# Probability of the cosmological constant having its value - how to understand this idea?

Definition of Fine-Tuning

and John Rennie's answer that we can calculate the probability that the cosmological constant has its observed value (the answer being around 1 in $$10^{120}$$.

I'm not a physicist. I'd like to understand what this probability means. When I think of probability, I think of a space of possibilities... for example a dice with 6 sides. The probability of getting a 3 is 1/6.

So what does it mean to say the probability of the cosmological constant being what it is, is 1 in $$10^{120}$$? My naive way to make sense of it is to say that there are multiple universes and around every 1 in $$10^{120}$$ of them has our particular cosmological constant. But I get the feeling this is the wrong way to think about probability in this situation.

• It is the correct way. The number says how improbable it is to have the observed universe. That is why some people advocate the "anthropic principle" en.wikipedia.org/wiki/Anthropic_principle . Apr 27, 2021 at 8:34
• @annav, so a physicist making this probability claim is implicitly saying there are multiple universes? Apr 27, 2021 at 8:37
• " and John Rennie's answer that we can calculate the probability that the cosmological constant has its observed value (the answer being around 1 in $10^{120}$ " . Is this number correct ? I find it hard to believe such a probability has been calculated. I would love to see some kind of citation, reference etc. Apr 27, 2021 at 8:45
• @silverrhaul $10^{120}$ is famous as being the order of magnitude difference in the naive QFT prediction of $\rho_{\Lambda}$ vs the observed value. I assume this is where it comes from. Apr 27, 2021 at 9:13
• @silverrahul aapt.scitation.org/doi/10.1119/1.17850 Apr 27, 2021 at 9:14

The probability mentioned here, the $$1$$ in $$10^{120}$$, is more akin to assuming the CC can randomly take any value, looking at its value and saying 'ah, the chance of having this value is 1 in whatever'. If I remember correctly, the $$10^{120}$$ figure is usually contrived by comparing the observed value of $$\Lambda$$ with the naive QFT vacuum prediction of $$\Lambda$$, which differ by around $$10^{120}$$ orders of magnitude. This is why I don't think there's any benefit to giving a probability to something like this. It also belittles the more serious theoretical problems with the cosmological constant, namely, it's radiative instability.
• I wouldn't get bogged down by the actual probability values, different analysis leads to wildly different numbers. The key message people are trying to make is that the observed $\Lambda$ is very very small but non-zero, whilst current QFT predictions are much larger. (I won't go into the details about why remedying this in QFT isn't as straightforward as it seems). Using numerical probabilities is just an attempt to encapsulate this point (and also hint that there should be some physical explanation, as opposed to being purely random/coincidence). Apr 27, 2021 at 9:20