2025ApJ...991..145Z

Gamma-ray bursts (GRBs) serve as important cosmological probes whose X-ray afterglow light curves (LCs) may exhibit a plateau phase (with temporal slope α between 0 and 0.5) that may originate from magnetar energy injection. Similar to Type Ia supernovae, GRBs with a common physical origin can be used as standardizable candles for cosmological studies. However, observational gaps in GRB LCs introduce significant uncertainties in plateau parameter estimation, thereby affecting cosmological constraints. In this work, we employ a stochastic reconstruction technique to reconstruct the X-ray afterglow LCs for 35 GRB samples exhibiting plateau features, generating 50 simulated data points for each LC. Using the reconstructed LCs, we calibrate three luminosity correlations: the L₀-t_b, L₀-t_b-E_p,i, and L₀-t_b-E_γ,iso relations, which are then applied to constrain both flat and nonflat ΛCDM cosmological models. The main results include (i) the L₀-t_b relation yields a slope b ≈ -1, supporting a constant magnetar energy injection rate; (ii) LC reconstruction has limited impact on cosmological parameter constraints; and (iii) for the flat ΛCDM model constrained by the L₀-t_b-E_p,i relation, the precision of Ω_m improves by 6.25%; for the non-flat ΛCDM model constrained by the L₀-t_b-E_p,i relation, the precision of Ω_Λ improves by 1.01%. Our findings suggest that increasing the number of LC data points provides limited improvement to cosmological constraints, while expanding the sample size of GRBs with identical physical origins may be more crucial.