Gravitational instantons in R4-gravity for open inflation

Abstract

In a Euclidean gravity we study the creation of an inflationary universe in a higher order theory of gravity making use of the Hawking–Turok instantons. Here we consider a nonlinear γR4 term to the Einstein gravitational action including a cosmological constant to obtain gravitational instantons relevant for describing the early universe. It is found that the theory permits gravitational instantons even in the absence of a cosmological constant. To explore instantons other than the de Sitter instanton in the framework of higher order theory of gravity, we use the conformal transformation. The higher order theory is converted into a theory of self-interacting scalar field minimally coupled to Einstein gravity. The singular instantons obtained in the conformally equivalent case is taken up to obtain an open inflationary scenario. The probability of creation of singular and non-singular instantons is evaluated here. We note that a non-singular instanton solution is permitted with a positive cosmological constant when γ < 0 and that with a negative cosmological constant when γ > 0. It is also noted that such instanton solutions are permitted even in the absence of a cosmological constant. The singular instanton solution relevant for the inflationary universe is obtained for . The potential obtained in the conformally equivalent case permits enough inflation necessary for a consistent cosmological model.