Conformal invariance, extra dimensions and nonsingular beginning of the Universe

Dynamical systems methods are used to investigate global behavior of the spatially flat Friedmann-Robertson-Walker cosmological model in gravitational theory with a non-minimally coupled scalar field. We found a special bifurcation value of the non-minimal coupling constant which is distinguished by dynamics of the model and may suggest some additional symmetry in matter sector of the theory. Using observational data coming from distant supernovae type Ia, the Hubble function H(z) measurements and information coming from the Alcock-Paczyński test we find cosmological constraints on the non-minimal coupling constant ξ between the scalar curvature and the scalar field. We obtain coherence with values needed for conformal coupling of the scalar field in higher dimensional theories of gravity. Scenario under investigations do not depend on a specific choice of initial conditions and is free from this degeneracy as opposed to the seminal Starobinsky scenario.

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                                       M. Kowal, W. Piechocki, L. Roszkowski, J. Skalski