New Tsallis holographic dark energy with the Granda-Oliveros cutoff in a non-flat universe: curvature tracking and DESI DR2 constraints

Abstract

Holographic dark energy ties the dark-energy density to an infrared length. We study new Tsallis holographic dark energy (NTHDE), built on the exponential Tsallis entropy, with the local Granda-Oliveros (GO) cutoff $L^{-2}=αH^2+γ\dot H$ in a spatially curved universe. Writing the background as an autonomous system for $(Ω_d,u,Ω_k)$, we obtain four exact results. (i) In the closed-form solution without the Tsallis deformation, the dark energy splits into a matter-like and a curvature-like part. (ii) Because the GO cutoff lacks the term $k/a^2$ of the Ricci scalar, the coefficient of $(1+z)^2$ in $H^2/H_0^2$ is $R_kΩ_{k0}$ with $R_k=(1-α+γ)^{-1}>1$, while distances and the Clarkson-Bassett-Lu test return $Ω_{k0}$; the Ricci completion restores $R_k=1$. (iii) Big-bang nucleosynthesis locks the matter-era dark-energy fraction to $1/(1+3|w_{\rm GO}|)$, where $w_{\rm GO}$ is the equation of state of the GO mode. (iv) The finite-time fold singularity of the flat model survives curvature. Against Pantheon+SH0ES supernovae, 32 cosmic chronometers and DESI DR2 BAO, curved GO-NTHDE gives $Ω_{k0}=-0.001^{+0.041}_{-0.043}$, consistent with flatness, and $Δχ^2=-2.82$ relative to flat $Λ$CDM, but the Bayesian evidence prefers flat $Λ$CDM ($\ln B=-2.66\pm0.24$), and allowing curvature costs $\ln B=-1.39\pm0.25$. The data cannot yet measure $R_k$: the GO and Ricci cutoffs fit equally well ($\ln B=+0.28\pm0.26$). With Union3 supernovae the model is on a par with $Λ$CDM ($\ln B=+0.53$). A fraction 0.91 of the posterior reaches the finite-time fold.