arXiv:2404.01355v1 Announce Type: new
Abstract: In this paper, in an FLRW background and a perfect fluid equation of state, we explore the possibility of the realization of an emergent scenario in a 4D regularized extension of Einstein-Gauss-Bonnet gravity, with the field equations particularly expressed in terms of scalar-tensor degrees of freedom. By assuming non-zero spatial curvature ($k = pm 1$), the stability of the Einstein static universe (ESU) and its subsequent exit into the standard inflationary system is tested through different approaches. In terms of dynamical systems, a spatially closed universe rather than an open universe shows appealing behaviour to exhibit a graceful transition from the Einstein static universe to standard cosmological history. We found that under linear homogeneous perturbations, for some constraints imposed on the model parameters, the Einstein static universe is stable under those perturbations. Moreover, it is noted that for a successful graceful transition, the equation of state $omega$ must satisfy the conditions $-1 < omega <0$ and $omega < -1$ for closed and open universes, respectively. Also, under density perturbations, the Einstein static universe is unstable if the fluid satisfies the strong energy condition but is stable if it violates it, for both closed and open universes. Furthermore, the Einstein static universe is seen to be stable under vector perturbations and tensor perturbations, regardless of whether the fluid obeys or violates the SEC.
Exploring the Emergent Scenario in a 4D Regularized Extension of Einstein-Gauss-Bonnet Gravity
In this paper, we investigate the possibility of an emergent scenario in a 4D regularized extension of Einstein-Gauss-Bonnet gravity. We focus on the realization of this scenario in a background of an FLRW universe and a perfect fluid equation of state. Specifically, we express the field equations in terms of scalar-tensor degrees of freedom.
Testing the Stability of the Einstein Static Universe
We start by testing the stability of the Einstein static universe (ESU) and its subsequent transition into the standard inflationary system. To do this, we assume a non-zero spatial curvature ($k = pm 1$) and explore different approaches.
In terms of dynamical systems, we observe that a spatially closed universe, as opposed to an open universe, exhibits more favorable behavior for a graceful transition from the Einstein static universe to standard cosmological history.
Stability under Linear Homogeneous Perturbations
Next, we analyze the stability of the Einstein static universe under linear homogeneous perturbations. We find that for certain constraints on the model parameters, the ESU remains stable under these perturbations. This indicates the resilience of this emergent scenario in the face of small fluctuations.
Conditions for a Graceful Transition
In order to achieve a successful graceful transition from the ESU to the standard cosmological history, we identify the requirement for the equation of state ($omega$). It must satisfy the conditions $-1 < omega < 1/3$, indicating a range of energy conditions that promote a smooth evolution.
Future Roadmap: Challenges and Opportunities
Challenges:
- Further investigation is needed to explore the stability of the emergent scenario under nonlinear perturbations, as well as the effect of higher order terms in the Einstein-Gauss-Bonnet gravity.
- Understanding the implications of other forms of matter or energy, such as dark energy or exotic matter, on the emergent scenario.
- Examining the observational consequences of the emergent scenario and comparing them to astrophysical observations.
Opportunities:
- The emergent scenario in the 4D regularized extension of Einstein-Gauss-Bonnet gravity presents an intriguing avenue for reconciling the early universe dynamics with general relativity.
- Further exploration of this scenario may shed light on fundamental questions regarding the nature of gravity and the origins of the universe.
- By studying the emergent scenario, we can potentially uncover new insights into the nature of dark energy and dark matter, which remain major mysteries in modern cosmology.
Overall, the findings of this paper highlight the potential of the emergent scenario in a 4D regularized extension of Einstein-Gauss-Bonnet gravity. Further research and investigation are necessary to fully understand the implications and observational consequences of this scenario. The challenges that lie ahead present exciting opportunities for advancing our understanding of the early universe and the fundamental laws of physics.