How does the modulation index of a phase-modulated emission vary with RF carrier frequency?

In both phase modulation (PM) and frequency modulation (FM), the modulation index is determined entirely by the characteristics of the modulating baseband signal (like your voice audio) and the design parameters of the modulator itself. The frequency of the actual RF carrier being modulated plays no role in calculating the modulation index. Whether you are transmitting on 28 MHz, 144 MHz, or 440 MHz, the modulation index remains exactly the same as long as the baseband audio and modulator settings do not change. Distractors suggest that the index scales directly or inversely with the carrier frequency, but this is a false premise. The carrier frequency only dictates where the signal sits on the radio dial, not how the phase changes relative to the audio.