Why the Universe is curved

The elder concept we live with is that the Universe or World is Euclidean, flat. Compared to the present, Euclid saw and assumed largely a flat world. His depiction of order reflected that in his works, and was accepted for a very long time.

But is that the way the world is found?

At least in the early 20th century it is brought out that Euclid's geometry of so long ago does not match with the geometry found of the universe. Euclid and his many many followers of his techniques followed a questionable approach. It is hard to justify the geometry always, everywhere as flat. Explorers of the 16th century in ships proved this globe is curved and basically round, not flat. Yet, afterwards scientists clung to flat planar concepts. (Likewise for static and earth-centered.)

Where could antigravity and repulsion have a role to play with flat planar concepts? They are in science also. The Universe expanded with antigravity to become the size it is today. That is the reason we have the life we have.

It may have taken until the early 20th century for at least one scientist to say there are other geometric gauges of lines to follow, and Euclidean space cannot explain all the nature. Another look by other scientists show another geometry, the metric, depicts accurately the geometry of the Universe.

 It was brought into science by 19th century by Riemann and it is named Riemannian geometry, which allows a wider scope to assess the Universe. It measures the points differently for the same configuration. It leads to depiction of the growth, which we live with, is non-Euclidean but with curvature. The universe may have a gentle curvature. This further encourages nonlinear computations. There also is a brief consideration of William Kingdon Clifford's and Riemann's influence in chapter 3 of "Einstein's Masterwork" by John and Mary Gribbin. Both of whom were earlier influenced by Gauss. 'it was Clifford, not Riemann, who anticipated some of the conceptual ideas of General Relativity', according to Ruth Farwell in 1990. It is said that Clifford, who believed in non-Euclidean geometry and likewise for space, translated some of Riemann's works into English. In 1992, Farwell and Knee published, "The Geometric Challenge of Riemann and Clifford".

This is confirmed by the Ricci scalar, which resorts to curvature more often. The establishment of curvature allows more room for liberal space which in turns illustrates a more flexible computation and understanding of the universe, plus room to explain expansion.

It is Alexander A. Friedmann II by the mid 1920's who is credited for producing the 'genuine, and evolving space' we know today, not Albert Einstein. The mathematician illustrated that Riemannian geometry (and Ricci scalar) is what depicts more accurately the Universe. Friedmann was critical of relying only on Euclidean geometry and was encouraging curvature and cosmos expansion. Friedmann is also credited for positing an "Open Universe" which continues expanding by his 1924 treatise, "Negative Constant Curvature". 

In more recent times it is considered-"Part of the problem is that it turns out that energy as we normally think of it elsewhere in physics is not a particularly well-defined concept on large scales in a curved universe. Different ways of defining coordinate systems to describe the different labels that different observers may assign to points in space and time (called different "frames of reference") can lead, on large scales, to different determinations of the total energy of the system. In order to accommodate this effect, we have to generalize the concept of energy, and, moreover, if we are to define the total energy contained in any universe, we must consider how to add up the energy in universes that may be infinite in spatial extent." , writes L.M. Krauss.

There also is the topological chance that basically we cannot see the early edge of the universe which repulsive energy expanded out at the beginning, and due to time lapse since then it is beyond detection of our instruments. The parts that are beyond detection might have topology (which might be curved) that is different compared to the observable universe.

"It is not, however, a flat universe in which is in principle infinite in spatial extent, and therefore the calculation of total energy become problematic." "Imagine these field lines going out to infinity, and as they spread out, getting farther apart. This implies that the strength of the electric field gets weaker and weaker.", writes L.M. Krauss in his 2000 book, "A Universe From Nothing" Finding the total count of energy in a universe is still crucial in determining its morphology.

There is room for expansion! Thus we live! Due to antigravity or repulsion. Can you breathe? The reason you can raise your chest is due to the fact that the crushing gravity is countered by a repulsing energy to allow your chest to fight against the crushing force! Vacuoles and blood vessels are not flat. There is enough antigravity on Earth so one may jump into the air, not so much on Jupiter with its bigger gravity or other giant planets. So, is it, or 'Dark Energy', then, virtually present everywhere?

Note: the material herein is not a reflection of entropy of current societies