Rajeev Kumar Jain

Can slow roll inflation induce relevant helical magnetic fields

We study the generation of helical magnetic fields during single field inflation induced by an axial coupling of the electromagnetic field to the inflaton. During slow roll inflation, we find that such a coupling always leads to a blue spectrum with

Primordial features due to a step in the inflaton potential

B^2(k) \propto k

On the non-Gaussian correlation of the primordial curvature perturbation with vector fields

, as long as the theory is treated perturbatively. The magnetic energy density at the end of inflation is found to be typically too small to backreact on the background dynamics of the inflaton. We also show that a short deviation from slow roll does not result in strong modifications to the shape of the spectrum. We calculate the evolution of the correlation length and the field amplitude during the inverse cascade and viscous damping of the helical magnetic field in the radiation era after inflation. We conclude that except for low scale inflation with very strong coupling, the magnetic fields generated by such an axial coupling in single field slow roll inflation with perturbative coupling to the inflaton are too weak to provide the seeds for the observed fields in galaxies and clusters.

Inflationary magnetogenesis without the strong coupling problem II: constraints from CMB anisotropies and B-modes

Certain oscillatory features in the primordial scalar power spectrum are known to provide a better fit to the outliers in the cosmic microwave background data near the multipole moments of l = 22 and 40. These features are usually generated by introducing a step in the popular, quadratic potential describing the canonical scalar field. Such a model will be ruled out, if the tensors remain undetected at a level corresponding to a tensor-to-scalar ratio of, say, r 0.1. In this work, in addition to the popular quadratic potential, we investigate the effects of the step in a small field model and a tachyon model. With possible applications to future datasets (such as PLANCK) in mind, we evaluate the tensor power spectrum exactly, and include its contribution in our analysis. We compare the models with the WMAP (five as well as seven-year), the QUaD and the ACBAR data. As expected, a step at a particular location and of a suitable magnitude and width is found to improve the fit to the outliers (near l = 22 and 40) in all these cases. We point out that, if the tensors prove to be small (say, r0.01), the quadratic potential and the tachyon model will cease to be viable, and more attention will need to be paid to examples such as the small field models.

Consistency relation for cosmic magnetic fields

We compute the three-point cross-correlation function of the primordial curvature perturbation generated during inflation with two powers of a vector field in a model where conformal invariance is broken by a direct coupling of the vector field with the inflaton. If the vector field is identified with the electromagnetic field, this correlation would be a non-Gaussian signature of primordial magnetic fields generated during inflation. We find that the signal is maximized for the flattened configuration where the wave number of the curvature perturbation is twice that of the vector field and in this limit, the magnetic non-linear parameter becomes as large as |bNL| ~ (103). In the squeezed limit where the wave number of the curvature perturbation vanishes, our results agree with the magnetic consistency relation derived in arXiv:1207.4187.

Resonant magnetic fields from inflation

Recent observational claims of magnetic fields stronger than 10?16 G in the extragalactic medium motivate a new look for their origin in the inflationary magnetogenesis models. In this work we shall review the constraints on the simplest gauge invariant model f2()F??F?? of inflationary magnetogenesis, and show that in the optimal region of parameter space the anisotropic constraints coming from the induced bispectrum, due to the generated electromagnetic fields, yield the strongest constraints. In this model, only a very fine tuned scenario at an energy scale of inflation as low as 10?2 GeV can explain the observations of void magnetic fields. These findings are consistent with the recently derived upper bound on the inflationary energy scale. However, if the detection of primordial tensor modes by BICEP2 is confirmed, the possibility of low scale inflation is excluded. Assuming the validity of the BICEP2 claim of a tensor-to-scalar ratio r = 0.2+0.07?0.05, we provide the updated constraints on this model of inflationary magnetogenesis. On the Mpc scale, we find that the maximal allowed magnetic field strength from inflation is less than 10?30 G.

Generation of helical magnetic fields from inflation

If cosmic magnetic fields are indeed produced during inflation, they are likely to be correlated with the scalar metric perturbations that are responsible for the Cosmic Microwave Background anisotropies and Large Scale Structure. Within an archetypical model of inflationary magnetogenesis, we show that there exists a new simple consistency relation for the non-Gaussian cross correlation function of the scalar metric perturbation with two powers of the magnetic field in the squeezed limit where the momentum of the metric perturbation vanishes. We emphasize that such a consistency relation turns out to be extremely useful to test some recent calculations in the literature. Apart from primordial non-Gaussianity induced by the curvature perturbations, such a cross correlation might provide a new observational probe of inflation and can in principle reveal the primordial nature of cosmic magnetic fields.

Duality and scale invariant magnetic fields from bouncing universes

We propose a novel scenario to generate primordial magnetic fields during inflation induced by an oscillating coupling of the electromagnetic field to the inflaton. This resonant mechanism has two key advantages over previous proposals. First of all, it generates a narrow band of magnetic fields at any required wavelength, thereby allaying the usual problem of a strongly blue spectrum and its associated backreaction. Secondly, it avoids the need for a strong coupling as the coupling is oscillating rather than growing or decaying exponentially. Despite these major advantages, we find that the backreaction is still far too large during inflation if the generated magnetic fields are required to have a strength of (10−15 Gauss) today on observationally interesting scales. We provide a more general no-go argument, proving that this problem will apply to any model in which the magnetic fields are generated on subhorizon scales and freeze after horizon crossing.

Cosmological Ohm's law and dynamics of non-minimal electromagnetism

The generation of helical magnetic fields during single field inflation due to an axial coupling of the electromagnetic field to the inflaton has been discussed. We have found that such a coupling always leads to a blue spectrum of magnetic fields during slow roll inflation. Though the helical magnetic fields further evolve during the inverse cascade in the radiation era after inflation, we have concluded that the magnetic fields generated by such an axial coupling can not lead to observed field strength on cosmologically relevant scales.

On the covariant formalism of the effective field theory of gravity and its cosmological implications

Recently, we had numerically shown that, for a non-minimal coupling that is a simple power of the scale factor, scale invariant magnetic fields arise in a class of bouncing universes. In this work, we analytically evaluate the spectrum of magnetic and electric fields generated in a sub-class of such models. We illustrate that, for cosmological scales which have wavenumbers much smaller than the wavenumber associated with the bounce, the shape of the spectrum is preserved across the bounce. Using the analytic solutions obtained, we also illustrate that the problem of backreaction is severe at the bounce. Finally, we show that the power spectrum of the magnetic field remains invariant under a two parameter family of transformations of the non-minimal coupling function.