Abstract. We consider the generation of primordial magnetic fields in a class of bouncing models when the electromagnetic action is coupled non-minimally to a scalar field that, say, drives the background evolution. For scale factors that have the power law form at very early times and non-minimal couplings which are simple powers of the scale factor, one can easily show that scale invariant spectra for the magnetic field can arise before the bounce for certain values of the indices involved. It will be interesting to examine if these power spectra retain their shape after the bounce. However, analytical solutions for the Fourier modes of the electromagnetic vector potential across the bounce are difficult to obtain. In this work, with the help of a new time variable that we introduce, which we refer to as the e-N -fold, we investigate these scenarios numerically. Imposing the initial conditions on the modes in the contracting phase, we numerically evolve the modes across the bounce and evaluate the spectra of the electric and magnetic fields at a suitable time after the bounce. As one could have intuitively expected, though the complete spectra depend on the details of the bounce, we find that, under the original conditions, scale invariant spectra of the magnetic fields do arise for wavenumbers much smaller than the scale associated with the bounce. We also show that magnetic fields which correspond to observed strengths today can be generated for specific values of the parameters. But, we find that, at the bounce, the backreaction due to the electromagnetic modes that have been generated can be significantly large calling into question the viability of the model. We briefly discuss the implications of our results.
Generation of primordial magnetic fields during inflation typically requires the breaking of conformal invariance of the Electromagnetic action. In this paper this has been achieved naturally in a higher dimensional cosmological model with a Gauss-Bonnet term in the action. The evolution of the scale factor of the extra dimension (whose dynamics is influenced by the Gauss-Bonnet term) acts as the cause for the breaking of conformal invariance. Different cases have been investigated, each of which is characterized by the number of higher dimensions, the value of the Gauss-Bonnet parameter, and the cosmological constant. Many of the scenarios considered are highly constrained by the requirements that the cosmic evolution is stable, that the normal dimensions expand and that there is no back reaction due to growing electric fields. However there do exist scenarios which satisfy the above requirements and are well suited for magnetogenesis. In particular, a scenario where the number of extra dimensions D = 4 and the cosmological constant is non-zero, turns out to be best suited for generating primordial magnetic fields. It is shown that for these values of parameters, a scale invariant magnetic field of the order of 10 −10 − 10 −9 G can be produced. Even in these most favorable scenarios, the higher dimensional space expands during inflation at the same rate as the normal dimension. Hence if a mechanism could freeze the evolution of the higher dimension, this seems to be a viable mechanism to produce acceptable primordial magnetic fields.
We study the inflationary generation of helical cosmological magnetic fields in a higher-dimensional generalization of the electromagnetic theory. For this purpose, we also include a parity breaking piece to the electromagnetic action. The evolution of extra-dimensional scale factor allows the breaking of conformal invariance of the effective electromagnetic action in $1+3$ dimensions required for such generation. Analytical solutions for the vector potential can be obtained in terms of Coulomb wave-functions for some special cases. We also present numerical solutions for the vector potential evolution in more general cases. In the presence of a higher-dimensional cosmological constant there exist solutions for the scale factors in which both normal and extra dimensional space either inflate or deflate simultaneously with the same rate. In such a scenario, with the number of extra dimensions $D=4$, a scale invariant spectrum of helical magnetic field is obtained. The net helicity arises, as one helical mode comes to dominate over the other at the superhorizon scales. A magnetic field strength of the order of $10^{-9}$ $G$ can be obtained for the inflationary scale $H\simeq 10^{-3}$ $M_{pl}$. Weaker fields will be generated for lower scales of inflation. Magnetic fields generated in this model respects the bounds on magnetic fields by Planck and $\gamma$-ray observations (i.e. $10^{-16}$ $G$ $<$ $B_{obs}<3.4\times 10^{-9}$ $G$).Comment: 4 postscript figures, version submitted to Physical Review
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