Maresuke Shiraishi, Daisuke Nitta, Shuichiro Yokoyama, Kiyotomo Ichiki
We investigate bounds on the strength of the primordial magnetic field (PMF)
from the cosmic microwave background (CMB) bispectra of the intensity
(temperature) modes induced from the auto- and cross-correlated bispectra of
the scalar and tensor components of the PMF anisotropic stress. At first, we
construct a general formula for the CMB intensity and polarization bispectra
from PMFs composed of any type of perturbation. Then we derive an approximate
expression which traces the exact shape of the CMB bispectrum in order to
reduce the computation time with respect to a large number of the multipole
configurations, and also show that the non-Gaussian structure coming from PMFs
is classified as the local-type configuration. Computing the signal-to-noise
ratio based on the approximate formula with the information of the instrumental
noises and resolutions, we find expected upper bounds on the magnetic field
strength, when the magnetic spectrum is nearly scale invariant, smoothed on $1
{\rm Mpc}$ scale at 95% confidence level from the WMAP and PLANCK experiments
as $B_{1 \rm Mpc} < 4.0 - 6.7 {\rm nG}$ and $3.8 - 6.5 {\rm nG}$, respectively,
depending on the energy scale of the magnetic field production from $10^{14}
{\rm GeV}$ to $10^3 {\rm GeV}$. Our new consequences imply slight
overestimations by the previous rough discussions.
View original:
http://arxiv.org/abs/1201.0376
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