  A fundamental theoretical framework is formulated for the investigation of
rovibronic spectra resulting from the coupling of molecules to one mode of the
radiation field in an optical cavity. The approach involves the computation of
(1) cavity-field-dressed rovibronic states, which are hybrid light-matter
eigenstates of the `molecule + cavity radiation field' system, and (2) the
transition amplitudes between these field-dressed states with respect to a weak
probe pulse. The predictions of the theory are shown for the homonuclear Na$_2$
molecule. The field-dressed rovibronic spectrum demonstrates undoubtedly that
the Born--Oppenheimer approximation breaks down in the presence of the cavity
radiation field. A clear fingerprint of the strong nonadiabaticity is found,
which can only emerge in the close vicinity of conical intersections. In this
work, the conical intersection is induced by the quantized radiation field, and
it is thus called a "light-induced conical intersection" (LICI). Dependence of
the cavity-field-dressed spectrum on the cavity-mode wavelength as well as on
the light-matter coupling strength is investigated. Essential changes are
identified in the spectra from the weak to the ultrastrong coupling regimes.
