Sound-Wave Lifetime Suppression for Long and Short Transitions: When the Source Switches Off Early

At strength unity and R* H = 0.1 the factor falls to 0.22, discarding most of the unsuppressed estimate for the strongest case tabulated. At strength 0.01 the factor is 1.00, no correction at all, because the gentle fluid motion takes many Hubble times to turn nonlinear; the weakness of such transitions enters through the small kinetic-energy fraction, not through the lifetime. At strength 0.1 with the same separation the factor is 1.00 with a lifetime of 1.12 Hubble times. The suppression instead bites the strong corner, where fast fluid motion crosses the separation quickly and the source switches off early; short separations sharpen the effect at fixed strength, because the shells meet sooner. This study is simulated and computed from stated assumptions; it is not a measurement.