Constraints on Dark Energy state equation with varying pivoting redshift

We assume the DE state equations w(a) = w_0+w_a(a_p-a), and study the dependence of the constraints on w_0 and w_a coefficients on the pivoting redshift 1+z_p=1/a_p. Coefficients are fitted to data including WMAP7, SNIa (Union 2.1), BAO's (including WiggleZ and SDSS results) and H_0 constraints. The fitting algorithm is CosmoMC. We find specific differences between the cases when neutrino mass is allowed or disregarded. More in detail: (i) The z_p value yielding uncorrelated constraints on w_0 and w_a is different in the two cases, holding 0.25 and 0.35, respectively. (ii) If we consider the intervals allowed to w_0, we find that they shift when z_p increases, in opposite directions for vanishing or allowed ν-mass. This leads to no overlap between 1-σ intervals already at z_p > 0.4. (iii) The w_0-w_a constraints found by using any pivot z_p can be translated into constraints holding at a specific z_p value (0 or the z_p where errors are uncorrelated). When we do so, most error ellipsoids exhibit a nice overlap, (iv) the only exception being the constraints found for vanishing ν-mass by using z_p=0, which turn out to be significantly more restrictive than others (up to 30%).