Hierarchical Gaussian-process reconstruction of late-time expansion with DESI BAO and compressed Planck priors
We reconstruct the late-time expansion history with a hierarchical Gaussian process (GP) that co-samples the kernel hyperparameters $(σ_f,l)$ together with $(\Hzero,\Om,\Ok,ω_b h^2)$. The data are 37 cosmic-chronometer $H(z)$ points, DESI DR2 BAO, Planck 2018 compressed distance priors, and Pantheon+ supernovae, coupled by a Monte-Carlo effective likelihood. DESI's headline Chevallier--Polarski--Linder (CPL) preference at $2.8$--$4.2σ$ uses the full Planck likelihood; we do not reproduce or refute that result. On this compressed-CMB pipeline the baseline posterior is $w(z\simeq 0)=-0.80^{+0.26}_{-0.23}$ (68\%~C.L.), less than $1σ$ from $w=-1$, with $l=3.79^{+0.81}_{-1.12}$. A CPL fit on the same data improves nested $\lcdm$ by only $Δχ^2\sim 1$; Akaike's criterion prefers nested $\lcdm$ ($Δ\mathrm{AIC}\simeq 3$), while BIC is quoted only as an indicative check for correlated supernovae. The reconstructed $f_{\rm DE}=1$ lies inside the 68\% band at every grid point with $z\le 1.6$. Ablations that fix $(σ_f,l)$, drop SN or LRG1/2 BAO, replace the radial-basis kernel by a Matérn family, swap the SN catalogue (Union3, DES-Y5, DES-Dovekie), or nest a residual GP around $\lcdm$ leave the median $w(0)$ within $\lesssim 1σ$ of $-1$.