arXiv:2402.18604v1 Announce Type: new
Abstract: 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 can not be expressed in the Friedmann equation. Therefore holographic vacuum density is defined with standard gravitational constant in stead 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 integration 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 $kappa$. Larger holographic contribution, $c$, and larger negative NMDC coupling increase slope and magnitude of the $w_{text{eff}}$ and $H(z)$. Negative NMDC coupling can contribute to phantom equation of state, $w_{text{eff}} < -1$. The NMDC-spatial curvature coupling could also have phantom energy contribution. Moreover, free negative spatial curvature term can also contribute to phantom equation of state, but only with significantly large negative value of the spatial curvature.
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 in this study. The holographic IR cutoff scale is the apparent horizon, which forms a trapped null surface similar to a black hole’s event horizon.
In the case of a non-flat universe, the effective gravitational constant cannot be expressed in the Friedmann equation. Therefore, the holographic vacuum density is defined with the standard gravitational constant instead of the effective one. By performing dynamical and stability analysis, it is found that there are four independent fixed points. One of these fixed points is stable and corresponds to an effective equation of state, $w_{text{eff}}$, of -1.
One branch of the stable fixed-point solutions corresponds to de-Sitter expansion. The other fixed points are either unstable or saddle nodes. Numerical integration of the dynamical system is performed and plotted against $H(z)$ data. The analysis reveals that for a flat universe, the observed $H(z)$ data favors a large negative value of $kappa$.
A larger holographic contribution, $c$, and a larger negative NMDC (non-minimally derivative coupling) increase the slope and magnitude of the effective equation of state, $w_{text{eff}}$, and the Hubble parameter, $H(z)$. The negative NMDC coupling can contribute to a phantom equation of state, $w_{text{eff}} < -1$. Additionally, the NMDC-spatial curvature coupling may also result in a phantom energy contribution. The inclusion of a negative spatial curvature term can also contribute to a phantom equation of state, but only if it has a significantly large negative value.
Future Roadmap
- Further exploration of the effects of holographic vacuum energy and the non-minimal derivative coupling on cosmological dynamics is warranted.
- Investigate the stability and behavior of the other fixed points identified in the analysis.
- Perform more extensive numerical integrations and comparisons with observational data to validate the findings.
- Examine the impact of different values of the holographic contribution, $c$, and the negative NMDC coupling on the evolution of the universe.
- Investigate the potential consequences of including the NMDC-spatial curvature coupling and the negative spatial curvature term on cosmological dynamics.
Challenges
- Obtaining accurate observational data for $H(z)$ to compare with the numerical results.
- The complexity of the dynamical system may pose challenges in obtaining precise numerical solutions.
- Understanding the physical interpretation of the fixed points and their implications for the evolution of the universe.
Opportunities
- The study provides insights into the effects of holographic vacuum energy and non-minimal derivative couplings on cosmological dynamics.
- Understanding the behavior of the stable fixed point and its link to de-Sitter expansion can shed light on the nature of accelerated expansion in the universe.
- The exploration of phantom equation of state and the potential contributions from different couplings and spatial curvature provides opportunities for testing and refining cosmological models.
- Further investigations can contribute to a deeper understanding of the fundamental properties and evolution of the universe.