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 _pl ², then the lowest-order contributions come from single (∼αT ²/m _pl ²) and double (∼T ⁴/m _pl ⁴) 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.