Gravitational wave background from Standard Model physics: qualitative features

Abstract

Because of physical processes ranging from microscopic particle collisions to macroscopic hydrodynamic fluctuations, any plasma in thermal equilibrium emits gravitational waves. For the largest wavelengths the emission rate is proportional to the shear viscosity of the plasma. In the Standard Model at T > 160 GeV, the shear viscosity is dominated by the most weakly interacting particles, right-handed leptons, and is relatively large. We estimate the order of magnitude of the corresponding spectrum of gravitational waves. Even though at small frequencies (corresponding to the sub-Hz range relevant for planned observatories such as eLISA) this background is tiny compared with that from non-equilibrium sources, the total energy carried by the high-frequency part of the spectrum is non-negligible if the production continues for a long time. We suggest that this may constrain (weakly) the highest temperature of the radiation epoch. Observing the high-frequency part directly sets a very ambitious goal for future generations of GHz-range detectors.

Science with the space-based interferometer eLISA. II: gravitational waves from cosmological phase transitions

“…Thermal loops of new bosonic modes can contribute 10 A GW spectrum is nonetheless generated by equilibrium phenomena in the electroweak plasma, such as scatterings between thermal constituents and collective phenomena. The resulting spectrum [41] is however tens of orders of magnitude below eLISA sensitivity.…”

Numerical simulations of acoustically generated gravitational waves at a first order phase transition

“…In Ref. [37], generation of gravitational waves in the Standard Model in the absence of such a cascade was discussed.…”

Gravitational wave background from Standard Model physics: complete leading order

“…On the other hand, the age of the universe (inverse Hubble rate) is ∼ m Pl , so that the total energy density emitted into gravitational radiation is only suppressed by 1/m Pl . This may motivate a precise computation of the production rate and its integration over the history of the universe [2].…”

“…(1.1) in the frequency range in which de GW peaks. This range is given by the typical thermal scale k ∼ πT [2], corresponding after red shift to the same microwave range at which most CMB photons lie. In this frequency range, the gravitational wave abundance is expected to be much below equilibrium, f GW n B (k), so that the right-hand side of eq.…”

“…, and O(g 4 ) refers generically to any 3-loop contribution. 2 Here s, f, g refer to effects from scalars, fermions, and gauge bosons, respectively; Φ a is a 1-loop diagram with a particle of type a; Φ a(b) is a 2-loop diagram where a particle of type a couples to T µν and a particle of type b appears in a loop; and Φ a|b is a 2-loop diagram involving a cross correlation between the energy-momentum tensors of particles of types a and b (in terms of matrix elements this corresponds to an interference term). The corresponding Feynman diagrams are shown in figure 1.…”