Since the Hubble Constant changes over time (it's a variable parameter), why can't the conflicting values of 67.4 and 73 both be right?

Question

Are the conflicting values from the 'early universe' (Planck) method and the 'late universe' (Distance ladder) method actually compatible? Since during the latter period of the universe 'dark energy' has taken over and accelerated the universe's expansion?

Are the values often given (67.4 vs. 73) actually averages over the lifetime of the universe? Since the Big Bang, or since the CMB release?

Even if the famously conflicting values of 67.4 and 73 are averages over the lifetime (or at least most of it) of the universe, why do all of the online Calculators giving an age of the universe based on your Hubble Constant input also insist you also input other parameters, especially the ratio of dark energy to all other mass and energy? (See Ned Wright's pages at IPAC at Caltech, e.g.) Shouldn't an average lifetime Hubble Constant already take that into account?

Think about it.... The rate of expansion of the Universe is constantly changing... And yet the Hubble 'Constant' gives a value per MegaParsec... Despite the fact that the Hubble Parameter has changed since the light from objects 3.26 million light years has reached us...

I am confused....

Answer 1

You are confusing the Hubble parameter $H(t)$, which is a function of time, with the Hubble constant $H_0=H(t=\text{today})$ which is the value of the Hubble parameter today, and so of course is a constant and doesn't depent on time. (when cosmologists say today, they mean 26th July 2022, as well as 13th May 30012 BCE, as well as 7th March 50987 CE. To a cosmologist 10000 years don't make much difference)

A nice analogy: if the universe were a person, called Alice, $H(t)$ could be the height of Alice, it is a function of time. Instead, $H_0$ would be the height of Alice today, when she is, say, 40 years old.

Researchers try to measure $H_0$ with different methods. Some of them are using the distance ladder, they are looking at the local universe and measuring how fast it is expanding. In the analogy, they would be measuring the Alice's height with a meter stick today.

On the contrary, measuring the Hubble constant from CMB is akin to looking at Alice when she was a child, recording her hight, weight, sex, and the height of her parents, and then using one of those tables that tell you how tall she would be as a grown up. Those tables are a model, they are the $\Lambda$CDM model that tells us how the universe got from being a hot mess at the time when the CMB was emitted, to being the universe we observe today.

Therefore, the Hubble tension can be explained in the following terms. There are three possibilities:

• the distance ladder measurement is wrong, Alice was wearing high heels at the time of the measurement and we didn't account for that.

• the Planck measurement was wrong, little Alice was standing on the tip of her toes to look taller, and we didn't notice.

• the Cosmological model is wrong. It doesn't correctly predict the future height of Alice.

Now, everyone always believed that Planck data is correct, they blamed the distance ladder measure, because it was affected by many uncertainties. But now we have a way more solid measure of $H_0$ from the distance ladder, and the tension has not disappeared. This leads many to conclude that the problem is in the model, and this is way theorethical cosmologists are so excited. A wrong model possibly means that new exciting physics is needed.

Answer 2

The values you quote are for $H_0$, which is the value of the Hubble parameter at the present cosmic epoch. It is not some sort of average value over time. So, yes, the fact that different methods give different results is a problem.

You correctly identify though, that a determination of $H_0$ from the cosmic microwave background does also involve a simultaneous estimation of the other important cosmological parameters - $\Omega_M$, $\Omega_\Lambda$ etc. because they determine the history of the Hubble parameter.

An imperfect analogy: If something is shot into the air, you might choose to characterise its trajectory using a locally determined velocity. But you might also have a means of measuring the velocity closer to the ground. To compare the two you would also need to know something about the acceleration or deceleration of the projectile, and if you can also measure those, you could translate your velocity close to the ground into the velocity it would have locally. Similarly, to work out when the projectile was fired, it is not sufficient to know what its velocity now is, you need to know about how it has accelerated or decelerated - and the same is true for the universe.