http://arxiv.org/abs/1505.04668
We study the simple gauge invariant model ${f^2}FF$ as a way to generate primordial magnetic fields (PMF) in Natural Inflation (NI). We compute both magnetic and electric spectra generated by the ${f^2}FF$ model in NI for different values of model parameters and find that both de Sitter and power law expansion lead to the same results at sufficiently large number of e-foldings. We also find that the necessary scale invariance property of the PMF cannot be obtained in NI in first order of slow roll limits under the constraint of inflationary potential, $V\left( 0 \right) \simeq 0$. Furthermore, if this constraint is relaxed to achieve scale invariance, then the model suffers from the backreaction problem for almost all values of model parameters. We show that there is a narrow range of the height of the potential $\Lambda $ around ${\Lambda _{\min }} \approx 0.00874{M_{{\rm{Pl}}}}$ and of the co-moving wave number $k$ around ${k_{\min }} \sim 0.0173{\rm{Mp}}{{\rm{c}}^{ – 1}}$, at which the problem of backreaction might be avoided. The value of ${\Lambda _{\min }}$ lies within the range of $\Lambda $ compatible with the BICEP2 results, and the range of $k$ lies within some the observable scale. However, the relatively short range of $k$ presents a serious challenge to the viability of this model.
A. AlMuhammad and R. Lopez-Mobilia
Tue, 19 May 15
67/78
Comments: 8 pages, 6 figures
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