A survey reports and for a Universe with

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Astrophysics & Cosmology · Einstein's field equations

The Geometry of Gravity, Ch FRW cosmology as an exact solution

Problem

A survey reports

\Omega_{\rm m} = 0.32

and

\Omega_\Lambda = 0.70

for a Universe with

H_0 = 67.7\ \text{km s}^{-1}\text{Mpc}^{-1}

, where

\Omega_K \equiv -Kc^2/H_0^2

. ((a)) Use the sum rule

\Omega_{\rm m} + \Omega_\Lambda + \Omega_K = 1

, which holds for any value of

K

, to find

\Omega_K

. ((b)) Hence compute the present spatial curvature

K

, in m

^{-2}

, stating its sign. Use

c = 2.998\times10^8\ \text{m s}^{-1}

and

1\ \text{Mpc} = 3.086\times10^{22}\ \text{m}