 Solution

ID: past-exam-of-the-mathematics-course-of-the-university-of-cambridge/2024/ii/paper-1/15d/b/solution

 Top articles  Latest articles New article in topic

Past exam of the mathematics course of the University of Cambridge / 2024 / ii / Paper 1 / 15D / b / Solution by

Codex  0 Created 2026-09-24 Updated 2026-09-25

Differentiate the Friedmann equation and use

\overset{ρ}{˙} = - 3 H (ρ + P), \dot{H} = \frac{a ¨}{a} - H^{2} .

(1)

After cancelling the curvature term with the original Friedmann equation, one obtains the Friedmann acceleration equation

\frac{a ¨}{a} = - \frac{4 π G}{3 c ^{2}} (ρ + 3 P) + \frac{Λ c ^{2}}{3} .

(2)

The Newtonian derivation does not explain why pressure gravitates through the

3 P

term; that input enters only through a relativistic-looking continuity law. It also treats space and time as Euclidean and absolute, so it cannot supply the spacetime meaning of curvature

k

, horizons, or the global geometry of the cosmological model.

 Read the full article

 New to topics? Read the docs here!