Primodial Curvature Perturbation Equation

[deadringer]

This equation gives us (delta (rho))/rho (which I understand is the fractional perturbation in the energy density), at the time of "horizon entry" (which I'm unsure about). Does this mean the time that decoupling occured?

[Dick]

"Horizon entry" has nothing to do with decoupling. Almost by the definition of inflation, during inflation the scale factor is growing faster than the hubble radius - so a given perturbation wavelength will eventually become larger than the hubble radius. Conversely, after inflation the scale factor is growing more slowly than the hubble radius - so that same scale will once again be smaller than the hubble radius. That's 'horizon entry'.