Double-graviton production from Standard Model plasma

The thermal plasma filling the early universe generated a stochastic gravitational wave background that peaks in the microwave frequency range today. If the graviton production rate is expressed as a series in a fine-structure constant, α, and the temperature over the Planck mass, T 2/m pl2, then the lowest-order contributions come from single (∼αT 2/m pl2) and double (∼T 4/m pl4) graviton production via 2 → 2 scatterings. We show that in the Standard Model, single-graviton production dominates if the maximal temperature is smaller than 4 × 1018 GeV. This justifies previous calculations which relied solely on single-graviton production. We mention Beyond the Standard Model scenarios in which the single and double-graviton contributions could be of comparable magnitudes. Finally, we elaborate on what these results imply for the range of applicability of General Relativity as an effective theory.