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.

Scalar Induced Gravitational Waves Review

Various pulsar timing array (PTA) experiments (NANOGrav, EPTA, PPTA, CPTA, including data from InPTA) very recently reported evidence for excess red common-spectrum signals in their latest datasets, with inter-pulsar correlations following the Hellings-Downs pattern, pointing to a stochastic gravitational wave background (SGWB) origin. Focusing for concreteness on the NANOGrav signal (given that all signals are in good agreement between each other), I inspect whether it supports an inflationary SGWB explanation, finding that such an interpretation calls for an extremely blue tensor spectrum, with spectral index $n_T \simeq 1.8 \pm 0.3$, while Big Bang Nucleosynthesis limits require a very low reheating scale, $T_{\rm rh} \lesssim 10\,{\rm GeV}$. While not impossible, an inflationary origin for the PTA signal is barely tenable: within well-motivated inflationary models it is hard to achieve such a blue tilt, whereas models who do tend to predict sizeable non-Gaussianities, excluded by observations. Intriguingly, ekpyrotic models naturally predict a SGWB with spectral index $n_T=2$, although with an amplitude too suppressed to be able to explain the signal detected by PTA experiments. Finally, I provide explicit expressions for a bivariate Gaussian approximation to the joint posterior distribution for the intrinsic-noise amplitude and spectral index of the NANOGrav signal, which can facilitate extending similar analyses to different theoretical signals.

Inflationary interpretation of the stochastic gravitational wave background signal detected by pulsar timing array experiments

We study whether the signal seen by pulsar timing arrays (PTAs) may originate from gravitational waves (GWs) induced by large primordial perturbations. Such perturbations may be accompanied by a sizable primordial black hole (PBH) abundance. We improve existing analyses and show that PBH overproduction disfavors Gaussian scenarios for scalar-induced GWs at 2σ and single-field inflationary scenarios, accounting for non-Gaussianity, at 3σ as the explanation of the most constraining NANOGrav 15-year data. This tension can be relaxed in models where non-Gaussianities suppress the PBH abundance. On the flip side, the PTA data does not constrain the abundance of PBHs.Received 4 July 2023Accepted 19 September 2023DOI:https://doi.org/10.1103/PhysRevLett.131.201401© 2023 American Physical SocietyPhysics Subject Headings (PhySH)Research AreasDark matterGravitational wavesInflationGravitation, Cosmology & Astrophysics 

Recent Gravitational Wave Observation by Pulsar Timing Arrays and Primordial Black Holes: The Importance of Non-Gaussianities

Primordial black holes formed in the early Universe via gravitational collapse of over-dense regions may contribute a significant amount to the present dark matter relic density. Inflation provides a natural framework for the production mechanism of primordial black holes. For example, single field inflation models with a fine-tuned scalar potential may exhibit a period of ultra-slow roll, during which the curvature perturbation may be enhanced to become seeds of the primordial black holes formed as the corresponding scales reenter the horizon. In this work, we propose an alternative mechanism for the primordial black hole formation. We consider a model in which a scalar field is coupled to the Gauss-Bonnet term and show that primordial black holes may be seeded when a scalar potential term and the Gauss-Bonnet coupling term are nearly balanced. Large curvature perturbation in this model not only leads to the production of primordial black holes, but it also sources gravitational waves at the second order. We calculate the present density parameter of the gravitational waves and discuss the detectability of the signals by comparing them with sensitivity bounds of future gravitational wave experiments.

Primordial black holes from Gauss-Bonnet-corrected single field inflation

Scalar metric fluctuations generically source a spectrum of gravitational waves at second order in perturbation theory, poising gravitational wave experiments as potentially powerful probes of the small-scale curvature power spectrum. We perform a detailed study of the imprint of primordial non-Gaussianity on these induced gravitational waves, emphasizing the role of both the disconnected and connected components of the primoridal trispectrum. Specializing to local-type non-Gaussianity, we numerically compute all contributions and present results for a variety of enhanced primordial curvature power spectra.

Non-Gaussianity and the induced gravitational wave background

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.

/pdf/nanograv-results-and-ligo-virgo-primordial-black-holes-in-4p2duwf0kp.pdf

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

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