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Abstract

Using DESI DR2 baryon acoustic oscillation (BAO) distance measurements and Planck cosmic microwave background distance priors, we have measured the dark energy density $\rho_X(z)$ and dark energy equation of state w_X(z) as free functions of redshift (smoothly interpolated from values at {z_i}={0, 1/3, 2/3, 1, 4/3, 2.33}, and find both to be consistent with a cosmological constant, with only deviations of 1\sigma for $\rho_X(z)$ & ~ 2$\sigma$ for w_X(z) at z=2/3. We also find that measuring {$\rho_X(z_i)$} is preferred to measuring {w_X(z_i)} by model selection using the Akaike Information Criterion (AIC) as well as the Bayesian Information Criterion (BIC). Varying the choice of redshift values of the $\rho_X(z)$ measurements leads to very consistent results, with AIC/BIC slightly favoring the case of our fiducial {z_i} with z=4/3 omitted. We find agreement with a cosmological constant except for the 1-2$\sigma$ deviation at 0.4 < z < 0.9, where DESI DR2 BAO measurements deviate from a cosmological constant at similar statistical significance. Our results differ noticeably from those of the DESI Collaboration, in which they used the same DESI DR2 data combined with Planck data and found a 3.1$\sigma$ deviation from a cosmological constant, which is primarily the consequence of their assuming parametrization w_X(z)=w_0+w_a(1-a). Our results indicate that assuming a linear w_X(z) could be misleading and precludes discovering how dark energy actually varies with time at higher redshifts. In our quest to discover the physical nature of dark energy, the most urgent goal at present is to determine definitively whether dark energy density varies with time. It is of critical importance to measure dark energy density as a free function of redshift from data. Future galaxy redshift surveys by Euclid and Roman at higher redshifts will significantly advance our understanding of dark energy.