Exploring Primordial Magnetism via Structure Formation, Galaxies, and Intergalactic Medium

This work examines Primordial Magnetic Fields (PMFs) and their effects on cosmological observables. PMFs can enhance the matter power spectrum on scales smaller than Megaparsec, because their presence before recombination induces additional baryon perturbations. This~has~various consequences; in this thesis we will present and discuss three directions: 1) PMF-related perturbations are different for baryons vs. dark matter, which leads to a higher baryon fraction in low-mass halos during early structure formation. 2) since PMFs are likely present in voids and the intergalactic medium (IGM), their disturbance on the neutral hydrogen fraction should have a limit based on Lyman-$\alpha$ forest observations. From this we obtain constraints on PMF parameters. 3) With newer JWST data on early galaxy formation, it is useful to explore how would PMFs contribute to high-redshift UV luminosity function, and what are the implications for reionization. The thesis is based on our original contributions to the field of PMFs and cosmology. We have advanced the theoretical, numerical, and observational understanding of PMFs in two directions: evolution from initial conditions and observational constraints. In our first study we have modified initial conditions of cosmological simulations so that the displacements due to Lorentz force are calculated directly from the magnetic field. Consequently, the non-linear evolution in cosmo-hydrodynamical simulations leads to low-mass galaxies with gas fraction several times larger than the cosmic average at high redshifts. This is a direct consequence of the initial conditions, where PMFs enhance perturbations of baryons, causing them to be larger than perturbations of dark matter. Some preliminary discussion is presented on how such a scenario could be tested by obtaining accurate estimates of the baryon fraction in high redshift galaxies. We also highlight the large theoretical uncertainty in the peak enhancement of the matter power spectrum due to PMFs, which was not considered in previous studies. Compatibility with other literature is shown through halo mass functions, and we show that they can be accurately reproduced using Sheth-Tormen formalism. In the second study, we find constraints on PMFs from the Lyman-$\alpha$ forest. Compared to previous works focusing on Lyman-$\alpha$ constraints, we employ full cosmological hydrodynamic simulations. At the scales and redshifts probed by the data, the Lyman-$\alpha$ flux power spectrum is extremely sensitive to the extra power induced by PMFs in the linear matter power spectrum, at a scale that we parametrize with $k_{\rm peak}$. We rely on a large set of flux models obtained by varying thermal and reionization histories and cosmological parameters. We find a hint of extra power that is well fitted by the primordial magnetic field model with $B \simeq 0.2 \,\,{\rm nG}$, corresponding to $k_{\rm peak} \simeq 50 \,\,{\rm Mpc}^{-1}$. However, when applying additional modeling of the noise or disregarding the data from the lowest scales, we obtain a competitive $3\sigma$ C.L. upper limit on the strength of primordial magnetic fields: $B_{1\rm Mpc} < 0.30 \,\,{\rm nG}$, for nearly scale-invariant case $n_B=-2.9$. We argue that the constraints can be extended to a broader $(B,\,n_B)$ plane. Finally, we present our ongoing work in the direction that explores how PMFs impact galaxy luminosity function and reionization, with the new JWST data.