Infrared cut-off proposal for the Holographic density

Abstract: We propose an infrared cut-off for the holographic the dark-energy, which besides the square of the Hubble scale also contains the time derivative of the Hubble scale. This avoids the problem of causality which appears using the event horizon area as the cut-off, and solves the coincidence problem.

• The paper introduces a new model incorporating both H² and dH/dt for holographic dark energy, addressing causality and coincidence problems of previous approaches.
• It presents an energy density formulation with constants α and β that aligns with observed transition redshift and Big Bang nucleosynthesis constraints.
• The model’s reliance on local Hubble-scale quantities offers a promising framework for further exploration of dark energy and potential modifications to general relativity.

Infrared Cut-off Proposal for the Holographic Density

The paper, authored by L.N. Granda and A. Oliveros, explores a notable proposition concerning the computation of dark energy within the framework of holography, specifically addressing and refining aspects of current infra-red (IR) cut-offs in holographic models. The researchers introduce an innovative infrared cut-off model for holographic dark energy that incorporates both the square of the Hubble scale and its time derivative, $\dot{H}$. This approach seeks to resolve the causality and coincidence problems that challenge the use of the event horizon as a standard cut-off in holographic models.

Theoretical Foundation

The background of the study is rooted in the intricate concepts of dark energy, which accounts for the observed accelerated expansion of the universe. The framework to address this is often through the cosmological constant or dynamic fields such as quintessence. However, these models face significant theoretical and observational challenges, leading researchers towards alternative approaches like holographic principles, which get inspiration from black hole physics and string theory.

The holographic principle as applied to cosmology suggests a maximum entropy bound within a given volume, specified by the enclosing surface area. The principle implies that the degrees of freedom in a spatial region are dictated by its boundary, not its volume. In cosmological models, one employs this principle aiming to explain the properties of dark energy by likening the dark energy density to the square of the Hubble parameter, although this method generally doesn't yield the parameter values consistent with the current cosmological observations.

Proposed Model

Granda and Oliveros put forward an adaptation to the holographic principle through the introduction of a new infrared cut-off model, represented mathematically by $\rho_\Lambda = 3(\alpha H^2 + \beta \dot{H})$, where $\alpha$ and $\beta$ are constants. This formulation includes the time derivative of the Hubble parameter, $\dot{H}$, a novel addition compared to traditional models. The model's advantage lies in its reliance on local quantities, bypassing issues of causality linked with the use of the event horizon.

Empirical Implications and Resolution of Problems

The formulation provides a dark energy density consisting of components that track matter and radiation densities as the universe evolves, thereby tackling the coincidence problem. Notably, the model remains consistent with observational constraints from Big Bang nucleosynthesis when the parameter $\beta$ is finely tuned. For $\beta \approx 0.5$, the model yields results viable with present cosmological observations, particularly correlating with the transition redshift, $z_T$, which describes the shift from a decelerating to an accelerating universe.

Key empirical observations include the tracking behavior of the dark energy density, which matches observed data, and the clear transition from decelerating to accelerating expansion at a consistent redshift. These results affirm the theoretical assumptions of the model and underscore its potential accuracy and utility in addressing real-world cosmological phenomena.

Conclusion and Future Directions

Granda and Oliveros propose an infrared cut-off for the holographic dark energy density based on the Hubble scale and its time derivative. The inclusion of $\dot{H}$ localizes the model's dependencies, surmounting earlier models' causality dilemmas, thus potentiating the model's coherence with empirical data. While theoretical validation of the inclusion of the $\dot{H}$ term needs further exploration, this model offers a compelling alternative framework for understanding dark energy within our universe.

Future research directions will likely focus on deeper theoretical delineation and observational validation through advanced cosmological measurements. Moreover, this model's implications for modifications in general relativity or quantum gravity might open novel investigatory pathways in foundational physics.