Exact plane-symmetric cosmological solutions for a massless scalar field and cosmological constant using the Riccati equation

Abstract

The Einstein–Klein–Gordon equations have been solved exactly for the case of a minimally coupled, plane-symmetric static massless scalar field with cosmological constant. Here, using the Riccati equation, we find additional, overlooked solutions, as well as anisotropic cosmologies derived by analytic continuation. Setting an integration constant equal to zero, the latter solutions become equivalent to known homogeneous, isotropic cosmologies featuring stiff matter. The interplay between the scalar field stress energy and cosmological constant allows several outcomes for universal evolution, including a singularity-free bounce cosmology. The Riccati equation appears to be particularly well suited for finding certain exact solutions in general relativity.