CosmoCoffee

One of the interesting things this paper mentions is that primoridal magnetical fields with a blue spectrum might give an interesting CMB signature on very small scales [tex]l \sim 10^6[/tex]. The reasoning being that if the spectrum is sufficiently blue the spectrum will actual grow on small scales (up to the magnetic field decay cut-off) despite damping and finite last scattering width effects. Such primordial fields would not be immediately inconsistent with anything else.

However if there is a nG field on 10kpc scales having a blue spectrum, I would have thought the fields would violate the gravitational wave production argument of astro-ph/0106244 - namely that scales that were superhorizon in the early universe would have generated tensor modes sufficient to violate the bounds on the relativisitic energy density at nucleosynthesis?

Hi Antony
Tina, Chiara and I have discussed a bit about this paper.
The limit in astro-ph/0106244 is relevant for magnetic fields on super horizon scales:
If the corresponding wavelength is super-horizon at generation, then the magnetic
field is severely damped due to gravity wave production until it passes through the
horizon. Once inside the horizon, gravity wave production becomes irrelevant.

Since they loose a significant amount (maybe 1/2 or more, we do not know since we have
not calculated back reaction) of their energy when passing through the horizon, this means
that the total energy energy on scales which are superhorizon at formation must be less
than the energy in typically 1/2 relativistic thermal degree of freedom (this is grossly the
nucleosynthesis bound). This has led to the serious limits presented in astro-ph/0106244.

So Banerjee and Jedamzik have to tell up whether their magnetic fields are
generated on super- or sub-horizon scales.
Another problem also is that causally produced fields can only have an n=2m spectrum,
where m is a positive integer, on scales on which it evolves linearly, so that B goes
like [tex]1/a^2.[/tex] It is not clear to me how this condition is taken into account in astro-ph/0410032.
Furthermore it would be interesting to know the critical wavelength [tex]\lambda_c(t) [/tex]at which
turbulence sets in and the spectrum is thus modified.