  We study theoretically the quantum dynamics and spectroscopy of rovibrational
polaritons formed in a model system composed of a single rovibrating diatomic
molecule, which interacts with two degenerate, orthogonally polarized modes of
an optical Fabry-P\'erot cavity. We employ an effective rovibrational
Pauli-Fierz Hamiltonian in length gauge representation and identify three-state
vibro-polaritonic conical intersections (VPCIs) between singly-excited
vibro-polaritonic states in a two-dimensional angular coordinate branching
space. The lower and upper vibrational polaritons are of mixed light-matter
hybrid character, whereas the intermediate state is purely photonic in nature.
The VPCIs provide effective population transfer channels between singly-excited
vibrational polaritons, which manifest in rich interference patterns in
rotational densities. Spectroscopically, three bright singly-excited states are
identified, when an external infrared laser field couples to both a molecular
and a cavity mode. The non-trivial VPCI topology manifests as pronounced
multi-peak progression in the spectral region of the upper vibrational
polariton, which is traced back to the emergence of rovibro-polaritonic
light-matter hybrid states. Experimentally ubiquitous spontaneous emission from
cavity modes induces a dissipative reduction of intensity and peak broadening,
which mainly influences the purely photonic intermediate state peak as well as
the rovibro-polaritonic progression.
