Feasibility of reconstructing the quintessential potential using type Ia supernova data

We investigate the feasibility of the method for reconstructing the equation of state and the effective potential of the quintessence field from type Ia supernova (SNIa) data. We introduce a useful functional form to fit the luminosity distance with good accuracy (the relative error is less than 0.1%). We assess the ambiguity in reconstructing the equation of state and the effective potential, which originates from the uncertainty in Omega (M). We find that the equation of state is sensitive to the assumed Omega (M), while the shape of the effective potential is not. We also demonstrate the actual reconstruction procedure using the data created by Monte Carlo simulations. Future high precision measurements of distances to thousands of SNIa could reveal the shape of the quintessential potential.