There are a lot of posts going on where people have questions about cosmology, particularly the more interesting parts like the Big Bang, dark matter, dark energy, and so on. So, I thought I'd type up a series on cosmology for interested parties. Plus, it's a good way for me to keep refreshed on the basics.
So where do we start with something as ambitious as studying the entire universe?
First, we have to get assumptions out of the way, but I think we can be convinced that they're reasonable ones.
- We assume that the laws of physics behave the same way here as they do over there; that they do not depend on their location in space and time (Lorentz invariance).
- The universe is homogeneous and isotropic: it contains the same sorts of things, and it contains the same sorts of things in the same way in every direction.
"Now hold on," we might object. "Surely there are different things in the universe. If I draw an imaginary cube with the Sun as the center, that box will contain completely different kinds of things than if I drew an imaginary cube of the same size somewhere in the middle of a nebula."
And that's true: when we say the universe is homogeneous and isotropic, we mean at certain
scales it is. Your room isn't homogeneous and isotropic, nor is planet Earth, nor the solar system, nor the Milky Way Galaxy or even the local cluster.
[GALLERY=media, 9486]Isohomo by Meow Mix posted Jun 23, 2021 at 8:31 PM[/GALLERY]
It's not until we "zoom out" to about 100 Mpc (that's Megaparsecs, or about 3.26
million light years) that we get a picture of the universe that's homogeneous and isotropic.
It would make things considerably easier if the universe were also time-invariant, but we know that isn't the case: the size of the universe itself changes with time, and the stuff within it behaves differently based on
when we're talking about.
[GALLERY=media, 9487]Sfrd by Meow Mix posted Jun 23, 2021 at 8:35 PM[/GALLERY]
Here, we see that the star formation rate differs with redshift, and we will discuss how looking at different redshifts is looking at the universe at different points in
time.
So, most of us here are probably at least colloquially familiar with the concept of redshift: the universe is expanding, so light that reaches us from distant sources will have their spectra redshifted compared to the spectrum of a similar object (say, a similar star) at rest with respect to the observer.
[GALLERY=media, 9488]Redshift by Meow Mix posted Jun 23, 2021 at 8:48 PM[/GALLERY]
(We use "z" for redshift)
This often gets misattributed to the Doppler effect, but it's actually not. The Doppler effect is related to the
actual motion of a source relative to an observer's location in space. In cosmology we call galaxies' actual motion
peculiar motion, because they do move with respect to one another, especially within the contexts of their local clusters. So, the redshift and blueshift of nearby galaxies may be due to a true Doppler effect, but when you zoom out enough (get to high enough redshifts), the redshifting is not technically a Doppler effect: it's due to
space itself stretching the wavelength of the light as it expands.
Perhaps I can convince you that this is different from a true Doppler effect with an analogy:
[GALLERY=media, 9490]Paperclips by Meow Mix posted Jun 23, 2021 at 8:56 PM[/GALLERY]
Here, a couple of ants (observers) are sitting on a couple of paperclips which do not move from their fixed positions on a rubber band. In a true redshift situation, whether the light is redshifted or blueshifted would depend on if a paperclip is moving towards you or away from you. But since the space itself (the rubber band) is expanding, all paperclips will receive redshifted light from all other paperclips. If the light had to travel across the rubber band (to be true to the space analogy), the distance between the peaks and troughs of the wavelength of the light would get stretched as it travelled.
[GALLERY=media, 9489]Expansion by Meow Mix posted Jun 23, 2021 at 8:56 PM[/GALLERY]
The above is a visualization of the expansion of space. Galaxies retain their positions with respect to one another, but the space between them expands.
Why does it matter that we make this distinction between true galactic motion (true redshift via peculiar motion) and redshift via spacetime expansion?
[GALLERY=media, 9491]Peculiar by Meow Mix posted Jun 23, 2021 at 9:05 PM[/GALLERY]
Because the redshift caused by the expansion is mostly linear (not perfectly, thanks to some relativistic effects, but consider it close enough for right now in this series). In the above image, the blue oval shows a large number of outliers in the data. Why?
Because the blue oval contains data from the Virgo cluster: galactic clusters tend (for gravitational reasons) to have galaxies that are moving with respect to one another (high peculiar motion), so it "fuzzies" up measurements of their redshift due to universal expansion. Imagine if the paperclips in the example above had multiple paperclips in a cluster around point E (in that image), all moving forward and backward, left and right, etc. An observer from paperclip A would see some of the paperclips moving away slower or faster simply because of their motions relative to each other being added to the apparent motion of the rubber band stretching.
Fortunately, there appears to be a physical "speed limit" to peculiar motion (around 1,000 km/s). Since, due to the expansion of the universe, objects that are further apart will appear to one another that they are receding away faster than closer objects (think of this like there is more space between them that's expanding, so each unit of space there is to expand means more expansion), we can look out far enough (to great enough redshifts) that the noise caused by peculiar velocity is negligible. This would be good if we wanted to, for instance, measure the Hubble parameter.
All this talk of expansion brings us to a good stopping point (and a good setting up point for all the stuff people really care about, like the Big Bang, dark matter, dark energy, etc. that people keep asking questions about on the forum) from here: the scale factor of the universe.
We define a scale factor a(t) of the universe such that when t = 0 (so,
now in time), a = 1. If at any point the universe is half the size of the universe today, a would equal 1/2, and so on. This is where we get the Hubble parameter with a simple differential: H = (da/dt) / a. The Hubble parameter relates the apparent recession velocity with the size of the universe at any given time relative to the size of the universe now (hence why people often mischaracterize the Hubble parameter as a
constant; which it clearly is not: the value of H changes as the value of a changes!)
Many things are related to the scale factor (remember, this is a, the size factor), and I'll have to decide if I want to spend time proving them or asking folks to take my word for it; but among things that are related are temperature (T is proportional to a^-1), redshift, and the age of the universe itself.
These are all the ingredients we need to make a real cosmology post next time, which will be about the Friedmann equations and how we will use them to answer a lot of these people have; and why we have good reason to do so.