Homoclinic chaos in axisymmetric Bianchi-IX cosmological models with an ad hoc quantum potential

Journal Article · Thu Apr 15 00:00:00 EDT 2010 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.81.083531· OSTI ID:21431043

Correa, G C; Stuchi, T J; Joras, S E ^[1]

---

1. Instituto de Fisica, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21941-972 (Brazil)

In this work we study the dynamics of the axisymmetric Bianchi-IX cosmological model with a term of quantum potential added. As it is well known, this class of Bianchi-IX models is homogeneous and anisotropic with two scale factors, A(t) and B(t), derived from the solution of Einstein's equation for general relativity. The model we use in this work has a cosmological constant and the matter content is dust. To this model we add a quantum-inspired potential that is intended to represent short-range effects due to the general relativistic behavior of matter in small scales and play the role of a repulsive force near the singularity. We find that this potential restricts the dynamics of the model to positive values of A(t) and B(t) and alters some qualitative and quantitative characteristics of the dynamics studied previously by several authors. We make a complete analysis of the phase space of the model finding critical points, periodic orbits, stable/unstable manifolds using numerical techniques such as Poincare section, numerical continuation of orbits, and numerical globalization of invariant manifolds. We compare the classical and the quantum models. Our main result is the existence of homoclinic crossings of the stable and unstable manifolds in the physically meaningful region of the phase space [where both A(t) and B(t) are positive], indicating chaotic escape to inflation and bouncing near the singularity.

• OSTI ID: 21431043
• Journal Information: Physical Review. D, Particles Fields, Vol. 81, Issue 8; Other Information: DOI: 10.1103/PhysRevD.81.083531; (c) 2010 The American Physical Society; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
79 ASTROPHYSICS
COSMOLOGY AND ASTRONOMY
ANISOTROPY
AXIAL SYMMETRY
CHAOS THEORY
COMPARATIVE EVALUATIONS
COSMOLOGICAL CONSTANT
COSMOLOGICAL MODELS
EINSTEIN FIELD EQUATIONS
GENERAL RELATIVITY THEORY
MATHEMATICAL SOLUTIONS
MATTER
ORBITS
PERIODICITY
PHASE SPACE
RELATIVISTIC RANGE
SINGULARITY
ENERGY RANGE
EQUATIONS
EVALUATION
FIELD EQUATIONS
FIELD THEORIES
MATHEMATICAL MODELS
MATHEMATICAL SPACE
MATHEMATICS
RELATIVITY THEORY
SPACE
SYMMETRY
VARIATIONS