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

Abstract

We investigate the possibility to restrict the chaotic inflationary scenario with the large nonminimally coupled inflaton field $\ensuremath{\varphi}$ considered by Fakir and Unruh by means of the observed cosmic microwave background radiation (CMBR) anisotropy. This model is characterized by the condition $\ensuremath{\xi}>1$ and $\ensuremath{\psi}\ensuremath{\equiv}8\ensuremath{\pi}G\ensuremath{\xi}{\ensuremath{\varphi}}^{2}\ensuremath{\gg}1$ where $\ensuremath{\xi}$ 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 $\ensuremath{\lambda}/{\ensuremath{\xi}}^{2}=1.8\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}8}/{\ensuremath{\psi}}_{i},$ where $\ensuremath{\lambda}$ is the self-coupling and ${\ensuremath{\psi}}_{i}$ means the initial value of $\ensuremath{\psi}.$ Combining this with the previously obtained constraint $\sqrt{\ensuremath{\lambda}/{\ensuremath{\xi}}^{2}}\ensuremath{\approx}(\ensuremath{\delta}{T/T)}_{\mathrm{rms}}=1.1\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}5},$ we conclude that the initial value has to be ${\ensuremath{\psi}}_{i}\ensuremath{\approx}1.6\ifmmode\times\else\texttimes\fi{}{10}^{3}.$ If the self-coupling has reasonable values of order ${10}^{\ensuremath{-}2},$ then $\ensuremath{\xi}\ensuremath{\approx}{10}^{4}$ and ${\ensuremath{\varphi}}_{i}\ensuremath{\approx}{10}^{\ensuremath{-}1}{m}_{\mathrm{Pl}}$ where ${m}_{\mathrm{Pl}}$ is the Planck mass.