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In addition to the revision notes for Expansion of the Universe on this page, you can also access the following Cosmology learning resources for Expansion of the Universe
| Tutorial ID | Title | Tutorial | Video Tutorial | Revision Notes | Revision Questions | |
|---|---|---|---|---|---|---|
| 22.9 | Expansion of the Universe |
In these revision notes for Expansion of the Universe, we cover the following key points:
Cosmology is the branch of Physics that studies the Universe in such a macroscopic level that galaxies are considered as small particles. It considers the Universe as homogenous and isotropic, i.e. its properties do not depend on the directions chosen. The main modern contributors in this branch are Hubble and Einstein but the viewpoint of Newton as a pioneer and promoter of Cosmology is important.
Through the Universal Law of Gravitation, Newton tried to explain that such a giant system of celestial bodies could be in equilibrium (despite the fact that gravitational forces have an attractive nature) but only if we consider the universe as static and infinite. Otherwise, the stars located in the outer layer of the universe would be attracted by the stars in the inner layers and as a result, the universe would shrink.
Einstein too, supported the idea of a static Universe without a beginning and an end, remaining faithful to the approach other scientists before him had embraced. However, Einstein radically reformed the existing concept of infinity. He believed that the Universe contains enough matter to fill all of space.
The advancements in technology during the last century made studying the spectra of chemical elements in remote galaxies possible - a process that led to the conclusion that the Universe is not static but expanding. EM radiation incident on earth received from remote galaxies has a longer wavelength (smaller frequency) that similar EM waves produced on Earth. Hence, the phenomenon of red-shift (the shift of light frequencies incident from remote galaxies towards the red colour) is observed and confirmed through the formula of Doppler Effect of light
where β = v/c (v is the speed of light source and c the speed of light in vacuum). This formula is true for light sources moving away from a stationary observer. The original frequency of EM waves emitted by the source is denoted as f0 and the frequency detected by any stationary observer on Earth is f.
The opposite effect of red-shift is blue-shift. It is observed only in nearby galaxies and it is a phenomenon that occurs occasionally (it is not a norm).
When studying the galaxies, Edwin Hubble discovered that their receding speed is proportional to the distance from us. Mathematically, we have:
where r is the distance of a galaxy from Earth. When this expression is written as equation, we obtain
where H0 is known as the Hubble Constant. This equation is the mathematical expression of Hubble's Law. The original value of Hubble Constant measured using the methods of that time was 500 km/(s·Mpc). However, this value is very far from the truth. The most exact value measured so far is
The Universe has a radius R(t) that varies (increases) with time. Since it is expanding, it is clear that the universe once had an origin, i.e. at a certain instant (at t = 0) the radius of universe was zero [R(0) = 0]. This instant represents the birth of the Universe. Since matter was concentrated at a small region of space, there must have been a huge explosion sufficient to make the pieces produced by this process spread away from each other in all directions. This explosion is known as the Big Bang and it marks the beginning of the Universe.
Depending on the amount of matter that exists in the Universe, these equations give different solutions for the R(t) function, which we can summarize in two groups which provide possible evolutions of the Universe in the future.
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 age of universe (if the universe is considered as expanding), is
and when it is considered as stationary, it is calculated by
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