The values of the fundamental constants such as $mu = m_P/m_e$, the proton to electron mass ratio and $alpha$, the fine structure constant, are sensitive to the product $sqrt{zeta_x^2(w+1)}$ where $zeta_x$ is a coupling constant between a rolling sca
lar field responsible for the acceleration of the expansion of the universe and the electromagnetic field with x standing for either $mu$ or $alpha$. The dark energy equation of state $w$ can assume values different than $-1$ in cosmologies where the acceleration of the expansion is due to a scalar field. In this case the value of both $mu$ and $alpha$ changes with time. The values of the fundamental constants, therefore, monitor the equation of state and are a valuable tool for determining $w$ as a function of redshift. In fact the rolling of the fundamental constants is one of the few definitive discriminators between acceleration due to a cosmological constant and acceleration due to a quintessence rolling scalar field. $w$ is often given in parameterized form for comparison with observations. In this manuscript the predicted evolution of $mu$, is calculated for a range of parameterized equation of state models and compared to the observational constraints on $Delta mu / mu$. We find that the current limits on $Delta mu / mu$ place significant constraints on linear equation of state models and on thawing models where $w$ deviates from $-1$ at late times. They also constrain non-dynamical models that have a constant $w$ not equal to $-1$. These constraints are an important compliment to geometric tests of $w$ in that geometric tests are sensitive to the evolution of the universe before the epoch of observation while fundamental constants are sensitive to the evolution of the universe after the observational epoch. Abstract truncated.
New PKS1830-211 radio frequency observations of methanol at a redshift of 0.88582 have established the most stringent limits on changes in the proton to electron mass ratio mu to date. The observations place the limit of (delta mu)/mu </= (0.0 +/- 1.
0) x 10^{-7} which is approximately a factor of four lower than the previous lowest limit at a redshift of 0.6742. This stringent limit at a look back time of roughly half the age of the universe has profound implications for rolling scalar field cosmologies and the new physics that they require. Many of these cosmologies invoke a scalar field phi that is also coupled to the electromagnetic field causing the values of the fundamental constants, mu and the fine structure constant alpha to roll with time. If the lowest expected value of the coupling to mu, zeta_{mu}$ is invoked the new limit requires a limit on the dark energy equation of state parameter w such that w+1 </= 0.001 at a redshift of 0.88582. This eliminates almost all of the expected parameter space for such cosmologies and new physics that have a coupling to the electromagnetic field. In these cases the limit requires that w must be extremely close to -1 for the last half of the age of the universe or that the coupling of the rolling scalar field to mu and the electromagnetic field be significantly below or at the limit of its expected range. The new observations solidify the role of fundamental constants in providing probes of the possible cosmologies and new physics to explain the acceleration of the expansion of the universe.
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 r
epresented 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(phi) 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 alpha and the proton to electron mass ratio mu. 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 w+1 times a new physics parameter zeta_mu^2, 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 zeta_mu 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 zeta_mu, very weakly coupled with gravity, w+1 ~ 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 alpha.
