| Summary: | I consider two gamma-ray burst (GRB) correlations: <i>Amati</i> and <i>Combo</i>. After calibrating them in a cosmology-independent way by employing Beziér polynomials to approximate the Observational Hubble Dataset (OHD), I perform Markov Chain Monte Carlo (MCMC) simulations within the <inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">Λ</mi> </semantics> </math> </inline-formula>CDM and the <i>w</i>CDM models. The results from the <i>Amati</i> GRB dataset do not agree with the standard <inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">Λ</mi> </semantics> </math> </inline-formula>CDM model at a confidence level <inline-formula> <math display="inline"> <semantics> <mrow> <mo>≥</mo> <mn>3</mn> </mrow> </semantics> </math> </inline-formula>–<inline-formula> <math display="inline"> <semantics> <mi>σ</mi> </semantics> </math> </inline-formula>. For the <i>Combo</i> correlation, all MCMC simulations give best-fit parameters which are consistent within 1–<inline-formula> <math display="inline"> <semantics> <mi>σ</mi> </semantics> </math> </inline-formula> with the <inline-formula> <math display="inline"> <semantics> <mi mathvariant="sans-serif">Λ</mi> </semantics> </math> </inline-formula>CDM model. Pending the clarification of whether the diversity of these results is statistical, due to the difference in the dataset sizes, or astrophysical, implying the search for the most suited correlation for cosmological analyses, future investigations require larger datasets to increase the predictive power of both correlations and enable more refined analyses on the possible non-zero curvature of the Universe and the dark energy equation of state and evolution.
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