Abstract

We generalize thermal WIMP (Weakly Interacting Massive Particle) freeze-out within Tsallis nonextensive statis-tics. Using Curado-Tsallis q-distributions f, (E; mu. T) we compute q-deformed number and energy densities, pres sure, entropy density and Hubble rate, (PPH). The Boltzmann equation is generalized accordingly to obtain the comoving abundance Y, (x) and relic density 2, h(2) for a dark-matter candidate x in a model-independent setup. The thermally averaged cross section is expanded as (sigma upsilon), = a+b(), up to p-wave. The freeze-out parameter x,(4) is determined from 1 (T) H(T) using a 4-logarithmic inversion, with the ex-pansion rate modified through ultra-relativistic rescalings R, (4) of the effective relativistic degrees of freedom g, and g... We show that x, increases with 4 and that QCD-threshold features propagate into Y(x) and 2. We then perform two 4-grid scans: fixing (sv), while varying the dark-matter mass m,, and fixing, while varying the s-wave coefficient a. For an s-wave dominated scenario we construct x profiles in these planes by comparing 12h with the Planck benchmark Omega_{e} * h <^> 2 = 0.12 plus/minus 0.001 In both cases we find a clear degeneracy in the preferred nonextensive parameter het along valleys in parameter space. However, fixed-mass scans (varying (sigma tau),) are sig-nificantly more constraining than fixed-cross-section scans, reflecting that 2, h(2) is mainly controlled by (or). so that for realistic cross sections the best-fit het remains close to the extensive limit 4 -> 1.