Background

Since light has a finite speed, the amount of time it takes light to travel to Earth (lookback time) we see distant objects as they were in the past. A galaxy with a lookback time of two billion years appears as it was two billion years ago.

Due to the expansion of the Universe, the actual distance to a galaxy derived from cosmological redshift is greater than its light travel time.

We can only characterize the part of the Universe that we can detect (the observable Universe) based on the age of the Universe and light travel time. We cannot observe the entire Universe.

The cosmological principle makes the assertion that the Universe looks the same in all directions, and the average density of matter is also the same when viewed on large scales. Observations support this assumption.

The large-scale structure of the Universe describes the distinct structure seen in the distribution of matter in the Universe on very large scales (beyond the scale of an individual galaxy or galaxy cluster). The structure changes over time, but in every direction it changes the same way over the same time scales. The large-scale structure has evolved from having a smooth appearance with an even distribution of galaxies in the early history of the Universe to having larger voids and galaxy clumps in recent times.

OpenStax Astronomy textbook links:

Observations of distant galaxies
The cosmological principle
The formation and evolution of large-scale structure

Teacher Notes

1. Our investigations are designed so that students cannot proceed to the next page without answering each question. If you would like to quickly preview the entire investigation, you can use “educator mode” on the Start page. Enter the passphrase: 3ducatorMod3 to activate it.
   
2. Many students struggle with the premise of the cosmological principle, because they may focus on variations on a small scale instead of reasoning about whether these variations are seen on the large scale. They may see a small concentration of galaxies or one image that has a color variation in one spot, and use this as evidence that the Universe is not uniform. Encourage them to focus on the structure and variation that is on the large scale.
3. Distances given in light-years in this investigation are calculated from the photometric redshift value using current cosmological models, and reflect the distance from Earth at which the object would be today.
4. The most accurate way to determine a galaxy’s redshift is by taking a spectrum of the galaxy’s light, but this is not possible for very distant galaxies due to their dimness and their sheer number. Rubin Observatory uses an alternative technique called photometric redshift. It is not as precise, but it’s the only practical way to determine the redshift for the billions of faint galaxies Rubin Observatory will detect.
   

   Photometric redshift is derived from measuring the broadband flux (brightness) of a galaxy through multiple filters to construct a shape that mimics the shape of a spectrum. To see how this works, look at Figure 1 below. The amount of light passed by the filters u, g, r, i, and z is shown in grey. Source: http://ogrisel.github.io/scikit-learn.org/sklearn-tutorial/auto_examples/tutorial/plot_sdss_filters.html

   

   
   

A model galaxy spectrum with a known redshift (such as the three colored spectra models in Figure 1) is matched to the curve produced by the amount of light collected through the filters. These models are built using a set of initial conditions, such as the star formation history of the galaxy, its mass, and the amount of dust it contains.

Although less precise, Rubin Observatory photometric redshifts over the range 0.3 < z < 3.0 generally have errors of less than 2% when compared with redshifts determined from spectra. Only 10% of this sample will have redshift errors larger than 6%.

4. The redness-distance plots in this investigation contain galaxy data only to a cutoff distance of 14 gigalight-years (Gly). This is an intentional cutoff, and does not represent the entire range of data. The educational goal is for students to see the trend that more distant galaxies are redder, and the trend is clear up to 14 Gly. Beyond that distance, different rest frame ultraviolet spectral features start to move through these bands and make the trend less obvious. When Rubin Observatory data are available, galaxies at greater distances can be incorporated. Note: until Rubin Observatory data are available, we will use a simple photometric ratio of two bands (i/z) as a proxy for redness. Rubin Observatory will produce its own definition of redness in the future.