Stability of the Einstein static universe in the Jordan-Brans-Dicke theory

Abstract

Emergent theory assumes that the universe originates from an Einstein static (ES) state rather than the big bang singularity, and, thus, provides a possible way to resolve the singularity problem. The stability against all kinds of perturbations that ensures the past eternity of the ES state is crucial for a successful realization of the emergent scenario. Recently, it has been found that in the context of the Jordan-Brans-Dicke (JBD) theory there exists a stable ES solution under homogenous and anisotropic perturbations. In this paper, we extend the analysis to the stability against tensor and inhomogeneous scalar perturbations. We find that, different from general relativity and fðRÞ theory, a stable ES solution is allowed in the JBD theory when different kinds of perturbations are considered, although the stability conditions are tighter for tensor and inhomogeneous scalar perturbations than those for homogenous and anisotropic ones.

Quantum effects on Lagrangian points and displaced periodic orbits in the Earth-Moon system

“…Ref. [68]), but, on the other hand, we need the advanced tools of relativistic celestial mechanics to test the tiny effect predicted in Eq. (2.38).…”

Pseudo-Newtonian planar circular restricted 3-body problem

“…For this new approximation, the Jacobian constant is strictly conserved (unlike the Jacobian obtained in the first-order post-Newtonian approximation see e.g [14]), and its equations of motion reduce to its classical counterpart in the limit 1/c → 0. Through the Poincaré section method and validated with the Largest Lyapunov exponent, we have shown that for the set of initial conditions and Jacobian constant selected, the Newtonian and pseudo-Newtonian CRTBP exhibit a mixed phase space, i.e regular and chaotic orbits coexist.…”

“…In fact, the number of real roots of the system, whenẍ =ÿ =ẋ =ẏ = 0 in Eqs. (14) and (15), varies when varying the mass parameter µ in the interval [0, 1/2].…”

“…In a later paper, they studied the post-Newtonian triangular solution for three finite masses, showing that such configuration is not always equilateral [13]. Recently, as a first study of chaos in the post-Newtonian CRTBP, Huang and Wu [14] studied the influence of the separation between the primaries, concluding that if it is close enough, the post-Newtonian dynamics is qualitatively different. In particular, some Newtonian bounded orbits become unstable.…”

Stability of the Einstein static universe in Eddington-inspired Born-Infeld theory

“…In GR, this was reconsidered, and it was found that the Einstein static universe can be stable against small inhomogeneous vector and tensor perturbations as well as adiabatic scalar density perturbations if the universe contains a perfect fluid with w = c 2 s > 1/5 [25,26,31]. Of course, the stability of the Einstein static universe has also been extensively studied in many modified gravities, for example, loop quantum cosmology [32], f (R) theory [33][34][35], f (T ) theory [36,37], modified Gauss-Bonnet gravity [38,39], Brans-Dicke theory [40][41][42][43], Horava-Lifshitz theory [44][45][46], massive gravity [47,48], braneworld scenario [49][50][51], Einstein-Cartan theory [52], f (R, T ) gravity [53], hybrid metric-Palatini gravity [54] and so on [55][56][57][58][59][60][61][62]. We refer to e.g.…”