Abstract
In the previous chapter we discussed the energy content of the universe, the different types of matter that we see, or actually don’t see. So far we have only briefly mentioned what forces come into play and what the nature of these forces is. We also haven’t discussed how the matter constituents interact with each other and what forces govern these interactions, from the smallest to the largest distance scales. We shall do this in the following, beginning with a discussion of what forces there are, and then move on to what a force actually is and discussing finally how these forces shape the evolution of the universe.
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Notes
- 1.
This is another example of physicists’ sometimes quirky sense of humour. The three different colour charges combine to colour neutral, in a similar way as the three primary colours combine to white.
- 2.
In principle, we should also worry about the region of space and the interval of time the field is supposed to be well behaved. It may of course be specified over all of space and for all time. Here we simply assume that the fields we are interested in are sufficiently well behaved over the regions of space and time we are interested in.
- 3.
The term “scalar field” is used precisely because these fields can be described by single number. The more mathematically inclined reader might recognise the scalar field as a function depending on time and the three spatial coordinates.
- 4.
This sounds rather complicated, but the mathematics behind it is straight forward. The technical term is to “integrate” or sum over all the individual contributions of the small volume elements.
- 5.
An “event” in this context could be an observation being undertaken, or an experiment performed.
- 6.
It might appear that in a situation as depicted in Fig. 6.8 we can decide which observer is at rest, but this is only due to the special experimental setup of laboratories being in s university and on a train. If both laboratories are on trains it becomes obvious that we can’t decide which one moves and which one is at rest relative to the other.
- 7.
John Archibald Wheeler (1911–2008), American theoretical physicist, recognised for his work on general relativity.
- 8.
Unfortunately it is much easier to solve the equations, than to use analogies and descriptions. This is usually not appreciated by non-physicists: physicists use equations because they are often much easier to handle than analogies and pictures!
- 9.
A black hole is an extreme example where a large amount of mass is confined to a very small region of space. We will discuss black holes below in Sect. 6.4.3.
- 10.
We can repeat this experiment using a rubber sheet, or using a Lycra cloth which is easier to purchase these days. Placing a larger mass body in the middle, and then a smaller mass body a short distance away inside of the dent made by the larger body, we will notice that the smaller body moves towards the larger one. Although the smaller mass body only follows the geometry of the rubber sheet and the larger mass body doesn’t exert a noticeable force on the smaller one, we would interpret this as the larger body attracting the small one.
- 11.
The observation of light bending as predicted by general relativity in 1919 convinced most physicists that the theory was correct.
- 12.
An inertial frame is a reference frame or coordinate system is one that isn’t accelerating. In the presence of gravitational fields this can be achieved if the observer is freely falling.
- 13.
Eratosthenes of Cerene (ca. 280–195 bc), Greek mathematician and astronomer.
- 14.
Eratosthenes calculated the circumference of Earth by measuring the angle under which the Sun appeared at noon at Alexandria, Egypt, and at the same time in a town about eight hundred kilometres to the south, Syene. From the difference in angle, and the known distance between the two places, he was able to calculate the Earth’s circumference.
- 15.
Claudius Ptolemy (ca. 90–170), Roman astronomer who lived in Alexandria, Egypt; influential work on astronomy and geography.
- 16.
Nicolaus Copernicus (1473–1543), Polish astronomer, introduced the heliocentric model of the universe.
- 17.
Johannes Kepler (1571–1630), German astronomer and mathematician, discovered the laws of motion of celestial objects.
- 18.
The recipe for bread with sunflower seeds is in Appendix A.5.
- 19.
The variables in the governing equations in this case only depend on time, they become independent of position, which simplifies the calculation considerably.
- 20.
- 21.
Hubble’s value was originally much larger, but the value of about 70 km/s per million parsec is in agreement with, and derived from, current observations.
- 22.
For distance measurements only the contribution to the redshift due to the expansion of the universe is relevant.
- 23.
We can imagine the point masses to be small, massive spheres, of equal size and mass.
- 24.
By convention the scale factor is “one” today, hence today comoving and physical coordinates coincide.
- 25.
Radiation can behave like fluid if we have a very large number of photons with sufficiently large energy per volume, we will return to this topic in Chap. 7.
- 26.
We can think of the gas as hydrogen, but it doesn’t really matter as long as it is made up of baryons.
- 27.
To see that a sphere minimises its gravitational potential energy, just recall the example of the marble in a bowl. The marble looses potential energy rolling down, see Fig. 6.9. On the surface of a sphere all particles constituting the surface “rolled down” as far as possible, they are now all equally close to the centre of the sphere.
- 28.
Only the “non-gravitational” forces give rise to pressure, gravity itself is in most circumstances to weak to give rise to pressure-like effects.
- 29.
James Hopwood Jeans (1877–1946), British physicist and astronomer, major contributions to cosmology and classical physics.
- 30.
The equations used to derive the Jeans length take the expansion of the universe into account, therefore the Jeans length is also proportional to the scale factor. As discussed above, only physical quantities held together by forces are not affected by the expansion of the universe. The Jeans length, since it is a theoretical construct, increases directly with the expansion.
- 31.
Subrahmanyan Chandrasekhar (1910–1995), Indian born astrophysicist, important contributions to theoretical astrophysics and stellar evolution.
- 32.
- 33.
Karl Schwarzschild (1873–1916), German astronomer and physicist, early work on general relativity.
- 34.
The escape velocity is the speed at which the potential energy of an object is equal to its kinetic energy. See Fig. 6.9 and the discussion on energy relating to it.
- 35.
The curvature of spacetime is equivalent to the presence of gravitational fields, and a clock in a gravitational field will tick slower than a clock very far away from the source of the field, where the field is weaker.
- 36.
We should stress here again, that the relations between the expansion rate and the energy content of the universe, and the rate of change of the Hubble parameter and energy content, are by no means “obvious”. They follow from the governing equations of Einstein’s theory of gravity.
- 37.
As discussed in Chap. 5, pressure is a small scale phenomenon arising from the interaction of particles. The interaction scales for normal matter are far too small. For radiation, owing to the infinite range of the electromagnetic interaction, we do need to take into account its pressure.
- 38.
Specks of dust can be seen floating in the sunlight, are not interacting with each other, providing a neat analogy for galaxies “floating” in space.
- 39.
Redshift is here, and elsewhere in cosmology, a convenient time coordinate, as it is directly related to the expansion of the universe and directly measurable, as discussed previously.
- 40.
We might however observe gravitational waves from these very early times, as we will briefly discuss in Chap. 9.
- 41.
Another effect is that the wavelength of the electro-magnetic radiation gets stretched by the expansion. However, this doesn’t affect how far we can see directly.
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Malik, K.A., Matravers, D.R. (2019). What Are the Forces That Shape the Universe?. In: How Cosmologists Explain the Universe to Friends and Family. Astronomers' Universe. Springer, Cham. https://doi.org/10.1007/978-3-030-32734-7_6
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