Dynamics of holographic dark energy with apparent-horizon cutoff and non-minimal derivative coupling gravity in non-flat FLRW universe

• Main Authors: Tita, Amornthep, Gumjudpai, Burin, Srisawad, Pornrad
• Format: Journal Article
• Language: English
• Published: 14-06-2024
• Subjects: Physics - Cosmology and Nongalactic Astrophysics; Physics - General Relativity and Quantum Cosmology
• DOI: 10.48550/arxiv.2402.18604

Phys. Dark Univ. 45, 101542 (2024) Background cosmological dynamics for a universe with matter, a scalar field
non-minimally derivative coupling to Einstein tensor under power-law potential
and holographic vacuum energy is considered here. The holographic IR cutoff
scale is apparent horizon which, for accelerating universe, forms a trapped
null surface in the same spirit as blackhole's event horizon. For non-flat
case, effective gravitational constant cannot be expressed in the Friedmann
equation. Therefore holographic vacuum density is defined with standard
gravitational constant instead of the effective one. Dynamical and stability
analysis shows four independent fixed points. One fixed point is stable and it
corresponds to $w_{\text{eff}} = -1$. One branch of the stable fixed-point
solutions corresponds to de-Sitter expansion. The others are either unstable or
saddle nodes. Numerical integrations of the dynamical system are performed and
plotted confronting with $H(z)$ data. It is found that for flat universe,
$H(z)$ observational data favors large negative value of NMDC coupling,
$\kappa$. Larger holographic contribution, $c$, and larger negative NMDC
coupling increase slope and magnitude of the $w_{\text{eff}}$ and $H(z)$.
Negative $\kappa$, can contribute to phantom equation of state, $w_{\text{eff}}
< -1$. The NMDC-spatial curvature coupling could have phantom energy
contribution. Free negative spatial curvature term can also contribute to
phantom equation of state, but only with significantly large negative value of
the spatial curvature. The model could give phantom equation of state for
$\kappa = -200$ and high value of $c$ for both flat and open cases.