Constraints on Extended Quintessence from High‐Redshift Supernovae

We obtain constraints on quintessence models from magnitude-redshift measurements of 172 type Ia Supernovae. The considered quintessence models are ordinary quintessence, with Ratra-Peebles and SUGRA potentials, and extended quintessence with a Ratra-Peebles potential. We compute confidence regions in the \Ωₘ₀-\α plane and find that for SUGRA potentials it is not possible to obtain useful constraints on these parameters; for the Ratra-Peebles case, both for the extended and ordinary quintessence we find \α\1.1, at the 1\σ level. We also consider simulated dataset for the SNAP satellite for the same models: again, for a SUGRA potential it will not be possible to obtain constraints on \α, while with a Ratra-Peebles potential its value will be determined with an error smaller than unity. We evaluate the inaccuracy made by approximating the time evolution of the equation of state with a linear or constant w\, instead of using its exact redshift evolution.