The present-day spatial curvature of an FRW model is

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

The present-day spatial curvature of an FRW model is K=−2.92×10−53 m−2K = -2.92\times10^{-53}\ \text{m}^{-2}, with the scale factor normalised to a(t0)=1a(t_0) = 1. ((a)) A negative KK picks out one of the three maximally symmetric spatial geometries: closed (spherical), flat, or open (hyperbolic). State which one, giving your answer as the code −1-1 for open, 00 for flat, +1+1 for closed. ((b)) Compute the curvature radius a(t0)/∣K∣a(t_0)/\sqrt{|K|} today, in gigaparsecs, using 1 Gpc=3.086×1025 m1\ \text{Gpc} = 3.086\times10^{25}\ \text{m}.

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