**Rodger I. Thompson**

Steward Observatory, University of Arizona

**Abstract**

One of the 12 challenges presented at the most recent Texas Symposium on Relativistic Astrophysics was: **What is the dark energy equation of state versus redshift?** The values of the fundamental constants such as µ=m_{P}/m_{e} the proton to electron mass ratio and α, the fine structure constant, are sensitive to the dark energy equation of state *w*. The rate of change of the fundamental constants is proportional to the product √ζ2(*w*+1) where ζ is a coupling constant between a rolling scalar field responsible for the acceleration of the expansion of the universe and the electromagnetic field with x standing for the particular fundamental constant such as µ or α. In standard ΛCDM *w* is a constant, -1, which predicts no changes in the constants and in the standard model of physics ζ is 0 again resulting in no change. In cosmologies, however, where the acceleration of expansion is due to a dynamical scalar field *w* takes on values different than -1 and the scalar field couples with the electromagnetic field to produce a non-zero ζ. In this case the values of the fundamental constants monitor the equation of state and are a valuable tool in answering the question what *w* is as a function of redshift. The dark energy equation of state is often given in parameterized form for comparison with observations. In this talk the predicted evolution of µ, is calculated for a range of parameterized equation of state models and compared to the observational constraints on Δµ/µ. We find that the current limits on Δµ/µ place significant constraints on the linear equation of state models and on thawing models were *w* deviates from -1 at late times. They also even 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 observation while fundamental constants are sensitive to the evolution of the universe after the observation. Recent low redshift radio limits on Δµ/µ provide the most significant constraints on the late time evolution of *w*. Improvements in the accuracy of optical limits on Δµ/µ at high redshift will be invaluable in placing similar constraints on the early evolution of *w*.

** 2013 July 15, 13:30**

**IA/U.Porto**

Centro de Astrofísica da Universidade do Porto (Auditorium)

Rua das Estrelas, 4150-762 Porto