What $\xi$? Cosmological constraints on the non-minimal coupling constant

Understand

In dynamical system describing evolution of universe with the flat Friedmann-Robertson-Walker symmetry filled with barotropic dust matter and non-minimally coupled scalar field with a constant potential function an invariant manifold of the de Sitter state is used to obtain exact solutions of the reduced dynamics.

• Using observational data coming from distant supernovae type Ia, the Hubble function $H(z)$ measurements and information coming from the Alcock-Paczy$\'n$ski test we find cosmological constraints on the non-minimal coupling constant $\xi$ between the scalar curvature and the scalar field.
• For all investigated models we can exclude negative values of this parameter at the $68\%$ confidence level.
• We obtain constraints on the non-minimal coupling constant consistent with condition for conformal coupling of the scalar field in higher dimensional theories of gravity.