Cosmic acceleration in f(Q) gravity: a nonlinear equation of state approach

We investigate late-time cosmic acceleration within the framework of f ( Q ) gravity supplemented by a phenomenological nonlinear equation of state of the form p = Aρ - B√ρ . p = A ρ - B ρ . Adopting a power-law ansatz f(Q)=γ ,(Q/Q₀)ⁿ, f ( Q ) = γ , ( Q / Q 0 ) n , we derive analytic expressions for the energy density and Hubble function and confront the model with a combined dataset consisting of CC, SNIa, BAO, quasar, and GRB observations covering $$0.106<z<2.33.$$ 0.106 < z < 2.33 . A Bayesian MCMC analysis constrains the parameter set H₀, A, B, c, n H 0 , A , B , c , n and yields H₀ 71.6+1.0-1.9~km~s⁻¹~Mpc⁻¹ H 0 ≃ 71 . 6 - 1.9 + 1.0 km s - 1 Mpc - 1 for the joint sample, together with a transition redshift zₜᵣ≈ 0.68. z tr ≈ 0.68 . Cosmographic diagnostics indicate a present-day deceleration parameter q₀≈ -0.59, q 0 ≈ - 0.59 , with mild deviations of the jerk and snap parameters from their Λ Λ CDM values at low redshift. Thermodynamic and causal consistency is ensured by the condition 0≤ cₛ²(z)≤ 1, 0 ≤ c s 2