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We study the observational constraints for the axion models in string theory which can successfully act as quintessence. The evolution of the universe in this model is sensitive to the initial value of the axion field. This initial value of the axion field controls deviation of the cosmic evolution from the behavior. We use the recent Union2 Supernova Type Ia dataset as well as the data from BAO measurements, the WMAP measurement of the shift parameter and the H (z) measurements. Using these data, we show that the reconstructed equation of state of the axion field has extremely small deviation from the cosmological constant =-1 even at 2 confidence level. Another interesting outcome of this analysis is that one can put bound on the supersymmetry (SUSY) breaking scale using cosmological measurements assuming the values of different string related parameters and vice versa.
Gupta et al. (Wed,) studied this question.