The Big Bang

It's currently accepted that the universe came into existence about 14 billion years ago, in the big bang. This was proven in the 20th century and since then, scientists have been trying to find out as much about this event as possible.

1. Einstein: a static universe

Russian mathematician Alexander Friedmann showed that spacetime could be expanding or contracting in 1922[1]. This is a consequence of German-Swiss-American physicist Albert Einstein's theory of general relativity[2].

Einstein added a constant, known as the cosmological constant, in order to make his equations predict a static universe, but this was purely arbitrary.

2. Hubble: an expanding open universe

In 1929, American astronomer Edwin Hubble attempted to find out if spacetime is expanding or contracting by measuring the Doppler shift of light from different galaxies, in order to see which are moving towards us and which are moving away[3].

Hubble discovered that almost every galaxy is red shifted, which means that almost every galaxy is moving away from us.

In order to measure the distance to galaxies, Hubble used a method devised by American astronomer Henrietta Swan Leavitt. Leavitt showed that there's a correlation between the pulsation periods of certain types of stars, known as Cepheid variables, and their intrinsic luminosity[4].

The intrinsic luminosity of a star can be used to determine how bright it would be if it took the place of the Sun. Once this was known, scientists were able to determine how far away the star must be in order to be as faint as it is observed to be.

Leavitt was unable to make use of her discovery herself because women were not allowed to use high-calibre telescopes until the 1960s[5].

By using the Cepheid variable method, Hubble was assuming that the cosmological principle is correct. This means that our observations are representational of the whole universe, and on a large enough scale, the universe is the same in all directions.

Hubble was able to determine the velocity at which the galaxies were moving away - the recession velocity - using spectroscopy. He found that closer, and therefore newer, galaxies appear to be moving apart at a slower rate than older galaxies. This is what we would experience if spacetime had been moving apart at a roughly constant rate.

Rate =
1/Time
, and so given Velocity =
Distance/Time
, Rate =
Velocity/Distance
.

If the rate of expansion is constant, then we would expect velocity (v) to increase as distance (d) increases; and so more distant galaxies have higher recession velocities. The rate of the expansion of the universe is known as 'Hubble's constant', H0.

Plot of distance against recession velocity, where galaxies form an approximate straight line at a 45-degree angle.

Hubble's distance-velocity relationship for galaxies. Image credit: modified by Helen Klus, original image by NASA/Public domain.

H0 = Rate = 1/Time = v/d, and so the age of the universe (time), can be determined from H0. This is equivalent to determining how long it would take for everything to be where it is now, if it were once all in the same place, assuming the rate of expansion is constant. Using this method, Hubble estimated that the universe is about 9 billion years old.

Hubble's discovery resolved Olbers' paradox, which suggests that if the universe is infinite and eternal, then stars should fill every part of the sky by now, just as trees can fill the whole horizon in a forest. This should make sky as bright as the surface of the Sun. Hubble showed that this is not the case because the universe is not eternal. The sky is dark at night because the universe had a beginning, and light has a finite speed, so not all of it has reached us yet.

British astronomer Fred Hoyle coined the term 'big bang' in 1949, although Hoyle favoured the steady state theory at the time[6]. The steady state theory proposed that there was no big bang, and instead matter is continually created as the universe expands. This was disproven in 1964.

Nothing is known of the first moment of the big bang. If everything was once in the same place, then general relativity predicts that this would cause a gravitational singularity, like a black hole. However, a theory that combines quantum mechanics and general relativity - such as string theory or loop quantum gravity - is needed to understand what this means, and these theories will probably not be proven for some time.

It's assumed that the early universe must have been very dense and very hot - it would have to be in order to have so much matter contained in such a small space. All of this heat would make it very energetic.

As the universe increased in size, everything could spread out, and so individual parts of the universe get cooler, and therefore less energetic, over time. This is why the big bang is sometimes referred to as the 'hot big bang'.

3. Other possibilities: open, flat, and closed universes

If the universe is expanding, then there are at least three possibilities for how it will end.

  • If the force of gravity is stronger than the force of expansion, then the universe will eventually collapse in on itself in a 'big crunch'. This is known as a closed universe. If the universe is closed, then it will rapidly increase and then decrease in its rate of expansion.

  • If the force of gravity is roughly equal to the force of expansion, then the universe will eventually reach a maximum size and stop expanding. This is known as a flat universe. If the universe is flat, then it will slow down in its rate of expansion over time.

  • If the force of expansion is stronger than the force of gravity, then the universe will continue to expand forever. This is known as an open universe. If the universe is open, then it will expand at a constant rate, and this is what Hubble assumed.

Plot showing the distance between galaxies over time. If the universe is open, then the distance will continue to increase forever. If the universe is flat, then the increase will reduce over time, and if the universe is closed, then the distance will one day begin to decrease again.

Possible fates of the universe. Image credit: ESA/CC-A.

All of this means that if we live in an open universe, then things should be further apart in the past than if we live in a flat universe, and they should be closest if we live in a closed universe.

Einstein showed that spacetime is shaped by mass, and so open, flat, and closed universes will have different shapes.

The shape of the universe depends on the density parameter (Ω0). This is a measure of the average energy density of the universe divided by the critical energy density, which is the energy needed for the universe to be flat:

  • In an open universe, where the force of expansion is stronger than the force of gravity, Ω0 < 1, and spacetime is curved inwards, like the base of a saddle.

  • In a flat universe, where the two forces are roughly equal, Ω0 = 1, and spacetime is flat, like a sheet of paper.

  • In a closed universe, where the force of gravity is stronger than the force of expansion, Ω0 > 1, and spacetime is curved outwards, like a sphere.

A closed universe must be finite, if this is not the case, however, then the universe may be both infinite, and expanding.

Diagram showing that an open universe appears saddle shaped, a flat universe appears flat, and a closed universe appears to be spherical.

Possible shapes of the universe. Image credit: modified by Helen Klus, original image by NASA & NASA/Hubble/Public domain.

We can measure the curvature of the universe by drawing an imaginary triangle and seeing how the sides bend, since we know a triangle will look different if it is drawn on a curved surface to a flat surface. We were not able to do this with sufficient precision, however, until NASA launched the WMAP (Wilkinson Microwave Anisotropy Probe) spacecraft in 2001.

4. Problems with Hubble's open universe

The two main problems with Hubble's big bang theory were both suggested in 1969, the same year that the first people stepped foot on the Moon.

Firstly, American physicist Charles Misner showed that some regions of space are too far apart to have ever been in contact with each other[7]. This is known as the big bang horizon problem.

Secondly, American physicist Robert Dicke showed that the universe is not as curved as it should be if it were expanding at a constant rate[8]. This is known as the big bang flatness problem.

5. Inflation: a flat universe

These problems were resolved in 1981, when American physicist Alan Guth showed that the universe must have gone through a period of rapid expansion, known as inflation[9].

Guth showed that the Hubble constant can change, and that we live in a flat universe. The Hubble constant is now referred to as the Hubble parameter.

The energy that caused inflation may have been released when the universe underwent a phase shift, in a similar way to how latent heat is released when a liquid freezes.

Theories of everything, such as string theory, predict that the four fundamental forces - the electromagnetic force, the strong and weak nuclear forces, and the force of gravity - are united at high enough energies; just as electricity and magnetism unite to form the electromagnetic force, and the electromagnetic force and the weak nuclear force unite to form the electroweak force.

The universe may have been energetic enough for all of the forces to be united in the first 10-43 seconds after the big bang. After this, the force of gravity would have to separate from the other forces. Theories of everything are highly speculative because they all depend on quantum theories of gravity.

The idea that the strong nuclear force may have once been connected to the electroweak force is far less speculative, although not yet proven, and is known as a grand unified theory (GUT).

The universe should have expanded, and hence cooled enough, for the strong nuclear force to have separated from the electroweak force about 10-36 seconds after the big bang. This is a lower energy state - just as a solid is a lower energy state than a liquid - and so energy was released, and this may have been the energy that fuelled inflation.

Inflation began about 10-36 seconds after the big bang and lasted for about 10-32 seconds (this is about 100,000, billion, billion, billionths of a second). During this time, the volume of the universe is thought to have expanded by a factor of over 1078 (this is a million, billion, billion, billion, billion, billion, billion, billion, billion). The universe continued to expand after this, just at a slower rate than before.

Inflation solved the big bang flatness problem. It also solved the big bang horizon problem because, during inflation, spacetime expanded faster than the speed of light. This does not contradict Einstein's theory of special relativity, as this only shows that nothing can accelerate beyond the speed of light when it's moving through spacetime.

Finally, inflation solved an additional problem in physics regarding magnetic monopoles. In 1931, British physicist Paul Dirac showed that if electric charges are quantised, then magnetic monopoles must exist[10]. These are magnetised particles that only possess one magnetic pole. Monopoles have never been detected, but Guth showed that this could be because they were produced before inflation, which may have caused them to be vastly separated throughout the universe.

In 1981, Russian physicists Viatcheslav Mukhanov and Gennady Chibisov showed that the universe is not perfectly symmetrical because of quantum fluctuations in spacetime that were present before inflation[11]. Inflation stretched the fluctuations so that energy and matter were unevenly distributed across the universe.

If this had not happened, and matter and energy were purely symmetrical, then there would be no life in the universe because everything would balance, and so clouds of gas would not be able to fall together to make objects like stars.

6. After inflation: a brief history of the universe

The first electrons and antielectrons are thought to have been created shortly after inflation, when any residual energy formed particles.

Within a second, the universe cooled enough for protons, antiprotons, neutrons, and antineutrons to form.

Dirac first showed that antimatter must exist in 1928, when he created the first quantum field theory of electromagnetism in order to describe the motion of electrons[12]. His results revealed that every particle has a corresponding antimatter partner, with an opposite spin, and charge. Russian physicist Andrei Sakharov showed that almost equal amounts of matter and antimatter were created in the big bang in 1967[13].

Matter and antimatter annihilate each other upon contact, and the total rest mass of the particles is converted to energy in accordance with special relativity. If just one kilogram of matter collided with one kilogram of antimatter, the resulting explosion would be equivalent to that of over 40 million tonnes of TNT*.

Within 10 seconds of the big bang, almost every particle and its corresponding antiparticle annihilated each other, emitting large amounts of energy in the form of photons - particles of light, although the universe was still too dense for it to illuminate anything.

It's assumed that there must have been more matter than antimatter; otherwise, almost all matter would have been annihilated. In 2011, NASA launched a device that is searching for signs of antimatter that has survived in isolation since its creation.

Atomic nuclei were created within 20 minutes of the big bang. American physicists George Gamow and Ralph Alpher explained how this occurred, in a process known as big bang nucleosynthesis, in 1948[14].

At this point, the universe had cooled enough for protons and neutrons to fuse together. Three times more hydrogen than helium was produced, by mass, as well as trace amounts of deuterium - an isotope of hydrogen - lithium, beryllium, and possibly dark matter, which was first predicted to exist by Swiss astrophysicist Fritz Zwicky in 1933[15].

Timeline

Timeline of the universe. Image credit: NASA/WMAP Science Team/Public domain.

Gamow and Alpher had originally proposed that all elements were created in the big bang, but this was soon shown to be false. German-American physicist Hans Bethe[16] and Indian-American physicist Subrahmanyan Chandrasekhar[17] had shown how stars are fuelled by nuclear fusion in 1939. In 1954, Hoyle showed how stars can synthesise all of the elements up to iron, after which, they explode in a supernova, which creates even heavier elements[18].

Gamow and Alpher predicted that it would take another 380,000 years before the universe had cooled enough for electrons to attach to the hydrogen and helium nuclei, neutralising the atom. This process is known as recombination.

After recombination, light was able to move freely about the universe. Gamow and Alpher predicted that this light would be visible in all directions, but would be extremely red shifted by now, from the expansion of the universe. They predicted that it would be observed in the microwave spectrum, at a temperature of about 2.7 Kelvin (-270 °C).

American astronomers Arno Penzias and Robert Woodrow Wilson accidently discovered Gamow and Alpher's cosmic microwave background radiation in 1964[19][20]. This provided overwhelming evidence that the big bang theory is correct, and the steady state theory was abandoned.

Physicists George Blumenthal, Sandra Moore Faber, Joel Primack, and Martin Rees showed that small objects like stars formed before larger objects like galaxies and galaxy clusters in 1984[21].

The first stars are thought to have formed about 200 million years after the big bang[22a], and planets began to form when the first generation of stars expired - after a few million years[23]. The first galaxies formed within 400 million years of the big bang[22b].

The oldest stars in the Milky Way are over 13 billion years old[24], but it is thought that the disc of the Galaxy formed about 9 billion years ago[25]. The Solar System is relatively new, having formed about 4.6 billion years ago - 9.2 billion years after the big bang[26].

7. Dark energy: a flat universe that will expand forever

In 1998, teams led by American physicists Adam Riess[27] and Saul Perlmutter[28] showed that while the universe geometrically flat, it is accelerating in its expansion.

This was surprising because it was assumed that in flat universes, gravity would gradually slow the rate of expansion. Some sort of unknown energy must be producing this effect, and physicists refer to this as 'dark energy'. It is still not known what causes dark energy, but if it continues, then it will make the universe expand forever.

NASA launched the Cosmic Background Explorer (COBE) in 1989. COBE was designed to measure temperature fluctuations in the cosmic microwave background radiation, and results from COBE showed that on large scales, the cosmic microwave background radiation is the same in all directions, confirming the big bang theory.

Animation blending the COBE, WMAP, and Planck maps.

COBE, WMAP, and Planck maps showing temperature fluctuations in the universe. Image credit: modified by Helen Klus, original images by NASA, NASA/WMAP Science Team, and ESA and the Planck Collaboration/CC-A.

COBE's successor, WMAP, launched in 2001. Scientists could use data from WMAP to measure the curvature of the universe, by drawing an imaginary triangle in the sky and seeing how its sides curved.

They were able to do this because they know the actual size of some patches on their map, these always have an apparent size of 1°, and are caused by sound waves. The triangle can be drawn by comparing their actual size to the size that they appear, since we know that shapes look different when they are drawn on a flat surface, to how they look when they are drawn on the inside or outside of a curved surface; the more parts of the image are curved towards each other, the closer they appear.

Diagram showing how we would view the WMAP results if the universe were open, flat, or closed.

If spacetime is curved, then light travels on a curved path, and so images of the universe will look different than they would if spacetime were flat. Image credit: NASA/WMAP Science Team/Public domain.

Data from WMAP was also used to measure energy density of the universe, assuming it is the sum of energy from:

  • Matter with rest mass, like normal matter and dark matter (Ωmass).

  • Matter with no rest mass, like photons (Ωrelativistic).

  • The energy of expansion, dark energy (ΩΛ).

The contribution from each type of energy can be determined from a plot of temperature fluctuations against angular size - this is known as a power spectrum. You can see how the different components create different shapes in the power spectrum using NASA's 'Build a Universe' tool.

Plot of size and temperature for the WMAP results.

Power spectrum of temperature fluctuations in the cosmic microwave background. Image credit: modified by Helen Klus, original image by ESA and the Planck Collaboration & NASA/CC-A.

Pie chart of the composition of the universe from the Planck results.

Composition of the universe using data from the Planck satellite. Image credit: ESA and the Planck Collaboration/CC-A.

Data from WMAP showed that about 70% of the energy density of the universe is currently composed of dark energy. Dark matter makes up about 25% of the energy density of the universe, and other types of matter make up the remaining 5%. Using this information, data from WMAP was used to confirm that the universe is flat, and to show that the universe is 13.77 ± 0.059 billion years old[29].

The European Space Agency (ESA) launched a successor to WMAP, the Planck spacecraft, in 2009, which was used to refine these parameters. Data from Planck confirmed that the universe is flat, and was used to show that the universe is 13.813 ± 0.038 billion years old[30].

Data from Planck also confirmed that there is an asymmetry in the average temperatures between hemispheres, and the presence of a cold spot.

If 1kg of matter collided with 1 kg of antimatter:

e = mc2,
e = 2 × 299,792,4582,
e = 1.8×1017 J.

1 ton TNT equivalent = 4.2×109 J.

1.8×1017/4.2×109
= 42,961,529.

8. References

  1. Friedmann, A., 1922, 'On the Curvature of Space', Zeitschrift für Physik, 10, pp.377-386.

  2. Einstein, A., 1916, 'The foundation of the generalised theory of relativity', Annalen der Physik, 354, pp.769-822, reprinted in 'The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity', 1920, Courier Corporation.

  3. Hubble, E., 1929, 'A relation between distance and radial velocity among extra-galactic nebulae', Proceedings of the National Academy of Sciences, 15, pp.168-173.

  4. Leavitt, H. S., 1908, '1777 variables in the Magellanic Clouds', Annals of Harvard College Observatory, 60, pp.87-108.

  5. Nichols, M., 'Mount Wilson and Palomar', Goodsell Observatory, last accessed 15-02-16.

  6. St John's College Cambridge, 'Fred Hoyle: An Online Exhibition', last accessed 15-02-16.

  7. Misner, C. W., 1969, 'Mixmaster universe', Physical Review Letters, 22, pp.1071.

  8. Dicke, R. H., 1970, 'Gravitation and the Universe: Jayne Lectures for 1969', American Philosophical Society. See also 'American Institute of Physics Oral Histories: Robert Dicke'.

  9. Guth, A. H., 1981, 'Inflationary universe: A possible solution to the horizon and flatness problems', Physical Review D, 23, pp.347-356.

  10. Dirac, P. A., 1931, 'Quantised singularities in the electromagnetic field', Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 133, pp.60-72.

  11. Mukhanov, V. F. and Chibisov, G. V., 1981, 'Quantum fluctuations and a nonsingular universe', JETP Letters, 33, pp.532-535.

  12. Dirac, P. A., 1928, 'The Quantum Theory of the Electron', Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character, 117, pp.610-624.

  13. Sakharov, A. D., 1967, 'Violation of CP invariance, C asymmetry, and baryon asymmetry of the universe', JETP Letters, 5, pp.24-27.

  14. Alpher, R. A., Bethe, H., and Gamow, G., 1948, 'The origin of chemical elements', Physical Review, 73, pp.803-804.

  15. Zwicky, F., 1933, 'Republication of: The redshift of extragalactic nebulae', Helvetica Physica Acta, 6, pp.110–127.

  16. Bethe, H. A., 1939, 'Energy production in stars', Physical Review, 55, pp.434-456.

  17. Chandrasekhar, S., 1958 (1939), 'An Introduction to the Study of Stellar Structure', Courier Corporation.

  18. Hoyle, F., 1954, 'On Nuclear Reactions Occuring in Very Hot Stars. I. the Synthesis of Elements from Carbon to Nickel', The Astrophysical Journal Supplement Series, 1, pp.121-146.

  19. Penzias, A. A. and Wilson, R. W., 1965, 'A Measurement of Excess Antenna Temperature at 4080 Mc/s', The Astrophysical Journal, 142, pp.419-421.

  20. Dicke, R. H., Peebles, P. J. E., Roll, P. G., and Wilkinson, D. T., 1965, 'Cosmic Black-Body Radiation', The Astrophysical Journal, 142, pp.414-419.

  21. Blumenthal, G. R., Faber, S. M., Primack, J. R. and Rees, M. J., 1984, 'Formation of galaxies and large scale structure with cold dark matter', Nature, 311, pp.517-525.

  22. (a, b) NASA, 'Understanding the Evolution of Life in the Universe', last accessed 15-02-16.

  23. NASA, 'Cooking up the First Stars', last accessed 15-02-16.

  24. NASA, 'Hubble Finds Birth Certificate of Oldest Known Star', last accessed 15-02-16.

  25. Del Peloso, E. F., Da Silva, L., de Mello, G. P., and Arany-Prado, L.I., 2005, 'The age of the Galactic thin disk from Th/Eu nucleocosmochronology - III. Extended sample', Astronomy & Astrophysics, 440, pp.1153-1159.

  26. NASA, 'Our Solar System: In Depth', last accessed 15-02-16.

  27. Riess, A. G., et al, 1998, 'Observational evidence from supernovae for an accelerating universe and a cosmological constant', The Astronomical Journal, 116, pp.1009-1038.

  28. Perlmutter, S., et al., 1999, 'Measurements of Omega and Lambda from 42 high-redshift supernovae', The Astrophysical Journal, 517, pp.565-586.

  29. Hinshaw, G., et al, 2013, 'Nine-year Wilkinson Microwave Anisotropy Probe (WMAP) observations: cosmological parameter results', The Astrophysical Journal Supplement Series, 208, pp.19.

  30. Planck Collaboration, 2015, 'Planck 2015 results. XIII. Cosmological parameters', arXiv preprint arXiv:1502.01589.

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