Eur. Phys. J. C (2026) 86: 134
https://doi.org/10.1140/epjc/s10052-026-15310-1

Regular Article - Theoretical Physics

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

¹ Institute of Graduate Studies in Sciences, Istanbul University, Vezneciler, 34134, Istanbul, Turkey
² Government Tilak PG College, 483501, Katni, M.P., India
³ Department of Physics, Faculty of Science, Istanbul University, Vezneciler, Fatih, 34134, Istanbul, Turkey
⁴ Department of Mathematical Sciences, University of Zululand, P Bag X1001, 3886, Kwa-Dlangezwa, South Africa
⁵ Faculty of applied and Health Sciences, Mangosuthu University of Technology, PO Box 12363, 4026, Jacobs, South Africa
⁶ National Institute for Theoretical and Computational Sciences (NITheCS), 7600, Stellenbosch, South Africa
⁷ DSTI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), 2001, Johannesburg, South Africa
⁸ Department of Mathematics, Institute of Sciences, Chandigarh University, Mohali, India

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Received: 6 September 2025
Accepted: 10 January 2026
Published online: 9 February 2026

Abstract

We investigate late-time cosmic acceleration within the framework of f(Q) gravity supplemented by a phenomenological nonlinear equation of state of the form $p=A\rho -B\sqrt{\rho }.$ Adopting a power-law ansatz $f(Q)=\gamma ,{(Q/Q_0)}^n,$ 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 $0.106<z<2.33.$ A Bayesian MCMC analysis constrains the parameter set $H_0,A,B,c,n$ and yields $H_0\simeq 71.6_{-1.9}^{+1.0}\text{km}{\text{s}}^{-1}{\text{Mpc}}^{-1}$ for the joint sample, together with a transition redshift $z_{\text{tr}}\approx 0.68.$ Cosmographic diagnostics indicate a present-day deceleration parameter $q_0\approx -0.59,$ with mild deviations of the jerk and snap parameters from their $\mathrm{\Lambda }$CDM values at low redshift. Thermodynamic and causal consistency is ensured by the condition $0\le c_s^2(z)\le 1,$ while the matter-sector energy conditions remain satisfied up to $z\sim \mathcal{O}(1).$ A statistical comparison with the concordance model shows that the proposed $f(Q)+$nEoS scenario achieves a goodness of fit comparable to $\mathrm{\Lambda }$CDM over the same dataset, with ${\chi }^{2_{min}^{\text{model}}}=255.93$ versus ${\chi }^{2_{min}^{\mathrm{\Lambda }\text{CDM}}}=260.5$ and ${\chi }_{\text{red}}^2\approx 0.96$ for both cases. The Akaike Information Criterion yields $\mathrm{\Delta }\text{AIC}\approx 1.4,$ indicating statistical equivalence with a mild preference for $\mathrm{\Lambda }$CDM due to its smaller parameter space. Therefore, the model provides a viable description of the late-time expansion history, allowing controlled deviations from $\mathrm{\Lambda }$CDM that modestly alleviate, though do not resolve, the $H_0$ tension. Several other interesting properties of a nEoS are also elucidated upon.