Earth and its Solar System are NOT SPECIAL
location principle, which asserts that it is unlikely that we occupy a special place in the universe
'all places in the universe are alike' - Einstein (1937)
If the universe extends infinitely, then eventually if we look out into the night sky, we should be able to see a star in any direction, even if the star is really far away.
Since the universe was infinitely old, the light from stars at extremely far distances would have already reached us, even if they were 40 billion light years away.
Then according to Steady State Theory we should be able to see a star anywhere in the night sky, and so the sky should have the same brightness everywhere. But as you all know, if you look at the sky at night, it's dark and speckled with bright points of light called stars! How can this be explained? Something seemed to be amiss....
There's too much dust to see the distant stars.
The Universe is young. Distant light hasn't even reached us yet. ✓
The Universe has only a finite number of stars.
The distribution of stars is not uniform. So, for example, there could be an infinity of stars, but they hide behind one another so that only a finite angular area is subtended by them.
The Universe is expanding, so distant stars are red-shifted into obscurity (Doppler effect). ✓
Olber's Paradox
No matter what direction you look, you will eventually see a bright object. Farther away objects are fainter, but there are more of them. So each shell has the same overall brightness. The night sky should be bright!
Homogeneity:
Consider an immense forest densely populated by identical trees. When you walk to a different location in the forest, your view will be the same and we say that the forest is homogenous: it looks the same from any location.
Another way of saying this is that it is translationally invariant. Notice, however, from any one place, when you rotate your head, the appearance of the forest will change.
Isotropy:
Many of the Islamic Geometric designs are ISOTROPIC. Focus your eyes on the centre of the circles. In this case, when you rotate your head, the painting will not appear any different. This painting is said to be isotropic: it looks the same in any direction.
This painting is said to be rotationally invariant. When you take a step sideways, however, your view of the painting changes: the painting is not homogeneous.
Homogeneous or Isotropic:
Most systems are either homogeneous or isotropic, but not both. The Universe is both
The Universe is both Homogeneous and Isotropic
ACCELERATING (GREEN): Ωm is increasing or ρm<ρc: the universe will continue to expand, A universe filled with a (positive) cosmological constant will naturally lead to a Λ−dominated (Dark Matter) era in which the universe will eventually enter an accelerating phase as the matter content dilutes and ceases to affect the universe's large-scale dynamic behavior. Observations confirm this type of expansion.
In a universe without Dark Matter
CLOSED (YELLOW): Ωm>1 or ρm>ρc: the universe will stop expanding in finite time, after which it will reverse and (re-)collapse, in other words, there will be a maximum separation between coordinates; will eventually collapse in on itself, resulting in a “Big Crunch”
FLAT (RED): Ωm=1 or ρm=ρc: the universe will halt expansion in infinite time, the physical distances between coordinates will reach a maximum size in infinite time
OPEN (BLUE): Ωm<1 or ρm<ρc: the universe will continue to expand, the physical distance between coordinates will continue to increase.
“Some say the world will end in fire, some say in ice…” *
What will be the final destiny of the Universe? Probably it will end in ice, if we are to believe this year’s Nobel Laureates in Physics. They have studied several dozen exploding stars, called supernovae, and discovered that the Universe is expanding at an ever-accelerating rate. The discovery came as a complete surprise even to the Laureates themselves.
In 1998, cosmology was shaken at its foundations as two research teams presented their findings. Headed by Saul Perlmutter, one of the teams had set to work in 1988. Brian Schmidt headed another team, launched at the end of 1994, where Adam Riess was to play a crucial role.
The research teams raced to map the Universe by locating the most distant supernovae. More sophisticated telescopes on the ground and in space, as well as more powerful computers and new digital imaging sensors (CCD, Nobel Prize in Physics in 2009), opened the possibility in the 1990s to add more pieces to the cosmological puzzle.
https://www.nobelprize.org/prizes/physics/2011/press-release/