Feasibility of Reconstructing the Quintessential Potential Using SNIa Data

We investigate the feasibility of the method for reconstructing the equation of state and the effective potential of the quintessence field from 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 simulation. Future high precision measurements of distances to thousands of SNIa could reveal the shape of the quintessential potential.