Shape Of The Universe

         The shape of the universe has been a very theoretical topic in the field of physics. Well, after all, no human species has ever had the opportunity to observe the entity of space. Because of this, many scientists have developed multiple theories on what they think the universe currently looks like. However, through images and reliable facts, we are able to estimate the shape of the universe.

The universe is infinite and it is rapidly expanding.

         One thing we know about the universe is that it is continuously expanding. Thus, the fate of the universe is determined by a struggle between the momentum of expansion and the pull of gravity. The rate of expansion is expressed by the Hubble Constant, H_o, while the strength of gravity depends on the density and pressure of the matter in the universe. If the pressure of the matter is low, as is the case with most forms of matter we know of, then the fate of the universe is governed by the density. If the density of the universe is less than the "critical density" which is proportional to the square of the Hubble constant, then the universe will expand forever. 

This equation represents the critical density of the universe where, H represents the Hubble Constant, and, G represents the universal constant for gravity. 

 If the density of the universe is greater than the "critical density", then gravity will eventually win and the universe will collapse back on itself, the so called "Big Crunch". However, the results of the Wilkinson Microwave Anisotropy Probe (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 "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.

So, is the universe infinite...?

         The density of the universe determines its geometry. If the density of the universe exceeds the critical density, then the geometry of space is closed and positively curved like the surface of a sphere. This implies that initially parallel photon paths converge slowly, eventually cross, and return back to their starting point (if the universe lasts long enough). In this case, the universe is not infinite, but it has no end (just as the area on the surface of a sphere is not infinite but there is no point on the sphere that could be called the “end”). The expansion will eventually stop and turn into a contraction. Thus, at some point in the future, the galaxies will stop receding from each other and begin approaching each other ass the universe collapses on itself. This is called a closed universe.

         If the density of the universe is less than the critical density, then the geometry of space is open (infinite) and negatively curved like the surface of a saddle. If this is the case, then the space has negative curvature; there is insufficient mass to cause the expansion of the universe to stop. In such a case, the universe has no bounds, and will expand forever. This is called an open universe.

         If the density of the universe exactly equals the critical density, then the geometry of the universe is flat like a sheet of paper, and infinite in extent. In this case space has no curvature (it is flat), there is exactly enough mass to cause the expansion to stop, but only after an infinite amount of time. Thus, the universe has no bounds and will also expand forever, but with the rate of expansion gradually approaching zero after an infinite amount of time. This is termed a flat universe or a Euclidian universe (because the usual geometry of non-curved surfaces that we learn in high school is called Euclidian geometry).

          The simplest version of the inflationary theory, an extension of the Big Bang theory, predicts that the density of the universe is very close to the critical density, and that the geometry of the universe is flat, like a sheet of paper. It can be depicted by the image below:

 Closed

 Open

 Flat

         

           The Wilkinson Microwave Anisotropy Probe (WMAP) spacecraft can measure the basic parameters of the Big Bang theory including the geometry of the universe. If the universe were flat, the brightest microwave background fluctuations (or "spots") would be about one degree across. If the universe were open, the spots would be less than one degree across. If the universe were closed, the brightest spots 

would be greater than one degree across. This is an example of microwave background fluctuations:

          Recent measurements (c. 2001) by a number of ground-based and balloon-based experiments, including MAT/TOCO, Boomerang, Maxima, and DASI, have shown that the brightest spots are about 1 degree across. Thus the universe was known to be flat to within about 15% accuracy prior to the WMAP results. WMAP has confirmed this result with very high accuracy and precision. We now know (as of 2013) that the universe is flat with only a 0.4% margin of error. This suggests that the Universe is infinite in extent; however, since the Universe has a finite age, we can only observe a finite volume of the Universe. All we can truly conclude is that the Universe is much larger than the volume we can directly observe.

By: Denny Na