  Studying the nature and origin of the intergalactic magnetic field (IGMF) is
an outstanding problem of cosmology. Measuring Faraday rotation would be a
promising method to explore the IGMF in the large-scale structure (LSS) of the
universe. We investigated the Faraday rotation measure (RM) due to the IGMF in
filaments of galaxies using simulations for cosmological structure formation.
We employed a model IGMF based on turbulence dynamo in the LSS of the universe;
it has an average strength of $< B > \sim 10$ nG and a coherence length of
several $\times\ 100\ h^{-1}$ kpc in filaments. With the coherence length
smaller than path length, the inducement of RM would be a random walk process,
and we found that the resultant RM is dominantly contributed by the density
peak along line of sight. The rms of RM through filaments at the present
universe was predicted to be $\sim 1\ {\rm rad\ m^{-2}}$. In addition, we
predicted that the probability distribution function of $|{\rm RM}|$ through
filaments follows the log-normal distribution, and the power spectrum of RM in
the local universe peaks at a scale of $\sim 1\ h^{-1}$ Mpc. Our prediction of
RM could be tested with future instruments.

Cosmology and Nongalactic Astrophysics