Baryon asymmetry and the scale of supersymmetry breaking

I discuss the constraints on supersymmetric grand unified theories (SSGUT's) imposed by requiring that such theories be compatible with the presently observed baryon asymmetry of the universe. I concentrate on those SSGUT's in which the scale of supersymmetry breaking is small compared to the scale at which the baryon asymmetry is generated. If one neglects the supersymmetry breaking, most models of this kind have, at zero temperature, degenerate vacuums which include the gauge-symmetric ground state. In general, it is very hard to obtain a realistic scenario for the phase transitions of these models in the early Universe (i.e., at large temperatures). One of the reasons for this difficulty is due to the following theorem: In SSGUT models with a simple unifying gauge group, one cannot have a situation in which the gauge symmetry decreases as the temperature is raised (in a regime where the coupling constant is small). I argue that if supersymmetry is relevant in grand unified models, it is probably broken at a fairly high scale: above the scale of baryon-number generation