Past exam of the mathematics course of the University of Cambridge 2025 iii Paper 310 2 c Solution Created 2026-09-24 Updated 2026-09-25
Neglecting baryon loading, the Sachs-Wolfe combination obeys a harmonic-oscillator equation with sound speed . Adiabatic initial conditions give a nonzero initial displacement and negligible initial velocity, henceProjection maps approximately to , and the angular power is quadratic in the transfer function, producing the observed approximate sequence of acoustic peaks. A phase would instead indicate vanishing initial displacement and nonzero initial velocity, characteristic of an isocurvature rather than adiabatic primordial mode.