  As galaxy formation and evolution over long cosmic time-scales depends to a
large degree on the structure of the universe, the assembly history of galaxies
is potentially a powerful approach for learning about the universe itself. In
this paper we examine the merger history of dark matter halos based on the
Extended Press-Schechter formalism as a function of cosmological parameters,
redshift and halo mass. We calculate how major halo mergers are influenced by
changes in the cosmological values of $\Omega_{\rm m}$, $\Omega_{\Lambda}$,
$\sigma_{8}$, the dark matter particle temperature (warm vs. cold dark matter),
and the value of a constant and evolving equation of state parameter $w(z)$. We
find that the merger fraction at a given halo mass varies by up to a factor of
three for halos forming under the assumption of Cold Dark Matter, within
different underling cosmological parameters. We find that the current
measurements of the merger history, as measured through observed galaxy pairs
as well as through structure, are in agreement with the concordance cosmology
with the current best fit giving $1 - \Omega_{\rm m} = \Omega_{\rm \Lambda} =
0.84^{+0.16}_{-0.17}$. To obtain a more accurate constraint competitive with
recently measured cosmological parameters from Planck and WMAP requires a
measured merger accuracy of $\delta f_{\rm m} \sim 0.01$, implying surveys with
an accurately measured merger history over 2 - 20 deg$^{2}$, which will be
feasible with the next generation of imaging and spectroscopic surveys such as
Euclid and LSST.
