Gravitational-wave background as a probe of the primordial black-hole abundance

Footprints of the QCD Crossover on Cosmological Gravitational Waves at Pulsar Timing Arrays

Pulsar timing arrays (PTAs) have reported evidence for a stochastic gravitational wave (GW) background at nanohertz frequencies, possibly originating in the early Universe. We show that the spectral shape of the low-frequency (causality) tail of GW signals sourced at temperatures around T≳1  GeV is distinctively affected by confinement of strong interactions (QCD), due to the corresponding sharp decrease in the number of relativistic species, and significantly deviates from ∼f^{3} commonly adopted in the literature. Bayesian analyses in the NANOGrav 15 years and the previous international PTA datasets reveal a significant improvement in the fit with respect to cubic power-law spectra, previously employed for the causality tail. While no conclusion on the nature of the signal can be drawn at the moment, our results show that the inclusion of standard model effects on cosmological GWs can have a decisive impact on model selection.

Gravitational Waves from Rapid Structure Formation on Microscopic Scales before Matter-Radiation Equality

The existence of scalar fields can be probed by observations of stochastic gravitational waves. Scalar fields mediate attractive forces, usually stronger than gravity, on the length scales shorter than their Compton wavelengths, which can be non-negligible in the early Universe, when the horizon size is small. These attractive forces exhibit an instability similar to the gravitational instability, only stronger. They can, therefore, lead to the growth of structures in some species. We identify a gravitational waves signature of such processes and show that it can be detected by future gravitational waves experiments.

Enhanced Gravitational Waves from Inflaton Oscillons

In broad classes of inflationary models the period of accelerated expansion is followed by fragmentation of the inflaton scalar field into localized, long-lived, and massive oscillon excitations. We demonstrate that matter dominance of oscillons, followed by their rapid decay, significantly enhances the primordial gravitational wave (GW) spectrum. These oscillon-induced GWs, sourced by second-order perturbations, are distinct and could be orders of magnitude lower in frequency than the previously considered GWs associated with oscillon formation. We show that detectable oscillon-induced GW signatures establish direct tests independent from cosmic microwave background radiation for regions of parameter space of monodromy, and logarithmic and pure natural (plateau) potential classes of inflationary models, among others. We demonstrate that oscillon-induced GWs in a model based on pure natural inflation could be directly observable with the Einstein Telescope, Cosmic Explorer, and DECIGO. These signatures offer a new route for probing the underlying inflationary physics.

Type I Shapovalov Wave Spacetimes in the Brans–Dicke Scalar-Tensor Theory of Gravity

Exact solutions for Shapovalov wave spacetimes of type I in Brans–Dicke’s scalar-tensor theory of gravity are constructed. Shapovalov wave spacetimes describe gravitational wave models that allow for the the separation of wave variables in privileged coordinate systems. In contrast to general relativity, the vacuum field equations of the Brans–Dicke scalar-tensor theory of gravity lead to exact solutions for type I Shapovalov spaces, allowing for the the construction of observational tests to detect such wave disturbances. Furthermore, the equations for the trajectories of the test particles are obtained for the models considered.

Signatures of Primordial Gravitational Waves on the Large-Scale Structure of the Universe

We study the generation and evolution of second-order energy-density perturbations arising from primordial gravitational waves. Such "tensor-induced scalar modes" approximately evolve as standard linear matter perturbations and may leave observable signatures in the large-scale structure of the Universe. We study the imprint on the matter power spectrum of some primordial models which predict a large gravitational-wave signal at high frequencies. This novel mechanism, in principle, allows us to constrain or detect primordial gravitational waves by looking at specific features in the matter or galaxy power spectrum, thereby allowing us to probe them on a range of scales unexplored so far.

Why Must Primordial Non-Gaussianity Be Very Small?

One-loop correction to the power spectrum in generic single-field inflation is calculated by using standard perturbation theory. Because of the enhancement inversely proportional to the observed red tilt of the spectral index of curvature perturbation, the correction turns out to be much larger than previously anticipated. As a result, the primordial non-Gaussianity must be much smaller than the current observational bound in order to warrant the validity of cosmological perturbation theory.

Search for a Scalar Induced Stochastic Gravitational Wave Background in the Third LIGO-Virgo Observing Run

The formation of primordial black holes from inflationary fluctuations is accompanied by a scalar induced gravitational wave background. We perform a Bayesian search of such background in the data from Advanced LIGO and Virgo's first, second, and third observing runs, parametrizing the peak in the curvature power spectrum by a log-normal distribution. The search shows no evidence for such a background. We place 95% confidence level upper limits on the integrated power of the curvature power spectrum peak which, for a narrow width, reaches down to 0.02 at 10^{17}  Mpc^{-1}. The resulting constraints are stronger than those arising from big bang nucleosynthesis or cosmic microwave background observations. In addition, we find that the constraints from LIGO and Virgo, at their design sensitivity, and from the Einstein Telescope can compete with those related to the abundance of the formed primordial black holes.

Cosmic Coincidences of Primordial-Black-Hole Dark Matter

If primordial black holes (PBHs) contribute more than 10% of the dark matter (DM) density, their energy density today is of the same order as that of the baryons. Such a cosmic coincidence might hint at a mutual origin for the formation scenario of PBHs and the baryon asymmetry of the Universe. Baryogenesis can be triggered by a sharp transition of the rolling rate of inflaton from slow-roll to (nearly) ultraslow-roll phases that produce large curvature perturbations for PBH formation in single-field inflationary models. We show that the baryogenesis requirement drives the PBH contribution to DM, along with the inferred PBH mass range, the resulting stochastic gravitational wave background frequency window, and the associated cosmic microwave background tensor-to-scalar ratio amplitude, into potentially observable regimes.

Beating the Lyth Bound by Parametric Resonance during Inflation

We propose a novel mechanism for enhancing primordial gravitational waves without significantly affecting the curvature perturbations produced during inflation. This is achieved due to nonlinear sourcing of resonantly amplified scalar field fluctuations. Our result is an explicit scale-dependent counterexample of the famous Lyth bound, which opens up a promising perspective of producing detectable inflationary tensor modes with low-scale inflation and a sub-Planckian field excursion. We explicitly demonstrate the testability of our mechanism with upcoming cosmic microwave background B-mode observations.

Constraints on primordial black holes

We update the constraints on the fraction of the Universe that may have gone into primordial black holes (PBHs) over the mass range 10^-5to 10⁵⁰ g. Those smaller than ∼10¹⁵ g would have evaporated by now due to Hawking radiation, so their abundance at formation is constrained by the effects of evaporated particles on big bang nucleosynthesis, the cosmic microwave background (CMB), the Galactic and extragalacticγ-ray and cosmic ray backgrounds and the possible generation of stable Planck mass relics. PBHs larger than ∼10¹⁵ g are subject to a variety of constraints associated with gravitational lensing, dynamical effects, influence on large-scale structure, accretion and gravitational waves. We discuss the constraints on both the initial collapse fraction and the current fraction of the dark matter (DM) in PBHs at each mass scale but stress that many of the constraints are associated with observational or theoretical uncertainties. We also consider indirect constraints associated with the amplitude of the primordial density fluctuations, such as second-order tensor perturbations andμ-distortions arising from the effect of acoustic reheating on the CMB, if PBHs are created from the high-σpeaks of nearly Gaussian fluctuations. Finally we discuss how the constraints are modified if the PBHs have an extended mass function, this being relevant if PBHs provide some combination of the DM, the LIGO/Virgo coalescences and the seeds for cosmic structure. Even if PBHs make a small contribution to the DM, they could play an important cosmological role and provide a unique probe of the early Universe.

Scalar Induced Gravitational Waves Review

We provide a review on the state-of-the-art of gravitational waves induced by primordial fluctuations, so-called induced gravitational waves. We present the intuitive physics behind induced gravitational waves and we revisit and unify the general analytical formulation. We then present general formulas in a compact form, ready to be applied. This review places emphasis on the open possibility that the primordial universe experienced a different expansion history than the often assumed radiation dominated cosmology. We hope that anyone interested in the topic will become aware of current advances in the cosmology of induced gravitational waves, as well as becoming familiar with the calculations behind.

NANOGrav Results and LIGO-Virgo Primordial Black Holes in Axionlike Curvaton Models

We discuss a possible connection between the recent NANOGrav results and the primordial black holes (PBHs) for the LIGO-Virgo events. In particular, we focus on the axionlike curvaton model, which provides a sizable amount of PBHs and gravitational waves (GWs) induced by scalar perturbations around the NANOGrav frequency range. The inevitable non-Gaussianity of this model suppresses the induced GWs associated with PBHs for the LIGO-Virgo events to be compatible with the NANOGrav results. We show that the axionlike curvaton model can account for PBHs for the LIGO-Virgo events and the NANOGrav results simultaneously.

Did NANOGrav See a Signal from Primordial Black Hole Formation?

We show that the recent NANOGrav result can be interpreted as a stochastic gravitational wave signal associated to formation of primordial black holes from high-amplitude curvature perturbations. The indicated amplitude and power of the gravitational wave spectrum agrees well with formation of primordial seeds for supermassive black holes.

Pulsar Timing Array Constraints on Primordial Black Holes with NANOGrav 11-Year Dataset

The detection of binary black hole coalescences by LIGO and Virgo has aroused the interest in primordial black holes (PBHs), because they could be both the progenitors of these black holes and a compelling candidate of dark matter (DM). PBHs are formed soon after the enhanced scalar perturbations reenter horizon during the radiation dominated era, which would inevitably induce gravitational waves as well. Searching for such scalar induced gravitational waves (SIGWs) provides an elegant way to probe PBHs. We perform the first direct search for the signals of SIGWs accompanying the formation of PBHs in the North American Nanohertz Observatory for Gravitational waves (NANOGrav) 11-year dataset. No statistically significant detection has been made, and hence we place a stringent upper limit on the abundance of PBHs at 95% confidence level. In particular, less than one part in a million of the total DM mass could come from PBHs in the mass range of [2×10^{-3},7×10^{-1}]  M_{⊙}.

Gravitational Waves Induced by Non-Gaussian Scalar Perturbations

We study gravitational waves (GWs) induced by non-Gaussian curvature perturbations. We calculate the density parameter per logarithmic frequency interval, Ω_{GW}(k), given that the power spectrum of the curvature perturbation P_{R}(k) has a narrow peak at some small scale k_{*}, with a local-type non-Gaussianity, and constrain the nonlinear parameter f_{NL} with the future LISA sensitivity curve as well as with constraints from the abundance of the primordial black holes (PBHs). We find that the non-Gaussian contribution to Ω_{GW} increases as k^{3}, peaks at k/k_{*}=4/sqrt[3], and has a sharp cutoff at k=4k_{*}. The non-Gaussian part can exceed the Gaussian part if P_{R}(k)f_{NL}^{2}≳1. If both a slope Ω_{GW}(k)∝k^{β} with β∼3 and the multiple-peak structure around a cutoff are observed, it can be recognized as a smoking gun of the primordial non-Gaussianity. We also find that if PBHs with masses of 10^{20} to 10^{22}  g are identified as cold dark matter of the Universe, the corresponding GWs must be detectable by LISA-like detectors, irrespective of the value of P_{R} or f_{NL}.

Reheating the universe once more: the dissipation of acoustic waves as a novel probe of primordial inhomogeneities on even smaller scales

We provide a simple but robust bound on the primordial curvature perturbation in the range 10(4)  Mpc(-1)<k<10(5)  Mpc(-1), which has not been constrained so far unlike low-wave-number modes. Perturbations on these scales dissipate the energy of their acoustic oscillations by the Silk damping after primordial nucleosynthesis but before the redshift z∼2×10(6) and reheat the photon bath without invoking cosmic microwave background distortions. This acoustic reheating results in the decrease of the baryon-photon ratio. By combining independent measurements probing the nucleosynthesis era and around the recombination epoch, we find an upper bound on the amplitude of the curvature perturbation over the above wave number range as P(ζ)<0.06. Implications for supermassive black holes are also discussed.

Testing General Relativity with Low-Frequency, Space-Based Gravitational-Wave Detectors

We review the tests of general relativity that will become possible with space-based gravitational-wave detectors operating in the ∼ 10-5 - 1 Hz low-frequency band. The fundamental aspects of gravitation that can be tested include the presence of additional gravitational fields other than the metric; the number and tensorial nature of gravitational-wave polarization states; the velocity of propagation of gravitational waves; the binding energy and gravitational-wave radiation of binaries, and therefore the time evolution of binary inspirals; the strength and shape of the waves emitted from binary mergers and ringdowns; the true nature of astrophysical black holes; and much more. The strength of this science alone calls for the swift implementation of a space-based detector; the remarkable richness of astrophysics, astronomy, and cosmology in the low-frequency gravitational-wave band make the case even stronger.

Torsion-bar antenna for low-frequency gravitational-wave observations

We propose a novel type of gravitational-wave antenna, formed by two bar-shaped test masses and laser-interferometric sensors to monitor their differential angular fluctuations. This antenna has a fundamental sensitivity to low-frequency signals below 1 Hz, even with a ground-based configuration. In addition, it is possible to expand the observation band to a lower limit determined by the observation time, by using modulation and up-conversion of gravitational-wave signals by rotation of the antenna. The potential sensitivity of this antenna is superior to those of current detectors in a 1 mHz-10 Hz frequency band and is sufficient for observations of gravitational waves radiated from in-spiral and merger events of intermediate-mass black holes.

Grand unification scale primordial black holes: consequences and constraints

A population of very light primordial black holes which evaporate before nucleosynthesis begins is unconstrained unless the decaying black holes leave stable relics. We show that gravitons Hawking radiated from these black holes would source a substantial stochastic background of high frequency gravititational waves (10(12) Hz or more) in the present Universe. These black holes may lead to a transient period of matter-dominated expansion. In this case the primordial Universe could be temporarily dominated by large clusters of "Hawking stars" and the resulting gravitational wave spectrum is independent of the initial number density of primordial black holes.