Exploring late-time cosmic acceleration in VCDM cosmology

Abstract In this work, we have considered a minimally modified gravity theory that effectively reproduces VCDM-like behavior to investigate its cosmological implications. The model parameters are constrained using a combination of CC, RSD, DESI BAO DR2, and Union3 datasets. The model parameters are constrained using an MCMC framework, ensuring a robust estimation of credible intervals. We examine both background and perturbation-level observables, analyzing the Hubble parameter, deceleration parameter, effective equation of state, distance modulus, and the growth rate of cosmic structures through the $$f\sigma _8(z)$$ <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:mo>(</mml:mo> <mml:mi>z</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> observable. Our results show that the model successfully reproduces the observed expansion history, featuring a smooth transition in the Hubble evolution around $$z \simeq 0.3$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>z</mml:mi> <mml:mo>≃</mml:mo> <mml:mn>0.3</mml:mn> </mml:mrow> </mml:math> , and consistent behaviour of cosmological parameters. The model outperforms $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM in the statistical comparisons for the full dataset combination (CC+RSD+DESI DR2+Union3). These results highlight the potential of minimally modified gravity theories with VCDM-like dynamics as consistent and competitive alternatives to the standard cosmological paradigm.