Constraining cosmologies with fundamental constants - I. Quintessence and K-essence

Many cosmological models invoke rolling scalar fields to account for the observed acceleration of the expansion of the Universe. These theories generally include a potential V(phi) which is a function of the scalar field phi. Although V(phi) can be represented by a very diverse set of functions, recent work has shown that under some conditions, such as the slow-roll conditions, the equation of state parameter omega is either independent of the form of V(phi) or part of family of solutions with only a few parameters. In realistic models of this type the scalar field couples to other sectors of the model leading to possibly observable changes in the fundamental constants such as the fine structure constant alpha and the proton to electron mass ratio mu. Although the current situation on a possible variance of alpha is complicated, there are firm limitations on the variance of mu in the early universe. This paper explores the limits this puts on the validity of various cosmologies that invoke rolling scalar fields. We find that the limit on the variation of mu puts significant constraints on the product of a cosmological parameter omega + 1 and a new physics parameter xi(2)(mu), the coupling constant between mu and the rolling scalar field. Even when the cosmologies are restricted to very slow roll conditions either the value of. mu must be at the lower end of or less than its expected values or the value of omega + 1 must be restricted to values vanishingly close to 0. This implies that either the rolling scalar field is very weakly coupled to the electromagnetic field, small xi(mu), very weakly coupled to gravity, (omega + 1) approximate to 0 or both. These results stress that adherence to the measured invariance in mu is a very significant test of the validity of any proposed cosmology and any new physics it requires. The limits on the variation of mu also produces a significant tension with the reported changes in the value of a.