The Expansion of the Universe

The Consequences of Hubble's Law

When Hubble formulated his law for the Recessional Velocities of stars and galaxies, he observed something important. Almost all galaxies he could measure showed Redshift, meaning that almost every object in the entire Universe was moving away from the Earth. Hubble also noted that the speed of Recession increased with distance (Hubble's Law), meaning that nearby galaxies were moving slowly and the most distant galaxies moving the fastest. The only explanation that Hubble could derive from this data was that the Universe was expanding. 

The diagram below shows a simple explanation as to why observing almost all objects moving away from a position implies the whole system is expanding:-

If we model the galaxies as fixed points in a material, the increasing Recessional Velocity can be explained by that material expanding equally in all directions. 

Note - Observing all objects moving away at increasing speeds from us does not mean we are at the centre of the Universe. Every point across the entire Universe will observe all other objects moving away.

The video below shows an explanation as to how the Universe can be expanding without the matter that makes up the Universe (and us!) expanding with it:- 

Age of the Universe

Hubble's Law also provides a method for measuring the age of the Universe. If all the galaxies are moving away from each other, we can conclude that at some time in the past, they must have been closer together. If this idea is taken to its limit, at some point all Matter must have been a an infinitely condensed point, before moving outwards. This idea is better known as the Big Bang Theory. 

By combining the formula for Hubble's Law with the formula for velocity, the Age of the Universe can be calculated:- 

V  =  d / t

t  =  d / V

However, as shown previously  through Hubble's Law:-

V  =  H0 d

t  =  d / (H0 d)

t  =  1 / H0 

t  =  1 /  2.3x10-18

t  =  4.347x1017

t  = 13.77x109 years

By analysis of Hubble's Law the Universe has an estimated age of 13.77 Billion years. 

The Future Of The Universe

Hubble's Law has shown that for the last 13.8 billion years, the Universe has been expanding. Whether or not this continues to happen depends on one thing only - Gravity. 

Gravity is the only fundamental Force that acts over cosmological distances. Gravity acts to oppose the expansion of the Universe by attracting objects together. The final fate of the Universe depends on whether the overall attraction due to Gravity is stronger enough to overcome the expansion. 

There are three possible outcomes :-

1. Universe has more than 'Critical Density' - Gravitational attraction will overcome expansion, and the process will reverse, ending in the Big Crunch.

2. Universe is equal to 'Critical Density' - Expansion will continue at an ever slowing rate

3. Universe has less than 'Critical Density' - Expansion will accelerate, ending either in the Heat Death of the Universe or the Big Rip.

At present, current observations point to the Universe having a Density less than 'Critical Density' and as such outcome three above is the most likely End to the Universe. 

How to 'Weigh' The Universe

In order to calculate the most likely End of the Universe, the Density of the Universe must be calculated. A good starting point to do this is to calculate the Mass contained within the Visible Universe, and make the assumption that our part of the Universe is representational of the whole Universe. 

By observing the rotation rate of a Galaxy, it is possible to calculate the Mass within it. This is because in order to stay in a circular path around the centre of a Galaxy, a star must experience a Force caused by the Gravitational field of the Galaxy. By calculating the orbital Velocity of a star and therefore finding the Force required to keep the stars orbiting the Galaxy, the Mass of the Galaxy can be found :-

Where :-

V  =  Orbital Velocity (ms-1

G  =  Gravitational Constant (6.67x10-11 m3kg-1s-2 )

M  =  Mass of galaxy within the star's orbit (kg) 

r  =  Radius of the star's orbit (m) 

Dark Matter 

As can be seen from the above formula, as the radius of an object's orbit increases, its Velocity decreases.

However, when observing stars at the edge of galaxies, it is seen that they move with a velocity that does not follow this relationship. In fact, the stars orbit at a Velocity that should allow them to escape the galaxy completely. The diagram below shows both the predicted and actual orbital Velocity for stars orbiting the core of a galaxy:-

As can be seen above, the stars are moving too fast the stay within their orbits, at least when only the visible Matter is taken into account. The fact that the stars DO remain within their orbits can only be explained by the galaxies being more Massive than expected. 

As the previous calculation accounted for all visible Matter, this additional Mass can only be accounted for by Mass that cannot be detected through current technology. This undetectable Mass is called Dark Matter. In order to explain the observations in the above diagram, up to 90% of a galaxy's Mass must be Dark Matter. 

Dark Energy

In recent years, a second problem has been discovered that at present cannot be explained by current theory. When observing very distant supernova, astronomers measured that the resulting explosions were fainter than expected. This could only be explained by the rate of the expansion of the Universe increasing. As Gravity should be slowing the expansion of the Universe, there is no known mechanism that could be increasing the rate of expansion. 

In order to increase the rate of expansion, there must be an increase in Energy which at present cannot be detected. In order to explain the observations, most of the Universe must be Dark Energy. The diagram below shows the approximate fractions of visible Matter, Dark Matter and Dark Energy within the Universe :- 

The video below shows a summary of what we know (and more importantly don't know) about Dark Matter and Dark Energy:-

The Big Bang 

The diagram below shows the processes that the Universe has undergone since the Big Bang:-

The video below shows a summary of the history of the Universe by Brian Cox:-

Evidence of The Big Bang

As was discussed above, Redshift and the Hubble Law are two concepts that have led to the understanding that the Universe began as an infinitely dense point, before rapidly expanding. However, there is other evidence that the Universe started in this way :-

1. The Cosmic Microwave Background (CMB).

2. Olber's Paradox.

The Cosmic Microwave Background

The CMB was first detected by two American radio astronomers Arno Penzias and Robert Wilson by accident in the 1964 (though it had been predicted several decades earlier). Whilst working on the World's most sensitive radio telescope (at that time), the two scientists found that no matter which direction the telescope was pointed, there was continuous unexplained interference. This interference was uniform across the entire sky and was detected in the microwave region of the E-M spectrum, and as such is known as the Cosmic Microwave Background. 

The diagram below shows an image of the CMB as taken by the Plank Spacecraft in 2013:-

Image result for cosmic microwave background

Note - When first detected, the CMB was seen as uniform, however, modern detectors show tiny variations (less than 5x10-5 K) around the average of 2.7 K. It is these tiny distortions in the uniform nature of the the Universe that went on to form the galaxies that now make up the Universe. 

The CMB is now known to have been caused by light emitted at the end of the Photon Epoch, when Photons began to travel freely through the Universe. At the time of emission, the Photons had a much shorter Wavelength, but due to the expansion of the Universe, these Photons have experienced huge amounts of Redshift and now are observable only in the microwave region. 

Olbers' Paradox

"Why is the Night Sky Black?" is a question that humans have considered since before recorded history. In 1823, German astronomer Heinrich Wilhelm Olbers postulated the Paradox that bears his name. 

Olbers' Paradox states that -  "In an infinitely old Universe with an infinite number of stars distributed in an infinitely large volume, the night sky would be bright, not dark."

The animation below shows a visual example of Olbers' Paradox, with each stage showing a dimming of stars due to distance, but an increase in Stellar number due to increased area of observation:-

If Olbers paradox was true, then the night sky (and indeed the day sky) would be a uniform brightness as bright as the Sun itself. As it is not, Olber could only explain this by stating that the Universe must be finite in size or age. 

Modern cosmology has shown that it is the age of the Universe that is finite, and Olber's Paradox can be explained by light only being visible if it was emitted within the Observable Universe,  and that the more distant stars are dimmer than expected due to expansion of the Universe. These two factors come together to give the night sky as we know it - Dark.