Constraints on extended quintessence from high-redshift supernovae

We obtain constraints on quintessence models from magnitude-redshift measurements of 176 Type Ia supernovae. The considered quintessence models are ordinary quintessence with Ratra-Peebles or supergravity (SUGRA) potentials, and extended quintessence with a Ratra-Peebles potential. We compute confidence regions in the Omega(m0-alpha) plane and find that for SUGRA potentials it is not possible to obtain useful constraints on these parameters; for the Ratra-Peebles case, for both the extended and ordinary quintessence we find alpha less than or similar to 0.8 at the 1 sigma level. We also consider simulated data sets for the Supernova/Acceleration Probe ( SNAP) satellite for the same models. Again, for a SUGRA potential it is not possible to obtain constraints on alpha, while with a Ratra-Peebles potential, its value is determined, with an error less than or similar to0.6. We evaluate the inaccuracy made by approximating the time evolution of the equation of state with a linear or constant w(z) instead of using its exact redshift evolution. Finally, we discuss the effects of different systematic errors in the determination of quintessence parameters.