The measured cosmological constant is

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

The Geometry of Gravity, Ch The Einstein field equations and the Newtonian limit

Problem

The measured cosmological constant is Λ≈1.1×10−52 m−2\Lambda \approx 1.1\times10^{-52}\ \mathrm{m^{-2}}, equivalent (through ρΛ=Λc2/8πG\rho_\Lambda = \Lambda c^2/8\pi G) to a mass density of about 5.9×10−27 kg m−35.9\times10^{-27}\ \mathrm{kg\,m^{-3}}. ((a)) Model the Sun as a uniform sphere of mass M⊙=1.99×1030 kgM_\odot = 1.99\times10^{30}\ \mathrm{kg} and radius R⊙=6.96×108 mR_\odot = 6.96\times10^8\ \mathrm{m} and find its mean mass density ρˉ⊙\bar\rho_\odot. ((b)) Estimate the ratio ρΛ/ρˉ⊙\rho_\Lambda/\bar\rho_\odot. ((c)) State in one sentence what this ratio implies about whether Λ\Lambda could ever show up in a measurement of the Sun's gravitational field.

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