Two Numbers

Cosmology used to be called the hunt for two numbers. It was simple and elegant. Nowadays we need at least six. It is neither simple nor elegant. So how did we get here?

The two Big Numbers are, or at least up till the early-90s were, the Hubble constant H0 and the density parameter Ω. These told us Everything. Or so we thought.

The Hubble constant is the expansion rate of the universe. Not only does it tell us how fast the universe is expanding, it sets the size scale through the Hubble distance-velocity relation. Moreover, its inverse is the Hubble time – essentially the age of the universe. A Useful and Important Number. To seek to measure it was a noble endeavor into which much toil and treasure was invested. Getting this right was what the Hubble Space Telescope was built for.

The density parameter measures the amount of stuff in the universe. Until relatively recently, it was used exclusively to refer to the mass density – the amount of gravitating stuff normalized to the critical density. The critical density is the over/under point where there is enough gravity to counteract the expansion of the universe. If Ω < 1, there isn’t enough, and the universe will expand forever. If Ω > 1, there’s more than enough, and the universe will eventually stop expanding and collapse. It controls the fate of the universe.

Just two numbers controlled the size, age, and ultimate fate of the universe. The hunt was on.

Of course, the hunt had been on for a long time, ever since Hubble discovered that the universe was expanding. For the first fifty years it largely shrank, then settled into a double valued rut between two entrenched camps. Sandage and collaborators found H0 = 50 km/s/Mpc while de Vaucoulers found a value closer to 100 km/s/Mpc.

The exact age of the universe depends a little on Ω as well as the Hubble constant. If the universe is empty, there is no gravity to retard its expansion. The age of such a `coasting’ universe is just the inverse of the Hubble constant – about 10 Gyr (10 billion years) for H0 = 100 and 20 Gyr for H0 = 50. If instead the universe has the critical density Ω = 1, the age is just 2/3 of the coasting value.

The difference in age between empty and critical ages is not huge by cosmic standards, but it nevertheless played an important role in guiding our thinking. Stellar evolution places a constraint on the ages of the oldest stars. These are all around a Hubble time old. That’s good – it looks like the first stars formed near the beginning of the universe. But we can’t have stars that are older than the universe they live in.

In the 80s, a commonly quoted age for the oldest stars was about 18 Gyr. That’s too old for de Vaucoulers’s H0 = 100 – even if the universe is completely empty. Worse, Ω = 1 is the only natural scale in cosmology; it seemed to many like the most likely case – a case bolstered by the advent of Inflation. In that case, the universe could be at most 13 Gyr old, even adopting Sandage’s H0 = 50. It was easy to imagine that the ages of the oldest stars were off by that much (indeed, the modern number is closer to 12 Gyr) but not by a lot more: Ages < 10 Gyr with H0 = 100 were right out.

Hence we fell into a double trap. First, there was confirmation bias: the ages of stars led to a clear preference for who must be right about the Hubble constant. Then Inflation made a compelling (but entirely theoretical) case the Ω had to be exactly 1 – entirely in mass. (There was no cosmological constant in those days.  You were stupid to even consider that.) This put further pressure on the age problem. A paradigm emerged with Ω = 1 and H0 = 50.

There was a very strong current of opinion in the 80s that this had to be the case. Inflation demanded Ω = 1, in which case H0 = 50 was the only sensible possibility. You were stupid to think otherwise.

That was the attitude into which I was indoctrinated. I wouldn’t blame any particular person for this indoctrination; it was more of a communal group-think. But that is absolutely the attitude that reigned supreme in the physics departments of MIT and Princeton in the mid-80s.

I switched grad schools, having decided I wanted data. Actual observational data; hands on telescopes. When I arrived at the University of Michigan in 1987, I found a very different culture among the astronomers there. It was more open minded. Based on measurements that were current at the time, H0 was maybe 80 or so.

At first I rejected this heresy as obviously insane. But the approach was much more empirical. It would be wrong to say that it was uninformed by theoretical considerations. But it was also informed by a long tradition of things that must be so turning out to be just plain wrong.

Between 1987 and 1995, the value of the Big Numbers changed by amounts that were inconceivable. None of the things that must be so turned out to be correct. And yet now, two decades later, we are back to the new old status quo, where all the parameters are Known and Cannot Conceivably Change.

Feels like I’ve been here before.

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