A Model-Independent Reconstruction of the Cosmic Expansion History from Pantheon+SH0ES Supernovae Using Gaussian Process Regression

We present a model-independent reconstruction of the cosmic expansion history using Type Ia supernovae from the Pantheon+SH0ES compilation. Using Gaussian Process regression on luminosity distance measurements from 1701 supernovae spanning redshifts $0.0012 < z < 2.26$, we reconstruct the Hubble parameter $H(z)$ and deceleration parameter $q(z)$ without assuming any specific cosmological model. The method employs Monte Carlo sampling from the Gaussian Process posterior to quantify uncertainties and compute the probability of cosmic acceleration as a function of redshift. We find that the transition from deceleration to acceleration is inherently probabilistic when reconstructed from data, with a median transition redshift of $z_{\rm trans} \approx 0.014$ and a 68\% confidence interval of $[0.008, 0.022]$. The broad uncertainty reflects both observational noise and the sensitivity of numerical differentiation in non-parametric methods. We emphasize that only the sign of $q(z)$ and its probability distribution carry robust physical information, as absolute values are numerically unstable due to differentiation. Our results are consistent with expectations from standard cosmology but are obtained independently of any dark energy model. This work demonstrates the utility of Gaussian Process methods for exploring expansion history directly from supernova data while highlighting the importance of careful uncertainty quantification in model-independent approaches