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Physics Lesson 22.9.5 - Possible Evolution of the Universe
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Welcome to our Physics lesson on Possible Evolution of the Universe, this is the fifth lesson of our suite of physics lessons covering the topic of Expansion of the Universe, you can find links to the other lessons within this tutorial and access additional physics learning resources below this lesson.
Possible Evolution of the Universe
The resulting motion during the expansion of the Universe is characterized by high values of kinetic energy of the galaxies involved. Gravitational attraction opposes this process to a certain extent to prevent any uncontrollable expansion. Hence, a certain equilibrium between these two opposing processes has been established over time. The future of this equilibrium will be determine the evolution of Universe. Physicists try to reach scientific conclusions on the evolution of the Universe by studying the R(t) function we mentioned earlier. The only difference is that unlike the balloon model, this time the R(t) function is 3 dimensional. It interferes in the equations of General Theory of Relativity used to solve the issue of the Universe evolution.
Depending on the amount of matter existing in the Universe, these equations provide different solutions for the R(t) function, which we can summarize in two groups that provide possible evolutions of the Universe in the future.
- If the mean density of matter in the universe is lower than a certain critical density pC, then we have an Open Universe. In such a case, the R(t) function increases to infinity with time, i.e. the Universe will continue to expand to infinity. This occurs even if the density of Universe is equal to the value of critical density pC.
- If the mean density of matter in the universe is lower than the value of critical density pC, then we have a Closed Universe. If this is the case, then the actual expansion process will reach up to a certain point, a maximum radius Rmax and then the Universe will stop expanding and start shrinking (contracting). This process will continue until the whole universe will be comprised into a small region of space, that is in a single point (R = 0).
In the General Theory of Relativity, the space-time relationship is not linear. We call this relationship the space-time curvature and it provides useful information on what is happening in a given instant at the point in space involved. In simple words, a negative space-time curvature means that the interior angles of a triangle have their sum less than 180°, a positive space-time curvature means that the interior angles of a triangle have their sum more than 180° while a zero space-time curvature (no bending therefore) means the sum of interior angles in a triangle is 180°. In the first two cases, the sides of triangle are also bent.
The equation used to calculate the critical density of the Universe is
where H0 is the Hubble Constant and G is the gravitational constant (G = 6.674 × 10-11 m3/kg·s2).
Example 3
What is the value of critical density of the Universe expressed in protons per cubic metre if we suppose all matter available consists only in protons? Take mp = 1.6726 × 10-27 kg.
Solution 3
We have to calculate the critical density in kg/m3 using the formula above. But first, we have to convert the Hubble Constant into SI units (we take the average value without the plus minus part). We have
= 73.8 km/106 pc ∙ s
= 73.8 km/106 pc ∙ 3.09 × 1013 km/pc ∙ s
= 2.389 × 10-18 s-1
Hence,
= (3 ∙ 2.389 × 10-18 s-1 )2/8 ∙ 3.14 ∙ (6.674 × 10-11 m3/kg ∙ s2 )
= 1.02 × 10-26 kg/m3
The number of protons contained in one cubic metre of space in these conditions (the concentration in protons per m3 therefore), is
= 1.02 × 10-26 kg/m3/1.6726 × 10-27 kg
≈ 6 protons/m3
This value is extremely small; this indicates that despite the enormous amount of matter existing in the Universe, the space available is even greater and matter is not sufficient to fill all space.
In practice, scientists prefer to use the dimensionless parameter
instead of critical density ρC, where ρ is the actual average density of the Universe. Thus, if Ω < 1, we are in the conditions of an open Universe, if Ω = 1, the Universe is stable and if Ω > 1, the Universe is closed.
The increase in distance between galaxies is determined by the expansion of space in an open universe. As for time, we call cosmic time t the universal time elapsing equally for all galaxies. It characterizes the universe evolution in a cosmic scale.
You have reached the end of Physics lesson 22.9.5 Possible Evolution of the Universe. There are 6 lessons in this physics tutorial covering Expansion of the Universe, you can access all the lessons from this tutorial below.
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