Abstract
In the previous three chapters we have described the fields and particles that make up the energy content of the universe, and the forces that govern the interaction of these constituents, how the energy content evolves, and how the interplay of the matter and the spacetime geometry leads to the formation of structure. We can use this to put the observations described in the other chapters of this book into a historical context.
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Notes
- 1.
The mass density, or to be precise the rest-mass density, and the energy density are proportional to each other, the constant of proportionality is the square of the speed of light. This is a direct consequence of Einstein’s famous mass-energy relation. We follow here the bad practice of many cosmologists and use both terms synonymously.
- 2.
Also, the neutron is just a tenth of a percent heavier than the proton, hence our estimate wouldn’t change if we had chosen neutrons instead.
- 3.
To be precise: the photon velocity is always the same (in vacuum), namely the speed of light. The kinetic energy resides in the “speed” or number of oscillations per second, that is the frequency of the electromagnetic radiation. The energy of a photon is directly proportional to the frequency; at low temperatures the photons have on average small energies and low frequencies, at high temperatures large energies and high frequencies.
- 4.
We assumed that the halo is a spherical cloud of dark matter, extending out to 250 thousand lightyears, or about 80 thousand parsec from the centre of the Milky Way (five times further than the stars in the galactic disk), and the mass of the Milky Way is 1012 or a trillion solar masses. For this rough estimate we can safely neglect that roughly 5% of the mass of the galaxy is in form of baryons.
- 5.
The Milky Way disc has a diameter of roughly 100 thousand lightyears, hence we choose as “typical” volume a sphere with the same diameter—the sphere that we can fit the Milky Way disc into. The volume of this sphere is roughly 10−5 cubic Megaparsec.
- 6.
Indeed, the volume taken up by a galaxy compared to the space surrounding it is negligible—cosmologists can therefore approximate galaxies frequently in their calculations as “point particles”, idealised objects that have a mass but no spatial extension.
- 7.
Using much more sophisticated arguments—taking into account the mass range of stars in galaxies, and that there are different types of galaxies with widely varying numbers of stars—we arrive at similar numbers. But we only want to give here an “order of magnitude correct” result.
- 8.
We will discuss the geometry of the universe in Sect. 9.3.2.2.
- 9.
- 10.
The temperature of the Cosmic Microwave Background is inversely proportional to the scale factor, as discussed in Sect. 6.4.4. This also implies that as we go back in time and the scale factor decreases, the temperature increases.
- 11.
After decoupling the photons do not interact with electrons any longer and the electrons can combine with the free protons to form neutral hydrogen. But as discussed above, there is therefore no more photon-baryon fluid and the photons can also no longer provide pressure to the baryons. The baryons can collapse.
- 12.
At redshift 100 there are about 7 × 1049 baryons in a volume of 1 cubic parsec.
- 13.
At the time of decoupling there are also helium nuclei, consisting of two protons and two neutrons, but they only make up a quarter of the baryonic mass and will also be ionised, so we can ignore them in our discussion.
- 14.
Because decoupling did not take place exactly instantaneously, we observe the Cosmic Microwave Background photons that originate from a thin shell, with a thickness today of about 50 million parsec. This is however tiny compared to its diameter and we can neglect this here.
- 15.
The distance to the horizon, the size of the visible universe is slightly larger, roughly 14.2 billion parsec or 46 billion lightyears, as discussed in Sect. 6.4.4.
- 16.
This is a slight simplification as also the photons and the baryons contribute to the potential wells—all forms of energy curve spacetime. But at decoupling there is nearly twice as much energy in the dark matter, than in the other components.
- 17.
A full oscillation cycle of compression and bounce back or rarefaction for oscillations of sound horizon size would take two times 380,000 years.
- 18.
We remind the reader of the Copernican principle discussed in Sect. 6.4.2.4, that the universe on the largest scales is the same in all directions and the same in all places—the universe is isotropic and homogeneous.
- 19.
As discussed previously, the density contrast describes the fluctuations of the density relative to the average density of the universe.
- 20.
Particles like protons and neutrons are made up “quarks”, held together by “gluons”, which mediate the strong force.
- 21.
Neutrinos also interact through gravity, but this is not relevant here.
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Malik, K.A., Matravers, D.R. (2019). Going Back in Time. In: How Cosmologists Explain the Universe to Friends and Family. Astronomers' Universe. Springer, Cham. https://doi.org/10.1007/978-3-030-32734-7_8
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DOI: https://doi.org/10.1007/978-3-030-32734-7_8
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