A new generic and structurally stable cosmological model without singularity

Dynamical systems methods are used to investigate a cosmological model with non-minimally coupled scalar field and asymptotically quadratic potential function. We found that for values of the non-minimal coupling constant parameter 3 16 < ξ 1 4 there exists an unstable asymptotic de Sitter state, free from parallelly propagated singularity 5 24 ≤ , giving rise non-singular beginning universe. The energy density associated this state depends on value can be much smaller than Planck density. For = we initial is in form static Einstein Proposed evolutional model, contrary seminal Starobinsky's do not depend specific choice conditions phase space, moreover, small change parameters evolution thus generic structurally stable. indicate new fundamental symmetry gravitational theory. show Jordan frame formulation theory physically nonequivalent.