Big bang nucleosynthesis with a stiff fluid

Models that lead to a cosmological stiff fluid component, with a density rho(S) that scales as a(-6), where a is the scale factor, have been proposed recently in a variety of contexts. We calculate numerically the effect of such a stiff fluid on the primordial element abundances. Because the stiff fluid energy density decreases with the scale factor more rapidly than radiation, it produces a relatively larger change in the primordial helium-4 abundance than in the other element abundances, relative to the changes produced by an additional radiation component. We show that the helium-4 abundance varies linearly with the density of the stiff fluid at a fixed fiducial temperature. Taking rho(S10) and rho(R10) to be the stiff fluid energy density and the standard density in relativistic particles, respectively, at T = 10 MeV, we find that the change in the primordial helium abundance is well-fit by Delta Y-p = 0.00024(rho(S10)/rho(R10)). The changes in the helium-4 abundance produced by additional radiation or by a stiff fluid are identical when these two components have equal density at a "pivot temperature," T-*, where we find T-* = 0.55 MeV. Current estimates of the primordial He-4 abundance give the constraint on a stiff fluid energy density of rho(S10)/rho(R10) < 30.