Constraints on the chaotic inflationary scenario with a nonminimally coupled “inflaton” field from the cosmic microwave background radiation anisotropy

We investigate the possibility to restrict the chaotic inflationary scenario with the large nonminimally coupled inflaton field [Formula Presented] considered by Fakir and Unruh by means of the observed cosmic microwave background radiation (CMBR) anisotropy. This model is characterized by the condition [Formula Presented] and [Formula Presented] where [Formula Presented] is the nonminimal coupling constant. We calculate the contributions of the long wavelength gravitational waves generated in the inflationary period to the CMBR anisotropy quadrupole moment. We obtain the constraint [Formula Presented] where [Formula Presented] is the self-coupling and [Formula Presented] means the initial value of [Formula Presented] Combining this with the previously obtained constraint [Formula Presented] we conclude that the initial value has to be [Formula Presented] If the self-coupling has reasonable values of order [Formula Presented] then [Formula Presented] and [Formula Presented] where [Formula Presented] is the Planck mass.