What evidence is there for a closed universe?

Answer 1

Hubble found the number of galaxies seen to increase more slowly than the cube of the distance. This is evidence of positive curvature and the finiteness of space.

The density of the university is also above the critical density that is evidence of a closed Universe.

Finally the redshift, when properly understood, is evidence of a bounded Universe. Hubble himself said that the redshift is a "hitherto unrecognized principle of Nature".

Here is an excerpt form a paper by Alan Sandavage on Hubble's view of Redshift.

See related link.

Hubble concluded that his observed log N(m) distribution showed a large departure from Euclidean geometry, provided that the effect of redshifts on the apparent magnitudes was calculated as if the redshifts were due to a real expansion. A different correction is required if no motion exists, the redshifts then being due to an unknown cause. Hubble believed that his count data gave a more reasonable result concerning spatial curvature if the redshift correction was made assuming no recession. To the very end of his writings he maintained this position, favouring (or at the very least keeping open) the model where no true expansionexists, and therefore that the redshift "represents a hitherto unrecognized principle of nature". This viewpoint is emphasized (a) in The Realm of the Nebulae, (b) in his reply (Hubble 1937a) to the criticisms of the 1936 papers by Eddington and by McVittie, and (c) in his 1937 Rhodes Lectures published as The Observational Approach to Cosmology (Hubble 1937b). It also persists in his last published scientific paper which is an account of his Darwin Lecture (Hubble 1953).

My own research indicates that the Redshift is a manifestation of the centrifugal force balancing the central gravitational centripetal force. The gravitational redshift is the ratio of v/c = cos(RV) where the angel (RV) is the angle between the velocity of the body and the radial direction of gravity. The redshift is also a manifestation of the so-called "Dark Energy". The Dark Energy is the vector energy mcV= cp or momentum energy. Newton and Einstein based gravity energy on a scalar energy not a Quaternion energy,

E = -mGM/r + mcV = [-mu/r, mcV]

The Forces are

F= [d/dr, DEL][-mu/r ,mcV] =

F= [mv2/r - mcDEL.V, dmcV/dr + DEL -mu/r + mcDELxV]

F = mcv/r[v/c - cos(RV), -1V + v/c1N + sin(RV) 1C]

At Continuity Condition d/dr -mu/r - mcDEL.V

mu/r2 = mcv/r cos(RV)

mv2/r = mcv/r cos(RV) gives v/c = cos(RV) the redshift.

The redshift for the earth is approximately 30Km/s/300Mm/s= .0001. The angle is is 89 59 39.5.

The Lorentz Transformation 1/sqrt(1- (v/c)2) = 1/sin(RV) includes the redshift.

The Fine Structure Constant is the redshift at the Atomic level Alpha = cos(RV)

Answer 2

One piece of evidence for a closed universe is if the total mass density is high enough to cause the universe to eventually stop expanding and start contracting. Another indicator could be the observation of positive spatial curvature, suggesting a finite volume for the universe. Additionally, measurements of the cosmic microwave background radiation could provide further insights into the overall geometry of the universe.