Testing the relation between the local and cosmic star formation histories

Recently, there has been great progress toward observationally determining the mean star formation history of the universe. When accurately known, the cosmic star formation rate could provide much information about Galactic e volution, if the Milky Way's star formation rate is representative of the a verage cosmic star formation history. A simple hypothesis is that our local star formation rate is proportional to the cosmic mean. In addition, to sp ecify a star formation history, one must also adopt an initial mass functio n (IMF);typically it is assumed that the IMF is a smooth function, which is constant in time. We show how to test directly the compatibility of all th ese assumptions by making use of the local (solar neighborhood) star format ion record encoded in the present-day stellar mass function. Present data s uggest that at least one of the following is false: (1) the local IMF is co nstant in time; (2) the local IMF is a smooth (unimodal) function; and/or ( 3) star formation in the Galactic disk was representative of the cosmic mea n. We briefly discuss how to determine which of these assumptions fail and also improvements in observations, which will sharpen this test.