Question

Imagine an enormous sphere in space with a radius R (light years). Suppose the surface area could be measured with negligible error and was A (square light years). If the universe is spatially homogeneous and isotropic, find the value of k (the curvature constant).

Answer 1

The curvature constant for a flat space is equal to zero.

The curvature constant for a helical space is less than zero.

The curvature constant for a spherical space is positive and greater than zero.

The curvature constant is equal to the reciprocal of the radius of the curvature.

The distance from the center of a circle or sphere to its surface is its radius. For other curved lines or surfaces, the radius of curvature at a given point is the radius of a circle that mathematically best fits the curve at that point.