R. I. Thompson, __C. J. A. P. Martins__, __P. E. Vielzeuf__

**Abstract**

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*(ɸ) which is a function of the scalar field ɸ. Although *V*(ɸ) can be represented by a very diverse set of functions, recent work has shown the under some conditions, such as the slow roll conditions, the equation of state parameter *w* is either independent of the form of *V*(ɸ) or is 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 a and the proton to electron mass ratio µ. Although the current situation on a possible variance of a is complicated there are firm limitations on the variance of µ 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 µ puts significant constraints on the product of a cosmological parameter *w* +1 times a new physics parameter ζ^{2}_{µ}, the coupling constant between µ and the rolling scalar field. Even when the cosmologies are restricted to very slow roll conditions either the value of ζ_{µ} must be at the lower end of or less than its expected values or the value of *w* + 1 must be restricted to values vanishingly close to 0. This implies that either the rolling scalar field is very weakly coupled with the electromagnetic field, small ζ_{µ}, very weakly coupled with gravity, (*w* + 1) ≈ 0 or both. These results stress that adherence to the measured invariance in µ is a very significant test of the validity of any proposed cosmology and any new physics it requires. The limits on the variation of µ also produces a significant tension with the reported changes in the value of α.

**Keywords**

cosmological parameters – dark energy – early Universe

**Monthly Notices of the Royal Astronomical Society**

Volume 428, Issue 3, Page 2232

2013 January