Models of inflationary magnetogenesis with a coupling to the electromagnetic action of the form f 2 Fµν F µν , are known to suffer from several problems. These include the strong coupling problem, the back reaction problem and also strong constraints due to Schwinger effect. We propose a model which resolves all these issues. In our model, the coupling function, f , grows during inflation and transits to a decaying phase post inflation. This evolutionary behaviour is chosen so as to avoid the problem of strong coupling. By assuming a suitable power law form of the coupling function, we can also neglect back reaction effects during inflation. To avoid back reaction post-inflation, we find that the reheating temperature is restricted to be below ≈ 1.7 × 10 4 GeV. The magnetic energy spectrum is predicted to be non-helical and generically blue. The estimated present day magnetic field strength and the corresponding coherence length taking reheating at the QCD epoch(150 MeV) are 1.4×10−12 G and 6.1 × 10 −4 Mpc, respectively. This is obtained after taking account of nonlinear processing over and above the flux freezing evolution after reheating. If we consider also the possibility of a non-helical inverse transfer, as indicated in direct numerical simulations, the coherence length and the magnetic field strength are even larger. In all cases mentioned above, the magnetic fields generated in our models satisfy the γ-ray bound below a certain reheating temperature.
Generation of magnetic fields during inflation is a promising mechanism for the origin of the observed large scale magnetic fields in the universe. Among several attempts, a popular model is one where the inflaton and the electromagnetic field are coupled through a coupling function f leading to a term in the Lagrangian density of the form, f 2 F µν Fµν . A number of potential difficulties with such models have been raised in the literature. In our earlier work, we have suggested viable models of inflationary magnetogenesis which avoid these problems and at the same time can lead to either nonhelical or helical magnetic fields of astrophysical interest. Our models require a low energy scale for inflation and reheating (reheating temperature, TR < 10 4 GeV) and generate a blue spectrum of electromagnetic (EM) field which peaks around the horizon scale of reheating. We show here that the anisotropic stress associated with these EM fields naturally source the production of a stochastic background of Gravitational waves (GW) with frequencies in the range of tens of nano Hertz to milli Hertz. These two extremes of the range can be probed respectively by pulsar timing arrays (PTA) experiments and the upcoming Laser Interferometric Space Array (LISA). The peak value of the GW spectrum energy represented by dΩGW /d ln k is 10 −6 for the models which lead to nonhelical primordial fields and 2 × 10 −6 for the helical case for TR = 100 GeV. In this case the spectrum peaks at a frequency 30µHz for non helical case and at 40µHz for helical case. These values are obtained when the ratio of EM energy density to the cosmological density at reheating ∼ 1 and decrease approximately as 2 for smaller values. The amplitude is similar for a lower value of TR, but the frequency at which the GW spectrum peaks decreases as TR. The gravitational waves generated are unpolarized if the EM fields are nonhelical but are circularly polarised for helical primordial fields. If detected in future these gravitational waves will provide a unique probe of such models of inflationary magnetogenesis. * ramkishor@iucaa.in † kandu@iucaa.in ‡ trs@physics.du.ac.in
The Saffman helicity invariant of Hosking & Schekochihin (Phys. Rev. X, vol. 11, issue 4, 2021, 041005), which we here call the Hosking integral, has emerged as an important quantity that may govern the decay properties of magnetically dominated non-helical turbulence. Using a range of different computational methods, we confirm that this quantity is indeed gauge invariant and nearly perfectly conserved in the limit of large Lundquist numbers. For direct numerical simulations with ordinary viscosity and magnetic diffusivity operators, we find that the solution develops in a nearly self-similar fashion. In a diagram quantifying the instantaneous decay coefficients of magnetic energy and integral scale, we find that the solution evolves along a line that is indeed suggestive of the governing role of the Hosking integral. The solution settles near a line in this diagram that is expected for a self-similar evolution of the magnetic energy spectrum. The solution will settle in a slightly different position when the magnetic diffusivity decreases with time, which would be compatible with the decay being governed by the reconnection time scale rather than the Alfvén time.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.