THE FINAL FATE OF THE UNIVERSE
 
 
 
 

The Universe in General Relativity
 

The first who considered the problem of the global structure of the Universe, was Einstein, in 1917. Two years after publishing  the theory of General Relativity, the scientist developed the first mathematical model of the Universe. In the context of this theory, time and space cannot be separated, they form a four dimensional continuum, the spacetime. According to General Relativity, spacetime is curved by the action of masses. Around every material body the space is distorted, in a greater way for larger masses. In turn, the trajectory of any body follows the spacetime curvature. The shortest path between two points is then no more the straight line, but a curve called "geodetic".
We can, for example, think about an elastic horizontal tissue, on which a heavy object is laid. The "valley" that is formed is deeper for heavier bodies. If a ball is run across the tissue, its path is a straight line away from the hole, and a curved line near it.

The Universe encloses an enormous mass inside it, it must then be globally curved. The spacetime curvature depends on the density of matter that is contained in it. According to Relativity, there exists a critical density (10^{- 29} g/cm ³ ),  beyond which the Universe would be so curved that it would completely fold upon itself. Hereby the need for a precise determination of the cosmic matter density. Indeed, it determines its final fate.

Einstein made a static, homogenous and isotropic model Universe. Its properties are then the same at each time, point and space direction. The receding motion of galaxies was in fact unknown in 1917. In order to obtain a static model, the scientist was forced to introduce an "ad hoc" term into his equations, the so-called cosmological constant.

In 1922, A. Friedmann noticed that, when the cosmological constant is dropped from the equations, the Einstein Universe is due to expand, and its curvature is a decreasing function of time, since matter gets "diluted" as time passes.
In real terms, it is not galaxies that move away, it is the space that expands, dragging all the objects that it contains.
 

A beautiful image taken by the Hubble Space Telescope. It shows very far galaxies, which are invisible to ground based telescopes. It is the deeper image of the cosmos ever obtained. (HST)

 

The fate of the Universe
 

The Big Bang theory describes the origin and evolution of the Universe until the present time, but what is its future evolution? We could think that the expansion that started from the Big Bang will go on forever. Actually, the fate of our Universe could also be different.
Inside the Universe, two opposite forces are acting. The expansion push and the gravitational force. The final fate of the Universe depends on which of the two will win.
We have learnt that there is a critical density of matter, above which the gravitational attraction can halt the expansion. Cosmologists use a parameter, called Omega, that describes the kind of Universe we are living in. Omega is the ratio of the total density of matter over the critical density.
If Omega is less than 1, the available matter is not able to counteract the expansion, and the Universe will expand forever. This is called an "open" Universe.
If Omega is larger than 1, the expansion will sooner or later be stopped, and then galaxies will slowly start approaching aging, until they will  collide and merge, in a giant impact called "Big Crunch". This is called a "close" Universe.
Finally, if Omega is exactly equal to 1, then the expansion will slowly decelerate, but the gravitational attraction will non be able to reverse the motion. This is called a "flat" Universe.

It is then clear that it is important to determine the amount of matter contained in the cosmos. How can we do? There are basically two methods. The first one consists of measuring the mean density of the matter, by summing the masses of all galaxies contained in a given volume, and then dividing for the volume itself. However, we learnt that most of the surrounding matter is dark, so it cannot be observed. For this reason, it is really important to determine its exact contribution to the total mass of the Universe.
The second way is to observe the receding speeds of galaxies at different distances, that is ages, and to compute the deceleration of the Universe during the last few billion years.

The quasar PKS 2349.  Quasars are among the youngest and most distant object that can be observed. This image shows the gravitational interaction and the merging of a quasar (central object) and a galaxy (whose remnants can be see on the left). (HST)