Barrow holographic dark energy: reconstruction within Saez-Ballester theory in Kantowski-Sachs universe

Abstract Within the framework of the Saez-Ballester theory, the Barrow Holographic Dark Energy (BHDE) has been reconstructed. This reconstruction was carried out in a homogeneous and anisotropic KS universe that was filled with BHDE. The study examined both non-interacting and interacting scenarios, with the future event horizon serving as the IR cut-off. The analysis focused on the evolution of the equation of State parameter for both cases, as well as the trajectories of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>w</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">DE</mml:mi> </mml:mrow> </mml:msub> <mml:mo>−</mml:mo> <mml:mi>w</mml:mi> <mml:msub> <mml:mrow> <mml:mo accent="true">′</mml:mo> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">DE</mml:mi> </mml:mrow> </mml:msub> </mml:math> . Additionally, the study investigated the inflation of the Universe filled with BHDE by plotting the slow-roll parameters. Furthermore, a connection between the canonical scalar field and BHDE was explored, as the presence of a scalar field is often associated with inflation. Finally, the tensor-to-scalar ratio r is plotted which seems to lie within the acceptable range.