\%\,\mathrm{CL}$.

Correlations between cosmic strings and extra relativistic species

The recent observation that the Cosmic Microwave Background (CMB) may prefer a neutrino excess has triggered a number of works studying this possibility. The effect obtained by the non-interacting massless neutrino excess could be mimicked by some extra radiation component in the early universe, such as a cosmological gravitational wave background. Prompted by the fact that a possible candidate to source those gravitational waves would be cosmic strings, we perform a parameter fitting study with models which considers both cosmic strings and the effective number of neutrinos as free parameters, using CMB and non-CMB data. We find that there is a correlation between cosmic strings and the number of extra relativistic species, and that strings can account for all the extra radiation necessary. In fact, CMB data prefer strings at a 2sigma level, paying the price of a higher extra radiation component. CMB data also give a moderate preference for a model with ns=1. The inclusion of non-CMB data lowers both the preference for strings and for the extra relativistic species.