Holographic Dark Energy

Abstract: We review the paradigm of holographic dark energy (HDE), which arises from a theoretical attempt of applying the holographic principle (HP) to the dark energy (DE) problem. Making use of the HP and the dimensional analysis, we derive the general formula of the energy density of HDE. Then, we describe the properties of HDE model, in which the future event horizon is chosen as the characteristic length scale. We also introduce the theoretical explorations and the observational constraints for this model. Next, in the framework of HDE, we discuss various topics, such as spatial curvature, neutrino, instability of perturbation, time-varying gravitational constant, inflation, black hole and big rip singularity. In addition, from both the theoretical and the observational aspects, we introduce the interacting holographic dark energy scenario, where the interaction between dark matter and HDE is taken into account. Furthermore, we discuss the HDE scenario in various modified gravity (MG) theories, such as Brans-Dicke theory, braneworld theory, scalar-tensor theory, Horava-Lifshitz theory, and so on. Besides, we introduce the attempts of reconstructing various scalar-field DE and MG models from HDE. Moreover, we introduce other DE models inspired by the HP, in which different characteristic length scales are chosen. Finally, we make comparisons among various HP-inspired DE models, by using cosmological observations and diagnostic tools.

• The paper derives the HDE model by linking dark energy density to the future event horizon through the holographic principle.
• It demonstrates that the parameter C influences cosmic acceleration, favoring a phantom-like scenario under observational constraints.
• It explores potential dark energy interactions with dark matter, opening avenues for addressing the cosmological coincidence problem.

Overview of Holographic Dark Energy

The reviewed paper, "Holographic Dark Energy," offers a thorough examination of the Holographic Dark Energy (HDE) model, which emerges from the application of the holographic principle to the dark energy conundrum in cosmology. This model represents an intriguing attempt to bridge quantum gravity concepts with observational cosmology. The authors explore the foundational aspects of HDE, its phenomenological implications, and its interaction with other cosmological components.

The holographic principle suggests that the description of a volume of space can be encoded on its boundary. When applied to cosmology, this principle hints that the energy density of the universe is bounded by a surface area rather than the volume—a principle that leads to the formulation of the HDE model. The paper derives the energy density of HDE as being inversely proportional to the square of a cosmological length scale, specifically choosing the future event horizon as this scale, to obtain DE that can account for the accelerating universe.

Notable Features and Results

1. Energy Density and EoS: The central formula for the energy density is derived as $\rho_{de} = 3C^2 M_p^2L^{-2}$, where $L$ represents the future event horizon. The authors calculate that the effective equation of state (EoS) of HDE is $w = -\frac{1}{3} - \frac{2\sqrt{\Omega_{de}}}{3C}$. Thus, the parameter $C$ governs whether the universe exhibits quintessence-like, cosmological constant-like, or phantom-like behavior.
2. Role of Observation: Empirical constraints suggest $C$ is slightly less than one, favoring a phantom-like scenario that posits a potential "big rip" in the universe's future. This paper emphasizes reconciling these theoretical frameworks with data from cosmic microwave background measurements, baryon acoustic oscillations, and Type Ia supernovae.
3. Theoretical Explorations: Several theoretical underpinnings for HDE are explored, including entanglement entropy and quantum field theories considering Casimir energy effects. This multifaceted approach underscores the model's foundation built upon holography principles and suggests new viewpoints on the DE paradigm itself.
4. Interacting HDE: The potential interaction between HDE and dark matter is probed, potentially addressing the cosmological coincidence problem—why the matter and DE densities are comparable today. While no definitive observational evidence yet justifies this interaction, it remains an active field of theoretical investigation.
5. Future Speculations: The HDE model, especially variants that include interaction terms or modified gravity theories, highlight speculative scenarios concerning the universe's fate and dark energy dynamics. This includes integration within broader frameworks like Brans-Dicke theory and other modified theories of gravity, reflecting on how HDE can unify quantum gravitational considerations with cosmological observations.

Implications and Future Directions

The holographic approach to DE encapsulates a promising yet intricate opportunity to link the fabric of quantum mechanics with observable universe phenomena. While offering comprehensive groundwork and suggestive empirical alignment, the paper acknowledges a degree of uncertainty involving the determination of the horizon scale parameter and its implications.

Future prospects involve a detailed confrontation between theoretical predictions and high-precision observational data from evolving astronomical projects. Enhanced datasets, particularly those emphasizing large-scale structure, weak lensing, and cosmic microwave background surveys, are crucial. Moreover, the theory's development may benefit from advances in theoretical physics domains, such as quantum gravity and string theory, which may further elucidate or modify the holographic predictions.

In summary, the reviewed paper compellingly places HDE as a pivotal element in the ongoing quest to understand dark energy, challenging conventional paradigms and stimulating discourse on integrating micro-physical and cosmological scales. While complete clarity remains elusive, the model undeniably enriches and expands both the phenomenology and theoretical landscape of dark energy.