Constraining Primordial Magnetic Fields with Weak Lensing

Abstract

Introducing primordial magnetic fields (PMFs) into the standard cosmological model, $\Lambda$CDM, has an impact on the matter power spectrum at the linear level, resulting in an increase of power on small scales. In this work, we use the enhanced spectrum as the initial condition for dark-matter-only N-body simulations and study its non-linear evolution. From the resulting non-linear matter power spectrum, we calculate the convergence power spectrum of weak lensing ($C_{\kappa }$) and show how the presence of PMFs causes an enhancement at high multipoles. We then construct an emulator for $C_{\kappa }$ that also includes intrinsic alignment and baryon feedback. We perform MCMC analyses using mock data generated for different PMF models and for three values of the maximum multipole, ${\ell }_{\max }=5000$, $10000$, and $20000$. The PMFs models are characterized by the two parameters that define the power-law power spectrum of the magnetic field $P_B(k)\propto B_{1Mpc}^2{k}^{n_B}$, where $B_{1Mpc}$ is the amplitude at a scale of $1$ Mpc and $n_B$ is the power spectral index. For $\Lambda$CDM mocks, corresponding to $B_{1Mpc}=0$, we obtain approximate upper limits of $B_{1Mpc}<1.6$, $1.0$, and $0.8\mathrm{nG}$ at the $95\%$ confidence level for the three values of ${\ell }_{\max }$ respectively. For non-zero input magnetic fields, the recovery of $B_{1Mpc}$ and $n_B$ depends strongly on the PMFs model and on the maximum multipole considered. Models with $n_B=-2.1$ are more easily constrained than models with $n_B=-2.7$, since they produce a stronger enhancement of the convergence power spectrum. We find no clear degeneracy between the PMFs parameters and the intrinsic alignment or baryon feedback parameters, while $B_{1Mpc}$ and $n_B$ can be degenerate. We characterize this degeneracy through linear fits to selected $2$D posterior distributions.