Holography, UV/IR Relation, Causal Entropy Bound and Dark Energy

TL;DR

This paper explores the holographic principle's implications for dark energy, proposing a model based on the causal connection scale that aligns with current cosmological observations.

Contribution

It introduces a holographic Ricci scalar dark energy model using the causal connection scale as the IR cutoff, connecting holography with cosmological dynamics and dark energy.

Findings

The model with R_CC^{-2} =  H + 2H^2 fits current observations.

Only the causal connection scale R_CC^{-2} =  H + 2H^2 is consistent with an independently conserved vacuum energy.

The approach links holography, UV/IR relation, and dark energy in a cosmological context.

Abstract

The constraint on the total energy in a given spatial region is given from holography by the mass of a black hole which just fits in that region, which leads to an UV/IR relation: the maximal energy density in that region is proportional to $M_p^2/L^2$, where $M_p$ is the Planck mass and $L$ is the spatial scale of that region under consideration. Assuming the maximal black hole in the universe is formed through gravitational collapse of perturbations in the universe, then the "Jeans" scale of the perturbations gives a causal connection scale $R_{\rm CC}$. For gravitational perturbations, $R^{-2}_{\rm CC}={\rm Max}(\dot H+2H^2, -\dot H)$ for a flat universe. We study the cosmological dynamics of the corresponding vacuum energy density by choosing the causal connection scale as the IR cutoff in the UV/IR relation, in the cases of the vacuum energy density as an independently conserved energy component and an effective dynamical cosmological constant, respectively. It turns out that only the case with the choice $R_{\rm CC}^{-2}= \dot H +2H^2$, could be consistent with the current cosmological observations when the vacuum density appears as an independently conserved energy component. In this case, the model is called holographic Ricci scalar dark energy model in the literature.