Classification of Spatially Flat Cosmological Solutions in the Presence of the Cosmological Constant and Backreaction of Conformally Invariant Quantum Fields : Astrophysics and Relativity

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We find all the spatially flat Robertson-Walker type solutions of Einstein's equations with the cosmological constant and quantum fluctuations of conformally invariant matter fields, which include effects of the conformal anomaly. We show that the relevant back-reaction equation is interpreted as an equation of motion for a classical one-dimensional potential problem with (anti-) dissipation. By considering the potential form, we can easily classify all the solutions and understand their qualitative behaviour, such as monotonic expansion (contraction), oscillation, contraction followed by expansion. Only two kinds of asymptotic behaviour are allowed, both in the past and in the future. They are (1) exponential expansion or contraction (asymptotically de Sitter) and (2) singularity (zero or infinity of the scale factor) at a finite cosmic time. Stability of de Sitter solutions (singular solutions) is also discussed. The Minkowski solution in the case of the vanishing cosmological constant is shown to be unstable, irrespectively of the sign of a parameter in the equation.
理論物理学刊行会の論文
1986-04-25