Parameter constraints and cosmographic analysis of Barrow agegraphic and new Barrow agegraphic dark energy models

Abstract This research focuses on examining a non-flat Friedmann–Robertson–Walker (FRW) cosmological model of the universe incorporating both dark matter and dark energy. Two intriguing dark energy models, Barrow agegraphic dark energy (BADE) and new Barrow agegraphic dark energy (NBADE), which were introduced in accordance with the holographic principle incorporating Barrow entropy, have been selected to play the role of dark energy. Using datasets from cosmic chronometers and baryon acoustic oscillations, we utilized the Markov Chain Monte Carlo (MCMC) technique to constrain the parameters of our model. This enables us to make several possible comparisons between these novel models of dark energy and the $$\Lambda $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Λ</mml:mi> </mml:math> CDM models. Here, we explore cosmological parameters, including the equation of state(EoS) parameter, jerk parameter, deceleration parameter, and cosmological planes such as the $$q-r$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>q</mml:mi> <mml:mo>-</mml:mo> <mml:mi>r</mml:mi> </mml:mrow> </mml:math> plane, $$\omega _d - \omega '_d$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msub> <mml:mi>ω</mml:mi> <mml:mi>d</mml:mi> </mml:msub> <mml:mo>-</mml:mo> <mml:msubsup> <mml:mi>ω</mml:mi> <mml:mi>d</mml:mi> <mml:mo>′</mml:mo> </mml:msubsup> </mml:mrow> </mml:math> for different values of the model parameters by considering both the presence and absence of mutual interactions of the dark sector of the universe. In addition, we examined the thermal stability and the Swampland criteria of our constructed models. Additionally, we analyze the energy conditions and find that NEC and DEC are fulfilled, but SEC is broken, indicating model stability and supporting the current acceleration of the universe. In order to give a more precise explanation of the origin of cosmic structures, we lastly conduct a linear perturbation analysis to examine the growth in matter density perturbations.