An important quantity in theories of the formation of galaxies is the jeans length. in this question, you will determine the jeans length at the time. suppose we have an infinite medium of temperature t and density pm now let the density increase slightly in one region the increased gravitational force will tend to compress the region. however this force will be countered by increased pressure, p - pktim, where k is the boltzmann constant and m is the mean mass of the particles. (a) how does temperature scale as the universe expands? how does density scale as the universe expands? suppose that t-3k at the present time, and that the present density is p-9x1030g. cm. what was the density at the time of recombination when t-3000k? (b) we can now use hydrostatic equilibrium to determine whether a small region of diameter l will collapse. the weight of a column of material of unit area and height l is roughly gm ,where m is the mass of material in the region l. show that the smallest l2 kt region which will collapse is given by l , where we can take m to be the mgp mass of the hydrogen atom, 1.67 x 102g. explain any assumptions you make. (c) what is the jeans length at recombination? find the corresponding jeans mass. what sort of object might this be in the universe today?