Abstract
The emergent mechanism provides a possible way to resolve the big-bang singularity problem by assuming that our universe originates from the Einstein static (ES) state. Thus, the existence of a stable ES solution becomes a very crucial prerequisite for the emergent scenario. In this paper, we study the stability of an ES universe in gravity theory with a non-minimal coupling between the kinetic term of a scalar field and the Einstein tensor. We find that the ES solution is stable under both scalar and tensor perturbations when the model parameters satisfy certain conditions, which indicates that the big-bang singularity can be avoided successfully by the emergent mechanism in the non-minimally kinetic coupled gravity.
Highlights
A natural generalization of the minimally coupled gravity is to assume a non-minimal coupling between the scalar field and the curvature, which can be generated naturally when quantum corrections are considered and is essential for the renormalizability of the scalar-field theory in curved space
Where R is the Ricci curvature scalar, G is the Newtonian gravitational constant, gμν is the metric tensor with g being its trace, Gμν is the Einstein tensor, V (φ) is the potential of the scalar field φ, κ stands for the coupling parameter with dimension of2, and Sm represents the action of a perfect fluid
We have analyzed the stability of an Einstein static (ES) universe under both scalar and tensor perturbations in gravity theory with a coupling between the kinetic term of the scalar field and the Einstein tensor
Summary
A natural generalization of the minimally coupled gravity is to assume a non-minimal coupling between the scalar field and the curvature, which can be generated naturally when quantum corrections are considered and is essential for the renormalizability of the scalar-field theory in curved space. This non-minimally coupled scalar field has been suggested to be responsible for both the early cosmic inflation [16,17] and the present accelerated expansion [18–20]. Miao et al [35] found that there is no stable ES solution when scalar perturbations and tensor ones are considered together in the scalar–tensor theory of gravity with a normal perfect fluid, such as radiation or pressureless matter. It is worthy to note that the stability of ES solutions have been analyzed in some other theories [36–82]
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