Generation of helical magnetic field in a viable scenario of inflationary magnetogenesis

Abstract

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

How primordial magnetic fields shrink galaxies

“…The employed configuration for the magnetic seed field is to be understood as the main component of a field coherent on ∼ comoving Mpc scales. This is consistent with some inflationary model predictions (Ratra 1992;Barrow & Tsagas 2011;Sharma et al 2018). As a word of caution we remind that these type of initial magnetic fields do not encapsulate any small scale fluctuations, which might have interesting local effects during the formation of galaxies (Brandenburg & Subramanian 2005;Kandus et al 2011).…”

Constraints on primordial magnetic fields from magnetically-induced perturbations: current status and future perspectives with LiteBIRD and future ground based experiments

“…Helicity of PMFs is also important, since is useful to sustain an efficient dynamo amplification and avoid saturation. It is possible to generate fields with an helical contribution by several mechanisms [69][70][71][72] and numerical simulations show how the fields rapidly reach the maximally helical confinguration independentely from the initial conditions [73][74][75][76][77]. Last, but not least, helicity can leave imprints onto the Cosmic Microwave Background [78][79][80][81][82][83].…”

Helical magnetic fields from Riemann coupling

“…II). Helical magnetic fields are generated by the terms that break conformal invariance and parity symmetry [26][27][28][29][30][31][32][33].…”