Reconstruction of X-Ray Afterglow Light Curves of GRBs and its implication for constraining Cosmological Parameters

Gamma-ray bursts (GRBs) serve as important cosmological probes, whose X-ray afterglow light curves (LCs) may exhibit a plateau phase (with temporal slope $\alpha$ 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 light curves 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 $L_0$-$t_b$, $L_0$-$t_b$-$E_{p,i}$, and $L_0$-$t_b$-$E_{\gamma,\mathrm{iso}}$ relation, which are then applied to constrain both flat and non-flat $\Lambda$CDM cosmological models. The main results include: (i) the $L_0$-$t_b$ relation yields a slope $b \approx -1$, supporting a constant magnetar energy injection rate; (ii) light curve reconstruction has limited impact on cosmological parameter constraints; (iii) for the flat $\Lambda$CDM model constrained by the $L_0$-$t_b$-$E_{p,i}$ relation, the precision of $\Omega_m$ improves by 6.25\%; For the non-flat $\Lambda$CDM model constrained by the $L_0$-$t_b$-$E_{p,i}$ relation, the precision of $\Omega_\Lambda$ 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.