Constraining Primordial Magnetic Fields with Future Cosmic Shear Surveys
  The origin of astrophysical magnetic fields observed in galaxies and clusters
of galaxies is still unclear. One possibility is that primordial magnetic
fields generated in the early Universe provide seeds that grow through
compression and turbulence during structure formation. A cosmological magnetic
field present prior to recombination would produce substantial matter
clustering at intermediate/small scales, on top of the standard inflationary
power spectrum. In this work we study the effect of this alteration on one
particular cosmological observable, cosmic shear. We adopt the semi-analytic
halo model in order to describe the non-linear clustering of matter, and feed
it with the altered mass variance induced by primordial magnetic fields. We
find that the convergence power spectrum is, as expected, substantially
enhanced at intermediate/small angular scales, with the exact amplitude of the
enhancement depending on the magnitude and power-law index of the magnetic
field power spectrum. We use the predicted statistical errors for a future
wide-field cosmic shear survey, on the model of the ESA Cosmic Vision mission
\emph{Euclid}, in order to forecast constraints on the amplitude of primordial
magnetic fields as a function of the spectral index. We find that the amplitude
will be constrained at the level of $\sim 0.1$ nG for $n_B\sim -3$, and at the
level of $\sim 10^{-7}$ nG for $n_B\sim 3$. The latter is at the same level of
lower bounds coming from the secondary emission of gamma-ray sources, implying
that for high spectral indices \emph{Euclid} will certainly be able to detect
primordial magnetic fields, if they exist. The present study shows how
large-scale structure surveys can be used for both understanding the origins of
astrophysical magnetic fields and shedding new light on the physics of the
pre-recombination Universe. (abridged)
