Abstract
We discuss the connection between black hole and holographic dark energy. We examine the issue of the equation of state (EOS) for holographic energy density as a candidate for the dark energy carefully. This is closely related to the EOS for black hole, because the holographic dark energy comes from the black hole energy density. In order to derive the EOS of a black hole, we may use its dual (quantum) systems. Finally, a regular black hole without the singularity is introduced to describe an accelerating universe inside the cosmological horizon. Inspired by this, we show that the holographic energy density with the cosmological horizon as the IR cutoff leads to the dark energy-dominated universe with ωΛ=−1.
Highlights
Observations of supernova type Ia suggest that our universe is accelerating [1]
We emphasize that the energy density ρBH of the black hole is used to derive the holographic dark energy
We propose that the singular-free condition for holographic dark energy ρΛ may determine the equation of state
Summary
Observations of supernova type Ia suggest that our universe is accelerating [1]. Considering the ΛCDM model [2, 3], the dark energy and cold dark matter contribute ΩoΛb ≃ 0.74 and ΩoCbDM ≃ 0.22 to the critical density of the present universe. The total energy density dilutes as L−3 due to the evolution of the universe, whereas its upper limit set by gravity (black hole) decreases as L−2 Even though it may explain the present data, this approach with L = H0−1 fails to recover the EOS for a dark energy-dominated universe. The future event horizon was introduced to obtain an accelerating universe [13, 14, 15, 16, 17] At this stage, we emphasize that the energy density ρBH of the black hole is used to derive the holographic dark energy. We do not use the pressure pBH of the black hole to find the correct EOS of holographic dark energy.
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