# FLATNESS PROBLEM

### The Geometry of the Universe

The shape of our universe has been a matter of debate for a long-time. The main possibilities were the universe being spherical, flat or saddle shape.

More information ...^{[1]}

### Cosmological Constant

In 1917, Einstein introduced the cosmological constant in order to explain how our universe is not falling into itself because of gravity. The repulsive force of cosmological constant supposedly counteracts the gravity forces of the bodies inside the universe. Therefore, it prevents the collapse and stabilizes the universe. According to its value, the constant would allow for an expanding, contracting or static universe. Since at the beginning of twentieth century universe was considered stationary, he chose a particular value for it, which would permit a static universe. The nature of this constant was not known or explained completely at the time.

When in 1929 Hubble's observation showed that universe is expanding and is not static, Einstein himself regarded the cosmological constant unnecessary. It was considered a non- contributory factor and everybody accepted a zero value for it.

### Big Bang Theory and Expansion

The introduction of Big Bang Theory introduced a force, which is supposed to be responsible for expansion of universe despite the presence of the attracting gravity. This would be the residual force that is left from the Big Bang explosion. It was anticipated though, that gravity would slow down and ultimate stop the expansion sometime in the future. That would be when the density of matter in the universe exceeds the critical density.

Critical density is that density of overall matter and energy in the universe that if we exceed it, the gravity has the strength to contract the universe. At critical density, the shape of universe will be flat. Above critical density, the shape of it will be convex and spherical. If the density falls below critical density, the shape of the universe will be concave and it will expand forever. All of this happens if we take the cosmological constant as zero. Which means if there is no other factor at work to expand the universe?

In January 1998, Alex Pilippenko in Astrophysist Conference in Southern California announced that cosmological constant could no longer be taken as zero. Different cosmologists reached to this point after long-term observation of supernovae IA in longer red shifts (far distances more than 3 billion light years away).

The Wilkinson Microwave Anisotropy Probe (WMAP) the probe launched by NASA in 2002 has determined, within the limits of instrument error, that the universe is almost flat. This is an explanation for the cosmologic constant effect released by NASA.

“The results of the WMAP mission and observations of distant supernova have suggested that the expansion of the universe is actually accelerating which implies the existence of a form of matter with a strong negative pressure, such as the cosmological constant. This strange form of matter is also sometimes referred to as the "dark energy". If dark energy in fact plays a significant role in the evolution of the universe, then in all likelihood the universe will continue to expand forever.”^{[2]}

### Density of the Universe

Since the cosmological constant is slightly positive, we conclude that space is nearly concave. That means that Omega M (world density/critical density) has to be less than 1. Ω M <1

To have a concave universe the sum of Ω M plus the effect of cosmological constant in the expanding universe (Ω Lambda) has to be smaller than one.

Ω M + Ω Lambda <1

Both the average density of the universe and the critical density change with time. When the universe was very young, and very dense, these numbers changed very rapidly. If the average density of the universe were even slightly greater or smaller than the critical density in the instant following the Big Bang, Omega would have zoomed to infinity (a quick Big Chill) or crashed to zero (the Big Crunch). The fact that we are still around, approximately 15 billion years later, is evidence that the critical density must have been extremely close--equal within 1 part in 10^{15}--to one after the Big Bang. ^{[3]}

Here we need to assume a factor at work, which provides the positive cosmological constant.

### Dark Energy

By definition, dark energy is the source for a hypothetical force which exerts negative pressure and is acting against the gravity at large scales. This energy is not only acts against gravity and prevents Big Crunch. Supposedly, it is also responsible for accelerated expansion of the universe. In addition, in a discrete space-time model, this energy can also be responsible for creation of space-time blocks.

Dark energy compensates for more than %70 of the mass/energy density. In a closed universe one expects to find a negative energy substance which dominates the total mass energy density. We have not found any evidence for such a fundamental substance within the universe yet.

**Dark Energy in this Model**

Alternatively, we can postulate that dark energy originates from outside of the boundaries. Previously, I have claimed that the source of dark energy is inherent in this model. In Singularity chapter, I have postulated that Zero Point Energy is out of our space-time. An out of space-time ZPF can open our eye to new possibilities and scenarios.

If the big bang theory postulates that space-time originated from the singularity, it is not far fetched if we speculate that the additional space-time blocks responsible for expansion of the universe have the same origin. To open our scope to new realms we need to challenge the boundaries.

The presence of the dark energy gives us the good news that big crunch will not happen, because the universe is going to expand forever. Then there comes this feeling of emptiness and the chilling sensation that our descendants will stay lonely in an infinitely vast and cold universe. One may say that, our own galaxy or branch of galaxies, which remain together, has many new places to explore. Why do we have to be so ambitious and greedy to dream about intergalactic traveling? Is there an end to human race greed? Is there an end to evolution's ambition? Are we a dead end branch of evolution? Is there an alternative for cold and disperse universe scenario in the future?

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