Cosmological dynamics of exponential quintessence constrained by BAO, cosmic chronometers, and DES-SN5YR/Pantheon$$^+$$ data

Abstract We perform a comprehensive observational test of a canonical quintessence model driven by an exponential potential, motivated by its emergence in higher-dimensional theories, string-inspired scenarios, and modified gravity. Using a Markov Chain Monte Carlo framework, we constrain the model with the latest high-precision observational datasets–Cosmic Chronometers, Baryon Acoustic Oscillation, Pantheon $$^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mmultiscripts> <mml:mrow/> <mml:mrow/> <mml:mo>+</mml:mo> </mml:mmultiscripts> </mml:math> , and DES-SN5YR Type Ia Supernovae. The combined data significantly tighten the parameter bounds on $$(H_0, \Omega _{m_0}, \eta _0, \gamma )$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>(</mml:mo> <mml:msub> <mml:mi>H</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>Ω</mml:mi> <mml:msub> <mml:mi>m</mml:mi> <mml:mn>0</mml:mn> </mml:msub> </mml:msub> <mml:mo>,</mml:mo> <mml:msub> <mml:mi>η</mml:mi> <mml:mn>0</mml:mn> </mml:msub> <mml:mo>,</mml:mo> <mml:mi>γ</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> and yield predictions for the Hubble parameter H ( z ), the distance modulus $$\mu (z)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>μ</mml:mi> <mml:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> , and the scaled comoving angular diameter distance that remain in excellent agreement with observations and closely follow the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM baseline. In addition, an information-theoretic model comparison based on the Akaike Information Criterion shows that the exponential quintessence model remains statistically comparable with the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM scenario, despite the penalty associated with its additional parameters. The model naturally reproduces the transition from matter domination to late-time acceleration, maintains total equation of state $$\omega _{\textrm{tot}} &gt; -1$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ω</mml:mi> <mml:mtext>tot</mml:mtext> </mml:msub> <mml:mo>&gt;</mml:mo> <mml:mo>-</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:math> as expected for canonical scalar fields, and provides an age of the universe consistent with Planck 2018. The Statefinder diagnostics show trajectories approaching the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM fixed point, while allowing small observable departures. Energy condition analysis confirms physical viability, with only the Strong Energy Condition violated at late times, as required for acceleration. Overall, our results show that quintessence with an exponential potential provides a stable, observationally consistent alternative to $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM. Using the latest high-precision datasets, we obtain some of the most stringent constraints on this exponential-potential quintessence model, reaffirming its viability as a compelling dynamical explanation for dark energy.