Holographic Dark Energy Models with a Hybrid Bounce in General Relativity

AbstractIn this paper, we investigate four distinct Holographic Dark Energy (HDE) models; Rényi HDE, Tsallis HDE, Sharma–Mittal HDE, and Barrow HDEin the framework of standard General Relativity with a spatially flat Friedmann–Robertson–Walker (FRW) metric, admitting a novel Hybrid Bounce scale factor of the form = + . Thisscale factor combines exponential and power-law growth to produce a non-singular bounce at = 0, thereby avoiding theinitial singularity problem. The Hubble parameter and the deceleration parameter are derived analytically. Foreach HDE model, we compute the energy density , equation of state (EoS) parameter , squared speed of sound, the diagnostic, the –′ phase plane, and the Null Energy Condition (NEC). We explore the dependenceof these physical quantities on the model parameters and discuss their cosmological implications. Our analysis revealsthat all four models exhibit quintom-like behavior, transit from the bouncing phase to accelerated expansion, and areconsistent with a bouncing cosmology that avoids the initial singularity. At late times the Gaussian factor drives a super-accelerating phase in which grows without bound and → −1 from below, a behavior distinct from an exact de Sitter( = const) state. The Barrow HDE, with its fractal horizon modification, shows distinctive behavior for higher values ofthe exponent , while the Rényi model provides the smoothest transition across the phantom divide. We emphasize thatthe scale factor is prescribed and the dark-energy content is reconstructed from it; the scope and limitations of thisapproach are discussed.