Thermodynamics of interacting holographic dark energy with apparent horizon as an IR cutoff (0910.0510v2)

Abstract: As soon as an interaction between holographic dark energy and dark matter is taken into account, the identification of IR cutoff with Hubble radius $H^{-1}$, in flat universe, can simultaneously drive accelerated expansion and solve the coincidence problem. Based on this, we demonstrate that in a non-flat universe the natural choice for IR cutoff could be the apparent horizon radius, $\tilde{r}_A={1}/{\sqrt{H^2+k/a^2}}$. We show that any interaction of dark matter with holographic dark energy, whose infrared cutoff is set by the apparent horizon radius, implies an accelerated expansion and a constant ratio of the energy densities of both components thus solving the coincidence problem. We also verify that for a universe filled with dark energy and dark matter the Friedmann equation can be written in the form of the modified first law of thermodynamics, $dE=T_hdS_h+WdV$, at apparent horizon. In addition, the generalized second law of thermodynamics is fulfilled in a region enclosed by the apparent horizon. These results hold regardless of the specific form of dark energy and interaction term. Our study might reveal that in an accelerating universe with spatial curvature, the apparent horizon is a physical boundary from the thermodynamical point of view.

• The paper demonstrates that using the apparent horizon as the IR cutoff maintains a constant dark energy to dark matter ratio, addressing the coincidence problem.
• It integrates thermodynamic principles with the Friedmann equation, showing modified compliance with the first law in non-flat cosmic settings.
• The research confirms the generalized second law of thermodynamics for interacting dark components, informing models of cosmic evolution.

Thermodynamics of Interacting Holographic Dark Energy with Apparent Horizon as an IR Cutoff

The paper presented in the paper examines the thermodynamic properties of interacting holographic dark energy (HDE) in non-flat universes, with a focus on the interaction between dark energy and dark matter. By utilizing the apparent horizon as the infrared (IR) cutoff, the research explores new dimensions in cosmological behavior, particularly in solving the long-standing coincidence problem and driving accelerated cosmic expansion.

The cornerstone of this analysis is the proposition that the IR cutoff, determined by the apparent horizon radius, creates a framework where dark energy and matter densities maintain a constant ratio, thereby addressing the coincidence problem. This is a vital aspect, as the choice of the IR cutoff can significantly affect cosmological models. The research demonstrates that when interaction is introduced, using the apparent horizon as the IR cutoff proves to be more practical for a universe with spatial curvature than the previously considered Hubble radius.

Furthermore, the paper integrates these findings with thermodynamic principles. The Friedmann equation is shown to comply with a modified version of the first law of thermodynamics within this context, underscoring the link between cosmic dynamics and thermodynamic laws. The consistency of these laws in a universe filled with interacting dark components is demonstrated under the condition of apparent horizon encapsulation.

Similarly, the research confirms that the generalized second law of thermodynamics holds within regions enclosed by the apparent horizon. This validation provides a deeper understanding of thermodynamic behavior in universes where HDE interaction occurs, reinforcing the apparent horizon as a viable physical boundary from a thermodynamic standpoint.

Implications of such findings are profound both in practical and theoretical realms. Practically, they provide a framework to modify models of cosmic evolution and expansion, potentially influencing observational cosmology and astrophysics. Theoretically, they articulate a coherent view that connects thermodynamics to cosmological models with a spatial curvature, implicating the apparent horizon as a critical component in understanding cosmic thermodynamics.

Future developments in AI could further refine such research, particularly in computational modeling and prediction of cosmic behaviors at a granular level. Artificial intelligence might improve our ability to simulate complex interactions within the universe, offering more precise and varied scenarios for understanding the nature of dark energy and its interactions.

In conclusion, the research sheds light on the critical choices of IR cutoff in cosmological models and substantiates essential thermodynamic principles within these models. The apparent horizon emerges as a promising candidate for IR cutoff in non-flat universes, thereby facilitating constant energy density ratios, accelerated expansion, and compliance with established thermodynamic laws. This paper contributes a significant perspective to the ongoing exploration of dark energy, spacetime curvature, and thermodynamic principles in cosmological research.