A cosmological analysis of Barrow holographic dark energy cosmological model within Brans–Dicke gravity

This study examines a holographic dark energy (HDE) model within the Brans–Dicke (BD) cosmology framework, integrating the holographic principle and employing Barrow entropy as an alternative to the conventional Bekenstein–Hawking entropy. Unlike standard HDE models, interacting and non-interacting cases are analyzed, incorporating sign-changeable and linear interactions to evaluate their role in explaining the universe’s accelerated expansion. Key cosmological parameters, including the deceleration parameter (DP) [Formula: see text], skewness parameter [Formula: see text], squared speed of sound [Formula: see text] and equation of state [Formula: see text], are investigated. Additionally, the evolution of the [Formula: see text] plane is studied. Graphical representations compare parameter behavior across different scenarios. The DP [Formula: see text] determines expansion rates, while the equation of state parameter [Formula: see text] distinguishes cosmic phases, such as quintessence and vacuum states. Stability is evaluated through squared sound speed analysis, and energy conditions offer insights into the universe’s ongoing rapid expansion. Comparative analysis with observational data indicates that the barrow holographic dark energy (BHDE) BD model effectively grows cosmic acceleration, maintains a modern EoS, [Formula: see text], aligns with [Formula: see text]CDM density ratios, and could decrease the [Formula: see text] tension, so establishing its validity as a dark energy model within scalar–tensor cosmology.