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Description
One parameter family of exact solutions in General Relativity with a scalar field has been found using the Liouville metric. The scalar field potential has exponential form. The solution corresponding to the naked singularity provides smooth extension of the Friedmann Universe with accelerated expansion through the zero of the scale factor back in time. All geodesics are found explicitly. Their analysis shows that the Liouville solution is a global one: every geodesic is either continued to infinite value of the canonical parameter in both directions or ends up at the singularity at its finite value. Moreover, analysis of geodesics shows that the naked singularity located outside the
Friedmann Universe attracts matter and therefore provides its accelerating expansion inside the light cone.
[1] D. E. Afanasev, M. O. Katanaev, “Liouville solution in General Relativity with a scalar field”, Phys. Lett. B, 864 (2025), 139439 , 5 pp.
[2] D. E. Afanasev, M. O. Katanaev, “Geodesics and global properties of the Liouville solution in general relativity with a scalar field”, JCAP, 2025:08 (2025), 045, 29 pp.
