Gravitational wave background from Standard Model physics: complete leading order

Abstract

We compute the production rate of the energy density carried by gravitational waves emitted by a Standard Model plasma in thermal equilibrium, consistently to leading order in coupling constants for momenta k ∼ πT. Summing up the contributions from the full history of the universe, the highest temperature of the radiation epoch can be constrained by the so-called N eff parameter. The current theoretical uncertainty ∆N eff ≤ 10 −3 corresponds to T max ≤ 2 × 10 17 GeV. In the course of the computation, we show how a subpart of the production rate can be determined with the help of standard packages, even if subsequently an IR subtraction and thermal resummation need to be implemented.

High-frequency graviton from inflaton oscillation

“…Lastly we discuss other contributions to the high-frequency stochastic GW background spectrum, which can hide the vacuum contributions that we found. The Standard Model thermal plasma emits gravitons through scattering processes and they also constitute a stochastic GW background [22,23]. The typical frequency of the emitted graviton at the temperature T is of order T and it is redshifted as a −1 (t).…”

Efficient numerical integration of thermal interaction rates

“…If the non-equilibrium particle is non-relativistic (M T ), it would be dangerous to incorporate 2 ↔ 2 or 1 ↔ 3 rates, without a full account of the virtual corrections to 1 ↔ 2 processes that may cancel most of the result. 11 A c code implementing the numerical parts of our procedure, and a form code implementing the algebraic ones, are attached as ancillary files to this paper. Even if their details are specific to the example in eq.…”

“…The story is similar for GeV-scale right-handed neutrino production from a Standard Model plasma in the early universe, where 2 ↔ 2 scatterings involving weak gauge bosons are numerically the largest individual contribution [3,4], or for the flavour equilibration rate of the most weakly interacting Standard Model particles, right-handed electrons [5]. There are even cases in which only 2 ↔ 2 scatterings need to be included at leading order, notably the production rates of axions, gravitinos, or gravitons [6][7][8][9][10][11], or particles which interact via the Fermi model, like neutrinos at low temperatures.…”

Universal 1020 Hz stochastic gravitational waves from photon spheres of black holes

“…In order to boost the study of high-frequency gravitational wave detectors, the existence of guaranteed sources which emit high-frequency gravitational waves is essential. So far, various high-frequency gravitational wave sources have been proposed [4,[9][10][11][12][13][14][15][16][17][18][19][20]. In particular, primordial black holes (PBHs) [21] are a possible source of highfrequency gravitational waves [22][23][24][25].…”

“…At present, however, it would be fair to say that the existence of these sources are not guaranteed. There is a more plausible source of highfrequency waves, namely those emitted by thermal fluctuations in the hot plasma, first proposed in [17] and further developed recently in [18,19]. These lead to peak emissions around 80 GHz, with an amplitude that scales with the reheating temperature, reaching Ω gw ∼ 10 −10 for grand unified theory-scale temperatures.…”