Helical cosmological magnetic fields from extra-dimensions

Abstract

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

Magnetogenesis in cyclical Universe

“…The coupled equations (22) and (23) are a stable system with respect to initial conditions, as we will see, and we have freedom in setting the parameter b, which is directly related to the Hubble parameter evolution. This parameter has no influence in the shape of the curves φ(t) and ψ(t), but it determines the strength of the generated magnetic field.…”

“…The effects of back reaction on the background expansion from the produced scale invariant magnetic spectrum restrict the amplitude of the primordial seed magnetic fields, constraining the viability of such models [15,20]. Additionally, the need to solve the strong coupling problem at the beginning of inflationary expansion [21] usually implies more complexity, such as an extradimensional scale factor coupling [22].…”

The origin, evolution and signatures of primordial magnetic fields

“…( 48), with a time dependent co-efficient Durrer et al (2011). If the same time dependent function couples both F µν F µν and F µν F µν , then one can also generate helical fields with a scale invariant spectrum (Atmjeet et al, 2015;Caprini and Sorbo, 2014). Such a situation naturally obtains in higher dimensional cosmology with say the extra dimensional scale factor b(t) multiplying the whole action (Atmjeet et al, 2015).…”

Constraining brane inflationary magnetic field from cosmoparticle physics after Planck

“…Next using Eq (3.11) in Eq (5.36) finally I get the following relationship between the density parameter of the magnetic field and the CP asymmetry parameter within the high energy regime of RSII braneworld as 21 :…”

“…See refs. [13][14][15][16][17][18][19][20][21][22][23][24][25][26] for the further details of this issue. Due to the breaking of conformal invariance of the electromagnetic theory the magnetic field gets amplified.…”