Scalar induced gravitational waves review

Abstract

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.

Testing Super-Heavy Dark Matter from Primordial Black Holes with Gravitational Waves

“…Ultra-light primordial black holes (PBHs), that is, black holes with mass M BH 10 9 g) [1][2][3] that exist and evaporate prior to Big Bang Nucleosynthesis (BBN) via Hawking radiation [4], can leave their traces by producing Gravitational Waves (GWs) [5][6][7][8][9][10][11][12], generating the Baryon asymmetry of the Universe (BAU) [13][14][15][16][17][18][19][20] and cosmologically stable relics [21,22]. Most importantly, owing to the fact that PBHs must be agnostic about Standard Model (SM) quantum numbers, as they evaporate they must also produce Dark Matter (DM) [13,[23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38][39][40].…”

Non-Gaussianity in inflationary scenarios for primordial black holes

“…If PBHs are to be produced in the numbers necessary to be responsible for these effects, then the power spectrum at small scales likely needs to be enhanced by ∼ O(10 7 ) relative to CMB measurements of A R [17][18][19][20][21], the precise enhancement required depending on the finer details of both the collapse and the shape of the power spectrum. For power spectra with a large peak at short scales, scalar induced gravitational waves (SIGWs) will also be produced at second order in perturbation theory [22][23][24][25][26][27][28][29][30][31][32].…”

“…As well as the necessary growth in the power spectrum, it is well understood that non-Gaussianity of the scalar perturbations can have important effects on both PBH production [33][34][35][36][37][38][39][40][41][42][43][44][45][46] and the spectrum of SIGWs [32,[47][48][49][50][51][52]. Although in reality the full probability distribution of perturbations is needed to accurately determine the production of PBHs, the reduced bipsectrum, f NL , can be used as a guide for when non-Gaussianity becomes important to the calculation.…”

NANOGrav Signal from double-inflection-point inflation

“…It is well known that at first order in perturbation theory the scalar and tensor perturbations are decoupled, however, at second order the free wave equation of tensor perturbations gets a source term of scalar perturbations. Thus, when the scalar perturbations reenter the Hubble radius in the radiation-dominated(RD) era, it can leads to the production of secondorder GWs [8,9], and if the power spectrum of scalar perturbations is enhanced at small scales, the induced GWs can be sizable to be detected by experiments in near future [10][11][12][13][14][15][16][17][18][19][20][21][22].…”