A primordial magnetic field (PMF) can affect the evolution of density-field fluctuations in the early universe. In this paper we constrain the PMF amplitude $B_{\lambda }$ and power spectral index $n_{\mathrm{B}}$ by comparing calculated density-field fluctuations with observational data, i.e. the number density fluctuation of galaxies. We show that the observational constraints on cosmological density fluctuations, as parametrized by ${\sigma }_8$, lead to strong constraints on the amplitude and spectral index of the PMF.

• Received 22 August 2008

DOI:https://doi.org/10.1103/PhysRevD.78.123001