Evolution of the cosmic matter density field with a primordial magnetic field

Abstract

A cosmological magnetic field affects the time evolution of the cosmic matter density field. The squared Alfven velocity of the cosmic fluid is proportional to an ensemble average energy density of a primordial magnetic field (PMF), and it prevents the matter density field from collapsing in the horizon scale. The matter-radiation equality time also is delayed by the presence of an ensemble average energy density of a PMF. The ensemble average energy density of the PMF also affects the matter power spectrum (MPS) through the Meszaros effect and the potential decay. Since the ensemble average energy density of the PMF is not a first order perturbation but a zero order source in the linear perturbation equations for the cosmology, to correctly understand the overall effects of the PMF on the MPS, we should significantly revise previous approaches to research for the MPS with the PMF by considering the both effects of the zero and first order sources from the PMF in the linear perturbation theory. We apply the effects of the zero order sources from the PMF to theoretical computations of the MPS for the first time. We also analyze the overall PMF effects on the MPS. The CMB polarizations are affected the weak lensing. The weak lensing is determined by the MPS. Therefore, we have to consider the zero order sources of the PMF to gain a correct understanding not only of the MPS but also the CMB polarization. * yamazaki.dai@nao.ac.jp 2

The New BBN Model with the Photon Cooling, X Particle, and the Primordial Magnetic Field

“…We derive the constraint on , and ∝ , where B is the comoving and scaleinvariant strength of the PMF [3,4,12,13]. The limited values of and are given by 4.06 log sec 6.10 2 , 95 % C. L. , 9.70 log GeV 6.23 2 , 95 % C. L. .…”

“…We find that the PMF energy density ( ) and the parameters of the X particle ( and ) have no significant degeneracies. The PMF parameters, however, can be strongly constrained by the CMB and the matter power spectrum (MPS) observations [6][7][8][9][10][11][12][13]. Therefore, if we limit the PMF energy density by the future CMB and MPS observations more strongly, we can limit the combined effects of the photon cooling, the X decay, and the PMF on BBN mote strongly and derive tighter constraints on these parameters.…”

“…Since B can boost the cosmic expansion rate and the results of the BBN model with a PMF differ from those without a PMF [3,4,12,13], the solution to the Li problem can be improved by a PMF. We calculate BBN taking into account the above three possible effects simultaneously, and extended the standard BBN to the new hybrid BBN (for details, see Refs [3,4]).…”

“…It is called ``Li problem'' [2]. To resolve this Li problem, previous studies have proposed three ideas: the photon cooling (possibly via the Bose-Einstein condensation of a scalar particle) [3,4], the decay of a long-lived X particle (possibly the next-to-lightest supersymmetric particle) [5], and an energy density of a primordial magnetic field (PMF) [6][7][8][9][10][11][12][13]. We introduce combined effects of these on BBN, and derive constraint on the X particles and the PMF parameters by observed light element abundances with likelihood analysis.…”

The new hybrid BBN model with the photon cooling, X particle, and the primordial magnetic field

“…[42][43][44] The peak position and the amplitude of the MPS is also changed by a PMF. 45,46 We can constrain the PMF parameters from the CMB and MPS observations. 47-54 When we consider the energy density of a PMF in the BBN epoch, the rate of the comic expansion is more rapid than without a PMF.…”