What is doing the pushing that compresses the fluid?
Gravity.
The photon-baryon fluid is sitting in the gravitational
potential wells that are the seeds of structure
in the universe. As gravity tries to compress the fluid, radiation
pressure resists resulting in acoustic oscillations.
Because it acts to resist compression, we will represent the radiation
pressure abstractly as
springs. Likewise we will represent
the inertia of the fluid, or loosely speaking its mass
(really
energy density), as massive balls
falling under gravity: