Abstract:
A new one-parameter global solution in general relativity with a scalar field has been found. The Liouville metric, which possesses four second-rank Killing tensors in involution, was used as an ansatz; consequently, the geodesic equations are integrable in the sense of Liouville. In such a model, the Einstein equations have a general solution only for an exponential potential of the scalar field. The found solution is conformally flat and invariant under global Lorentz transformations centered at the origin. Inside the light cone centered at the origin, the spacetime is homogeneous and isotropic and can be interpreted as the Universe. The corresponding scale factor vanishes on the light cone; however, all geometric invariants have no singularity on the light cone and extend in an infinitely smooth manner to the exterior of the light cone. In this region of spacetime, homogeneity and isotropy disappear, and a white hole, which attracts matter, is located there. This leads to the accelerated expansion of the Universe.
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