Model‐Independent Cosmography with Logarithmic Polynomial using Recent Observational Data

Abstract The accelerated expansion of the Universe remains a fundamental challenge in cosmology, motivating model‐independent methods to reconstruct its expansion history without relying on specific dark energy models. Cosmography, which employs series expansions of cosmological observables around the present epoch, provides a powerful kinematic framework rooted in the cosmological principle. However, standard Taylor expansions suffer from limited convergence at high redshift, prompting the exploration of alternative expansions. In this work, logarithmic polynomial cosmography is investigated, which expands observables in powers of the logarithm of redshift, thereby enhancing convergence over a broad redshift range while maintaining physical insight. The logarithmic polynomial parameters are constrained using recent datasets, including gravitational‐wave standard sirens, DESI DR2, cosmic chronometers , and multiple Type Ia supernova compilations (DES‐SN5YR, Union3, Pantheon+SH0ES). The analysis demonstrates the efficacy of the logarithmic approach in accurately modeling the cosmic expansion history, providing an interpretable alternative to traditional cosmographic techniques.