22 CHAPTER 1. GENERAL INTRODUCTION
is clearly against the observations of our Universe, and demonstrates that our Universe cannot
be originated from a Big-Bang.
- By the cosmological principle, given the energy densityρ 0 >0 of the Universe, based
on the Schwarzschild radius, the Universe will always be bounded in black hole, which is an
open ball of radius:
Rs=√
3 c^2
8 πGρ 0.
This immediately shows that there is no unbounded universe.Consequently, since a black
hole is unable to expand and shrink, we arrive immediately from the above analysis that our
Universe must be static, and not expanding.
Notice that the isotropy requirement in the cosmological principle excludes the globular
open universe scenario. Consequently, we have shown that our Universe must be a closed 3D
sphereS^3.
In summary, we have proved two theorems, Theorems7.27-7.28, on the geometry and
structure of our Universe, which have been discovered and proved in (Ma and Wang,2014a,
Theorems 6.2 & 6.3):
Theorem on Structure of our Universe.Assume the Einstein theory of gen-
eral relativity, and the principle of cosmological principle, then the following
assertions hold true:1) our Universe is not originated from a Big-Bang, and is static;
2) the topological structure of our Universe is the 3D sphere S^3 such that to
each observer, the corresponding equator with the observerat the center
of the hemisphere can be viewed as the black hole horizon;
3) the total mass Mtotalin the Universe includes both the cosmic observable
mass M and the non-observable mass, regarded as dark matter,due to the
space curvature energy; and
4) a negative pressure is present in our Universe to balance thegravitational
attracting force, and is due to the gravitational repellingforce, also called
dark energy.It is clear that this theorem changes drastically our view onthe geometry and the origin
of the Universe. Inevitably, a number of important questions need to be addressed for this
scenario of our Universe. Hereafter we examine a few most important problems.
Redshift problem
The natural and important question that one has to answer is the consistency with as-
tronomical observations, including the cosmic edge, the flatness, the horizon, the redshift,
and the cosmic microwave background (CMB) problems. These problems can now be eas-
ily understood based on the structure of the Universe and theblackhole theorem we derived.
Hereafter we focus only on the redshift and the CMB problems.
The most fundamental problem is the redshift problem. Observations clearly show that
light coming from a remote galaxy is redshifted, and the farther away the galaxy is, the larger