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As galaxy formation and evolution over long cosmic time-scales depends to alarge degree on the structure of the universe, the assembly history of galaxiesis potentially a powerful approach for learning about the universe itself. Inthis paper we examine the merger history of dark matter halos based on theExtended Press-Schechter formalism as a function of cosmological parameters,redshift and halo mass. We calculate how major halo mergers are influenced bychanges 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 $w(z)$. Wefind that the merger fraction at a given halo mass varies by up to a factor ofthree for halos forming under the assumption of Cold Dark Matter, withindifferent underling cosmological parameters. We find that the currentmeasurements of the merger history, as measured through observed galaxy pairsas well as through structure, are in agreement with the concordance cosmologywith 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 withrecently measured cosmological parameters from Planck and WMAP requires ameasured merger accuracy of $\delta f_{\rm m} \sim 0.01$, implying surveys withan accurately measured merger history over 2 - 20 deg$^{2}$, which will befeasible with the next generation of imaging and spectroscopic surveys such asEuclid and LSST.

Galaxy Formation as a Cosmological Tool. I: The Galaxy Merger History as a Measure of Cosmological Parameters