Leading-order nonlinear gravitational waves from reheating magnetogeneses

Abstract

We study the leading-order nonlinear gravitational waves (GWs) produced by an electromagnetic (EM) stress in reheating magnetogenesis scenarios. Both nonhelical and helical magnetic fields are considered. By numerically solving the linear and leading-order nonlinear GW equations, we find that the GW energy from the latter is usually larger. We compare their differences in terms of the GW spectrum and parameterize the GW energy difference due to the nonlinear term, ∆EGW, in terms of EM energy EEM as ∆EGW = (pEEM/k * ) 3 , where k * is the characteristic wave number, p = 0.84 and 0.88 are found in the nonhelical and helical cases, respectively, with reheating around the QCD energy scale, while p = 0.45 is found at the electroweak energy scale. We also compare the polarization spectrum of the linear and nonlinear cases and find that adding the nonlinear term usually yields a decrease in the polarization that is proportional to the EM energy density. We parameterize the fractional polarization suppression as |∆PGW/PGW| = rEEM/k * and find r = 1.2 × 10 −1 , 7.2 × 10 −4 , and 3.2 × 10 −2 for the helical cases with reheating temperatures Tr = 300 TeV, 8 GeV, and 120 MeV, respectively. Prospects of observation by pulsar timing arrays, space-based interferometers, and other novel detection proposals are also discussed.

Modified propagation of gravitational waves from the early radiation era

“…[78] for a detailed calculation. Previous numerical work was usually restricted to specific eras, e.g., radiation (RD) [73,[79][80][81][82][83][84][85] or matter domination (MD) [86][87][88], using a constant equation of state (EOS), defined to be w ≡ p/ρ, being p the pressure and ρ the energy density, such that w = 1/3 and 0 during RD and MD, respectively. The dynamical thermal history of the universe during RD, represented by the relativistic g * and adiabatic g S degrees of freedom, was also ignored.…”

Gravitational wave signal from primordial magnetic fields in the Pulsar Timing Array frequency band

“…We also show, for comparison, the SGWB obtained in ref. [27] from an inflationary magnetogenesis scenario with an end-ofreheating temperature around the QCD scale, both for a non-helical magnetic field with Ω * M 0.04 and k * 2.9 H * at T * = 150 MeV, and a helical field with Ω * M 0.1 and k * 6.7 H * at T * = 120 MeV.…”

“…The dotted lines correspond to the inflationary magnetogenesis scenario of ref. [27] with an end-of-reheating temperature around the scale of the QCD phase transition.…”

“…by adding a forcing term in the induction equation to model the magnetic field generation. The dotted lines correspond to the inflationary magnetogenesis scenario of ref [27]. with an end-of-reheating temperature around the scale of the QCD phase transition.…”

“…Several sources could produce such a signal, in particular a population of merging supermassive black hole binaries [19][20][21]. Cosmological sources have also been proposed, including inflationary GWs [22][23][24][25][26][27], cosmic strings and domain walls [24,[28][29][30][31][32][33][34][35][36], primordial black holes [37][38][39][40], supercooled and dark phase transitions [41][42][43][44], and the QCD phase transition [45,46], as well as primordial magnetic fields [47,48].…”