5. The Universe is expanding (Inflationary perturbations 1)

This is the 3rd post in the series based on my lectures on inflationary perturbations at the University of Helsinki (previous ones can be found here and here).

Today I am going to finally start constructing some theoretical basis for the future posts on inflationary perturbations

Probably, the most important observation ever made by an astronomer is that the Universe is actually expanding. Moreover, as it turns out, it is expanding according to the linear Hubble law: distant objects are running away from us with velocity

proportional to the distance between us and them. You are certainly well aware of it already but I would still want to emphisize a couple of points related to the way how the expansion of the Universe is actually detected. To check the Hubble law, one needs to make al least two independent observations: to measure velocity of the object (galaxy, supernova etc.) and to measure the distance between us and the object.

The first measurement (velocity) is done as follows. Galaxies as well as other bright sources of radiation on the sky typically have in their spectrum well determined emission and absorbtion lines, so the relative velocity of such a source can be easily determined by its redshift

,

where is the velocity of light.

The second measurement (distance) is much trickier. Distances within our galaxy can be measured by parallax (for example, as you remember, Proxima Centauri 1 pc away from us has a parallax 1 arcsec). On the other hand, galaxies at the distance of few Mpcs (millions of parsecs) have an unmeasurable parallax < 1 milliarcsec, so the parallax measurement is of no help to determine the distance to them.

In practice, one uses the concept of standard candle at distances larger than 100 Pcs. Standard candle is an object which emits light in some particular well known way (for example, we know very well the physics behind emission processes), has a known brightness. One example of such class of objects is Type 1a supernovae which blow up in very similar way everywhere around the Universe (i.e., parameters of their blow up such as the change of brightness with time are the same).

To determine distances to galaxy clusters, we also use brightness-distance relations (considering only similar clusters, picking the brightest galaxies in the cluster and using the law to determine the distance from the flux of photons sourced by these galaxies), period-luminocity relations finding cepheid variable stars in galaxies (cepheids are also remarkable standard candles), Tully-Fisher relation (relation between the stellar mass of a spiral galaxy and the ampltude of its rotation curve) and many other methods.

The bottom line is that these different methods used to measure distance give the same Hubble law determining how rapidly distant objects are running away from us. On the picture below (W. Friedman et al.) you can see results of actual observations. Up to the distance of 100 MPcs away from us, there are tons of data since we are able to resolve fine structure of clusters (and galaxies at smaller scales). However, at larger distances there are simply no so many bright sources of radiation (and only IIa supernovae are standard candles among them).

I will discuss supernovae (and Ia in particular) the next time.

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