Geometry of the Universe

Bibhuti Bikramaditya, Daejeon, South Korea

Abstract: Microscopically, We are in a revolutionary world of brains where new advances in the convergence of technologies and their digitization made people to be a part of one global family. But at the same time, macroscopically the universe in which we exist are uncertain, undefined, unshaped and may be propounded as some thing called “mysterious” because of the unknown facts, inadequate technologies, insufficient theories & their description. This article tries to put those facts and figures and advancement made in the recent past in the direction of the shaping of the universe.


Do we know where we are? What is our existence in the so-call ed Universe? What are the constituents of the Universe? Is our Universe finite in size? If so, what is “outside” the Universe? The answer to these questions involves a discussion of the intrinsic geometry of the Universe. Different scientists have made many speculations time to time. Moreover, there are three possible shapes and types of the universe namely 1. Flat Universe (Euclidean or zero curvature), 2. Spherical or closed Universe (positive curvature) and 3. Hyperbolic or open Universe (negative curvature).

It is to be noted that this curvature is similar to space-time curvature due to stellar masses except that the entire mass of the Universe determines the curvature. So a high mass/high energy Universe has positive curvature, a low mass/low energy Universe has negative curvature. Fig 1 shows the shapes.

All three geometries are classes of what is called “Riemannian geometry”, based on three possible states for parallel lines Never meeting (flat or Euclidean) Must cross (spherical) Always divergent (hyperbolic)

It can be explained in terms of triangles where for a flat Universe the sum of angles of a triangle

sides are connected. Anything crossing one edge reenters from the opposite edge (like a video game see 1 above).

Although this surface cannot exist within our three-dimensional space, a distorted version can be built by taping together top and bottom (see 2 above) and scrunching the resulting cylinder into a ring (see 3 below). For observers in the pictured red galaxy, space seems infinite because their line of sight never ends (below). Light from the yellow galaxy can reach them along several different paths, so they see more than one image of it. A Euclidean 3-torus is built from a cube rather than a square.


Mysterious fabric of the Universe

The possible shapes of the universe that has been given by astrophysics are described but they are unable to give clear picture for the same because of the insufficient technology and theories. For past 70 years when Einstein gave his famous theory of dark energy trying to give shape of the universe, later he denied his own idea/theory saying it as “ great mistake”, physicist were and are working on the real geometry of the universe. Physicists were in view that universe comprises of ordinary matter, which we are the part. The dark matter about which we have little knowledge, researches are going on. A real journey started in the year, 2000 by the Australian led team of international scientists who did a remarkable break through in the word of science. They claimed to have confirmed Einstein’s dark energy theory, that came into limelight according to which the majority of the universe is made up of dark energy—an unknow n quantity that fuels the constant expansion of the universe.

energy. Although there were several speculation among scientists and philosophers over the constituents of the universe and the evolution of the universe since ancient times and it was a cynosure of research also but this clarification about the shaping of the universe certainly created a flurry of hot debates among the physicists on the question of its validity. First we would like to discuss the history of the gradual clarification (since ancient era to modern times) on the ordinary matter and its constituents.

Ordinary Matter: The great Indian philosopher and the follower of the’ Vaisheshik Darsahan, Maharshi Kanad ‘(much before Sankaracharya Period) argued that “Kshithij, Jal, Agni, Vayu, Aakash, Kal, Disha and Mon and Atma” are the constituent of matter in which first five are physical. These five physical components can be neither created nor destroyed. Empedocles (490-430 BC) demonstrated that there are four indivisible and unchangeable elements Fire, Air, Water, Earth eternally brought into union and parted form each other by two divine forces Love and Discord. Nothing new comes into being, the only changes that can be made, are Juxtaposition of elements to elements.

A sea of changes unearthed in the idea of ordinary matter took place in the 19 th and 20th century. Now the primary constituent of matter i.e. atom, are already sub divided into fragments known as elementary particles. More than 37 fundamental particles have been found to exist within the atom (yet numbers are increasing as researches are going on).It is still known which one is the basic unit of the atom. It is to be noted that the physics of this elementary particle is as complex as that of the of the universe Dark Matter:

Dark matters are the matter in which strong gravitational forces and its effects are present. Several stars, galaxies and black holes come under the purview of this. Let us discuss about its unambiguous facts. Black holes are said to be the graves of massive stars which on dying first explode, then collapsed to a point and disappear completely from our universe but before it disappears completely it leaves behind its imprints on the cosmic fabric of space and time in the form of what is called black hole—region of space from which neither matter nor light can escape. According to Stephen Hawkins super large holes are billion times more massive tha scientists could not give proper explanation. It is in itself area of research. What is dark energy? As yet, no scientist can give the answer to this fundamental question. We do not know what the nature of dark energy is, and unveiling this mystery will most probably reveal new physics and even might shake modern particle physics to its very foundations. Nevertheless, we have considerable astronomical knowledge about the properties of dark energy:
• Dark energy acts as a repulsive force, or anti-gravitation. It is responsible for the acceleration of the Universe today.
• Dark energy is probably related to a vacuum energy density.
• Dark energy is distributed homogeneously in the universe – it does not cluster like matter.
Source of Dark Energy:
There are two main ideas for the source of dark energy. It might percolate from empty space, as Einstein theorized, and is unchanging and of a fixed strength. The other ho lds that dark energy is associated with a changing energy field
called "quintessence," something akin to a magnetic field. In that scenario, the field causes the current acceleration of the universe.
Another research team re cently theorized that if the repulsion from dark energy gets stronger than Einstein's prediction, the universe could expand so incredibly that it would end in a Big Rip . All matter — galaxies, then stars, then planets, and everything right down to the atomic level — would be torn apart.
There are other methods for probing dark energy, but none are as developed as the supernova observations. So in the near term, progress toward understanding dark energy will rely heavily on more observations of exploded stars that are even fart her away and deeper in time.

the space shuttle in July 1999 in the name of famous Indian astrophysicist Chandrasekhar, leaves little doubt the opposite is true. They believe the accelerating influence of "dark energy" began about 6 billion years ago . With the help of Chandra, the two astronomers studied 26 galactic clusters ranging in distance from one billion to 10 billion light years. Developed to examine high temperature matter that radiates X-ray energy, Chandra was able to observe the large gas clouds invisible to ordinary telescopes that surround the sprawling clusters.

The findings revealed an accelerating influence at work on the most distant galaxies. The Chandra observations confirm those made with two other spacecraft -- by NASA's Hubble Space Telescope in 1998 and another NASA spacecraft in 2003.

Concluding remarks

On the issue of validity of dark energy theory, it seems, physicists direct ly or indirectly accepted and trying to be of unanimous view but still could not define the dark energy yet which is said to be aroused from anti gravity, a missing force/energy from dark matter. According to Mr. T. E. Bardon who wrote in his article “Dark Matter or Dark Energy” and concluded that “Dark energy is a bench-testable, still-unaccounted entity in astrophysics and is definitely generating more gravitation in and around the observed and evidenced energetic masses than is accounted for in present theory. With the present dark matter theories stumbling, as pointed out by Musser, the fact that this dark energy is certifiably there, as is


must be equal to 180 degrees, in a closed Universe the sum must be greater than 180, while in an open Universe the sum must be less than 180.



The usual assumption is that the universe is, like a plane, "simply connected," which means there is only one direct path for light to travel from a source to an observer. A simply connected Euclidean or hyperbolic universe would indeed be infinite. But the universe might instead be "multiply connected," like a torus, in this case there are many different such paths. An observer would see multiple images of each galaxy and could easily misinterpret them as di stinct galaxies in this endless space, much as a visitor to a mirrored room has the illusion of seeing a huge crowd. df

Figure 2: One possible finite geometry is don space or more properly known as the Euclidean 2- torus. This is basically a flat square whose opposite sd

Figure 4:

Now Collese led team did laudable effort to reach on the conclusion that ordinary matter, dark matter and dark energy are the constituents of the universe which are in the ratio of 1:5:14 of which dark energy (70% of the universe) is the major part. Carlos Frenk, at Durham University, UK, was involved in the 2dF work and agrees: "This new work provides a powerful confirmation that this quality exists in the Universe. Dark energy is unassessable now and that was not the case a year ago."

A series of breakthroughs in the quest to identify the mysterious fabric of the Universe are now confirmed by many scientist It was topped a list of the 10 key scientific advances of 2003 by New Scientist).

In February 2003, the Wilkinson Microwave Anisotropy Probe (WMAP) satellite took the most detailed picture yet of the cosmic microwave background - an image of the infant cosmos when it was less than 400,000 years old.

In July 2003, astronomers from the Sloan Digital Sky Survey (SDSS), which aims to map out a million galaxies, published a research paper in which they superimposed their own galaxy- clustering data on WMAP's microwave data. They claim the results
prove that dark energy must exist. But on 12 December 2003, an international group of astronomers claimed analysis of data returned from the European Space Agency's (ESA) XMM-Newton satellite observatory casts doubt on the existence of dark Sun. The universe could be populated by trillions of “mini holes”, each having the mass of the small mountains and with the tiny size of atomic nucleus. We can now imagine the complexities of the black holes. Yet we are not in a position to count the number of black holes exist in the world (some of them are given in table). Hubble Telescope only gives the direct evidence of the black holes.

Stellar Black Holes in the Milky Way


Dark energy: Big bang theory says that the creation or evolution of the univers e was the random event occurred 12 billion years ago, just a second after big –bang (popularly known as Planck time), nascent universe was in the shape of the atom (whose radius was of the order of 10 -12 cm) and the process of expansion began. It took 30, 0000 years to settle the universe when the shape and volume of the universe formed into the pattern. At present, it is said that there are 1, 70,000 galaxies in our universe, each having millions of starts. In “Mandakini” to which we are the part, have uncountable no .of stars. Wi th the advent of time, new stars and its existents come into being. Number of stars and galaxies are set to increase because universe is still in the phase of expansion. A time will come when the expansion of the universe stops and continuous shrinking of the universe will start. According to Stephan Hawkins, after infinite time, universe will be collapsed to a naught.

This is “controversial approach” and needs a vast area of research. But as far as expansion of the universe is concerned, it is said to be due to dark energy. But what is dark energy, still needs to be resolved. Even collese led team and othe Note: These are Hubble images of the three of the most distant supernova. By tracking these exploding starts, astronomers can trace the expansion rate of the universe and determine how it is affected by dark energy . Some MORE Researches in support of Dark Energy:

The new findings, which have been submitted to the Astrophysical Journal for publication, come from National Science Foundation-sponsored observations using a sensitive new receiver, called the Arc minute Cosmology Bolo meter Array Receiver, or ACBAR, mated to the Viper telescope. The investigators looked at subtle temperature differences in the microwave background, which equate with variations in the density of energy. From a physics point of view, energy and matter are equivalent.

Microwave radiation is absorbed by water vapor, so observations of the cosmic background are best made in areas with dry, thin air, such as Antarctica, or space. The results from ACBAR are similar to those reported in the summer by the Cosmic Background Imager, a set of radio antennas located high in Chile's Atacama Desert.

Berkeley's William Holzapfel, a Peter’s native, said the MAP satellite is surveying the entire sky, while those using the South Pole telescope studied just a small chunk of sky in much greater detail. The two results should be complementary, much as a map of the United States would complement a street map of Pittsburgh. For years, cosmologists have talked about dark matter, arguing that the universe behaved in ways suggesting that it contained more mass than could be found in visible stars.

Though the ACBAR findings indeed suggest that dark matter is a major component of the universe, "I think the story is all about dark energy," Peterson a noted astrophysicist claimed. By combining data from WMAP, SDSS and other sources, four independent groups of researchers have reported evidence for a phenomenon known as the integrated Sachs-Wolfe effect. These groups have found that the gravitational repulsion of dark energy has slowed down the collapse of over dense regions of matter in the universe. After this, the case for the ex istence of dark energy has suddenly become a lot more convincing.

Chandra Telescope observation:

The new work by Allen and Fabian using Chandra, a powerful space telescope launched by
appreciable excess gr avitation from it, should be closely examined. The long missing gravity could well be a problem resulting from the arbitrarily discarded and unaccounted "dark energy" rather than from the hypothetical missing "dark matter."

According to explanation given by astrophysicist, we can summarize that only 4-5% of the constituents of the universe are, to the some extent, known. New stars and galaxies can come and are coming into existence; rest 95% is still unknown. It would be a milestone for the physicists if the dark ener gy theory is accepted as a positive step. It is believed that the mere existence of dark energy may open a window to new and unpredictable physics. It may pave the path for deciding the geometry of the universe. Let us see what 21st century has stored in for us. For the time being, I may conclude by saying “Science is neither mora l nor immoral but it’s revelatory”.

About the Author

: The author is presently working as Senior R&D Engineer in StarVray Co., Ltd ( ) at Daejeon, South Korea in the field of Bio-imaging based chip design and development. He is a member of Science for society, Bihar under NCST C Network, Department of Science and Technology, Govt. of India. He is also the chairman and moderator of the organization called “BiharBrains” ( ). More information about the author can be obtained from




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