Inflationary magnetogenesis with reheating phase from higher curvature coupling

Abstract

We investigate the generation of magnetic fields from inflation, which occurs via breakdown of the conformal invariance of the electromagnetic field, when coupled with the Ricci scalar and the Gauss-Bonnet invariant. For the case of instantaneous reheating, the resulting strength of the magnetic field at present is too small and violates the observational constraints. However, the problem is solved provided there is a reheating phase with a non-zero e-fold number. During reheating, the energy density of the magnetic field is seen to evolve as a −6 H 2 and, after that, as a −4 up to the present epoch (here a is the scale factor and H the Hubble parameter). It is found that this reheating phase -characterized by a certain e-fold number, a constant value of the equation of state parameter, and a given reheating temperature-renders the magnetogenesis model compatible with the observational constraints. The model provides, in turn, a viable way of constraining the reheating equation of state parameter, from data analysis of the cosmic microwave background radiation.extent, in various modified theories of gravity [56,[61][62][63][64][65][66][67][68].In this paper, we propose an inflationary magnetogenesis model, in which the electromagnetic field couples to the background spacetime curvature, specifically with the Ricci scalar and the Gauss-Bonnet invariant; i.e we include in our model a higher curvature coupling of the EM field. Such coupling breaks the conformal invariance of the electromagnetic action and allows the production of photons from the Bunch-Davies vacuum. Moreover, being this a higher-order operator, the coupling is suppressed at the Planck scale and, thus, the model becomes free from the strong coupling problem. In regard to the background spacetime, we consider the scalar-Einstein-Gauss-Bonnet gravity theory, which is known to provide viable inflationary models (consistent with the latest Planck results), for suitable choices of the Gauss-Bonnet coupling function and the scalar field potential [69][70][71][72][73][74][75][76][77][78][79][80][81][82]. In such scenario, we try to explore the dynamics of the electric and magnetic fields along with the cosmological expansion of the universe, starting from the inflationary stage. During the first steps of the cosmic expansion, the universe enters a reheating phase, after the end of inflation; and depending on the reheating mechanism, we consider two different scenarios: (1) instantaneous reheating at the end of inflation and (2) a Kamionkowski like reheating model with non-zero e-fold number, in which case the reheating phase is parametrized by a constant effective equation of state (EoS) parameter (ω eff ) [83] (for recent results on the reheating phase, see [84][85][86][87][88][89][90][91][92]). These two scenarios make qualitative differences in the evolution of electric and magnetic fields. In particular, the presence of the reheating phase with a non-zero e-fold number enhances the strength of the magnetic field, in comparison with the instantaneous re...

Addendum to: Dynamical torsion suppression in Brans–Dicke inflation and Lorentz violation (Eur Phys J C (2022)): Einstein–Cartan–Brans–Dicke–Maxwell universe with a chiral dynamo?

“…More on GR magnetogenesis may be found in the last reference [26]. Actually, Bamba et al [28] have investigated the non-helical magnetic fields in the reheating phase in higher-order curvature coupling. This is an interesting subject to work and to review in order to perform extensions to modified gravity magnetogenesis.…”

Effective Theory of Inflationary Magnetogenesis and Constraints on Reheating

“…Most importantly, introducing reheating era not only helps to obtain the right magnitude of the large scale magnetic field, it allows one to obtain valuable information about the reheating EoS parameter (ω eff ) which in turn can potentially constraint the inflationary model itself, which has been discussed before in some of our recent works [24,25]. Therefore, probing large scale magnetic field opens up a new probe to look into the reheating phase which is otherwise very difficult to constrain.…”

Inflationary magnetogenesis in the perturbative regime

“…[52,53]). However, if the reheating is perturbative as originally suggested in the new inflationary scenario [54] the effect of the duration of the reheating phase may be relevant (see also [47]).…”

“…As already suggested in the previous paragraph the continuity of the extrinsic curvature is an excellent starting point also in this case. More detailed models of reheating could be certainly useful and might affect the magnetogenesis scenarios (as suggested in [47]). In this paper we adopted the approximation of the sudden reheating which is also the one often employed in order to set limits on the tensor to scalar ratio and on the total number of inflationary e-folds.…”