As I've discussed before, Cepheid variable stars are a fundamental method to the entire understanding of the scale of our universe. These standard candles were first used to conclusively demonstrate that fuzzy patches of light were entire “island universes” or, as we call them today, galaxies. From there, they've been used to calibrate most of the rest of our cosmic distance ladder.
So what would happen to our cosmic distance ladder if they'd never been discovered?
A paper in the June 1 ApJ is the third in a series that asks just this question. Sadly, only the first is available on the preprint server currently.
The first paper looks at how possible it is to rebuild the distance ladder without the use of Cepheids. As a replacement, they use the tip of the Red Giant Branch (RGB). As stars die, they expand. The larger surface area corresponds to a greater luminosity, but also means that the same energy is being spread out more, so the temperature drops. In more practical terms, this means that the star's position on the HR diagram moves up and to the right.
Overall, stars will max out at an absolute luminosity of about 106 times the luminosity of the sun. If astronomers can isolate those stars, as with other distance indicators, they know how bright they should be, and then comparing them to how bright they are (and correcting for other dimming effects), they can then get a new distance estimate. Fortunately, the RGB tip method works very well because it's fairly insensitive to the chemical composition of the star (how much “metal” the star has).
This study used the RGB stars to calibrate the distance to 14 galaxies which was in turn used as a reformulation of the secondary distance indicator, the Tully-Fisher (TF) relation. Although there was some difference, it was very slight. In fact, it was very nearly within the error range (0.19 ± 0.13 mag).
Using this in turn, to recalculate the Hubble constant (which the inverse of gives the age of the universe) they got a value of 73 ± 5 km s-1 Mpc-1. This is amazingly close to the most recent calculation of 74.2 ± 3.6 km s-1 Mpc-1!
Since this paper was published in 2008 (before that most recent Hubble constant), the authors instead compared their value to that from Sakai et al. (2000) which gave a value of 67 ± 10 km s-1 Mpc-1.
In one case, a bit higher. In one a bit lower. In either case, a very consistent value! No matter how you approach it, the universe is 13 billion years old.
(PS: If anyone can get the next two articles in the series for me, I'd greatly appreciate it! DOI numbers are 10.1088/0004-637X/694/2/1331 and
Mould, J., & Sakai, S. (2008). The Extragalactic Distance Scale without Cepheids The Astrophysical Journal, 686 (2) DOI: 10.1086/592964