Cosmic structure growth and perturbation analysis in logarithmic f(Q) gravity

Abstract In this work, we explore a cosmological model within the framework of modified gravity, specifically a logarithmic form of f ( Q ) gravity. Using recent observational datasets including RSD and DESI, we constrain the model parameters via Markov Chain Monte Carlo (MCMC) techniques. Our analysis focuses on both background and perturbation-level cosmological diagnostics, evaluating the evolution of cosmographic parameters and the growth rate of structure through $$f\sigma _8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>f</mml:mi> <mml:msub> <mml:mi>σ</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:mrow> </mml:math> . The results demonstrate consistency with observational data, particularly supporting a quintessence-like accelerated expansion. Additionally, the model addresses the $$S_8$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>S</mml:mi> <mml:mn>8</mml:mn> </mml:msub> </mml:math> tension and provides insights into the late-time behavior of dark energy.