  In this paper, we study the simultaneous evolution of baryon asymmetry and
hypermagnetic field amplitude assuming an early matter domination. We contrast
our results to the conventional case where radiation domination in early
universe is assumed. We show that the values of baryon asymmetry and the
hypermagnetic field amplitude at the onset of electroweak phase transition may
be orders of magnitude different if we assume a non-standard history of
cosmology. One reason is that a change in Hubble rate leads to a change on when
the weak sphalerons become active, and thus changes the evolution of baryon
asymmetry. If we turn-off the hypermagnetic field ($\vec B_Y = \vec 0$), it is
possible to guess the effect of early matter domination on baryon asymmetry
beforehand. The effect of early matter domination on the interplay between
baryon asymmetry and hypermagnetic field amplitude, however, is non-trivial. We
perform a numerical study of the Boltzmann equations of baryon asymmetry and
hypermagntic field amplitude, assuming a few benchmarks, to highlight some of
the non-trivial effects of an early matter domination. To illustrate our point,
we consider two main cases (1) the baryons starting with a primordial asymmetry
and (2) baryons gaining an asymmetry through a slow decay of another asymmetric
particle.
