We consider the power law and the entropy corrected holographic dark energy (HDE) models with Hubble horizon in the dynamical Chern–Simons modified gravity. We explore various cosmological parameters and planes in this framework. The Hubble parameter lies within the consistent range at the present and later epoch for both entropy corrected models. The deceleration parameter explains the accelerated expansion of the universe. The equation of state (EoS) parameter corresponds to quintessence and cold dark matter ([Formula: see text]CDM) limit. The [Formula: see text] approaches to [Formula: see text]CDM limit and freezing region in both entropy corrected models. The statefinder parameters are consistent with [Formula: see text]CDM limit and dark energy (DE) models. The generalized second law of thermodynamics remain valid in all cases of interacting parameter. It is interesting to mention here that our results of Hubble, EoS parameter and [Formula: see text] plane show consistency with the present observations like Planck, WP, BAO, [Formula: see text], SNLS and nine-year WMAP.

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Among various dark energy models, Tsallis holographic dark energy model shows the dynamical enthusiasm to describe the transition phase of the universe. In this paper, we consider Tsallis holographic dark energy with event and apparent horizon as an infrared cutoff in the framework of dynamical Chern–Simon modified gravity and non-flat FRW universe. We explore Hubble, equation of state and deceleration parameters and found that Hubble parameter lies in the range [Formula: see text] and [Formula: see text] for event and apparent horizon trajectories, respectively. It is mentioned here that the equation of state parameter lies within the range [Formula: see text] (event) and [Formula: see text] (apparent). Also, deceleration parameter for both cases show accelerated and decelerated phase of universe as well as cosmological constant. Moreover, we also checked the stability of our model through square speed of sound, which shows the positive behavior (exhibits the stability of the model). Finally, we observe that the generalized second law of thermodynamics remains valid in both cases of horizon.

In the present manuscript, the evolution of the cosmic parameters and planes are being investigated in the framework of the DGP braneworld model. In this scenario, the interaction Γ between the Barrow holographic dark energy model (whose infrared cutoff scale is set by Hubble and event horizons) and pressureless dark matter are considered. We check the behavior of different cosmological parameters such as Hubble, equation of state, deceleration and squared speed of sound from the early matter-dominated era until the late-time acceleration. It is found that the range of Hubble parameter lies in the interval 95−35+35 (for Hubble horizon) and 97−23+23 (for event horizon). For both horizons, the equation of state parameter favors the phantom dominant era as well as the ΛCDM model while the deceleration parameter illustrates the accelerated expansion of the universe. Furthermore, stability of the underlying model is found through squared speed of sound. Furthermore, it is observed that ω−ωϑ′ plane corresponds to freezing and thawing region for Hubble and event horizons, respectively. Furthermore, statefinder plane shows the ΛCDM and Chaplygin gas behavior for both models. Finally, we investigate the thermodynamical nature of the underlying model through Barrow entropy as horizon entropy and found validity for both horizons.

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