  The vacuum Rabi splitting (VRS) in molecular polaritons stands as a
fundamental measure of collective light-matter coupling. Despite its
significance, the impact of molecular disorder on VRS is not fully understood
yet. This study delves into the complexities of VRS amidst various
distributions and degrees of disorder. Our analysis provides precise analytical
expressions for linear absorption, transmission, and reflection spectra, along
with a "sum" rule, offering a straightforward protocol for extracting accurate
collective light-matter coupling values from experimental data. Importantly,
our study cautions against directly translating large VRS to the onset of
ultrastrong coupling regime. Furthermore, for rectangular disorder, we witness
the emergence of narrow side bands alongside a broad central peak, indicating
an extended coherence lifetime even in the presence of substantial disorder.
These findings not only enhance our understanding of VRS in disordered
molecular systems but also open avenues for achieving prolonged coherence
lifetimes between the cavity and molecules via the interplay of collective
coupling and disorder.
