Stability of cosmological solutions of the Hoyle-Narlikar C-field theory

In order to maintain the strong form of the cosmological principle in the face of the Hubble expansion of the Universe, Hoyle and Narlikar proposed the continuous creation of a "C"-field and claimed that it has a unique non-singular solution to the Einstein field equations. It is shown here, by second variation of the C-field action, that this solution is unstable. It is also demonstrated here that there does exist a singular solution, which corresponds to the Friedmann model with cosmological constant, and a genuine steady-state solution, which corresponds to the de Sitter Universe. Further, the Friedmann model with positive cosmological constant is unstable, while the de Sitter Universe and the Friedmann model with negative cosmological constant are stable solutions of the theory. We point out the importance of the test of stability of solutions for a given action.