Inflationary Scenario in Bianchi Type IX Space–Time with Massless Scalar Field

Inflationary scenario in Bianchi type IX space–time with massless scalar field and flat potential is discussed. To get the deterministic solution in terms of cosmic time t, it is assumed that the scale factor \( \sim \,e^{3Ht} {\text{ i}} . {\text{e}} . \quad { }R^{3} \, \sim \,e^{3Ht} \) as introduced by Kirzhnits and Linde (Ann Phys 101:195–238, 1976 [15]). Potential V(ϕ) is constant, where ϕ is Higg’s field. We find that spatial volume increases with time. The model represents an anisotropic accelerating universe in general. However, if we assume a = e Ht , b = e Ht then the model leads to constant acceleration, shear (σ) = 0 and deceleration parameter (q) = −1. Hence it leads to de-sitter universe.