Estimates of the density parameter

Question

I’m looking for the most up-to-date information about the density parameter (i.e., the density of the universe relative to the critical density). As a layman, I don’t know how to navigate the relevant literature. Hence, I would like to ask if someone here could provide me with some references.

I’m looking for some fairly detailed information (even though it may be difficult for me to understand as, you know, a layman). That is, in addition to the best estimate, I would also like to understand the evidence for that estimate and the level of uncertainty. If there are recent textbooks or popular texts that cover this, that would be great; but I’m also interested in references to research papers.

Answer 1

I’m looking for the most up-to-date information about the density parameter

I guess I would look up to the Planck 2018 data, but it seems it's been edited recently (14 September 2020, see arXiv:1807.06209)

There are multiple $\Omega_K$ values listed for different constraints, on page 41, section 7.3

(i.e., the density of the universe relative to the critical density)

Total density of the universe can be written as

$$1 = \Omega_{tot} + \Omega_K$$ for $a(t_{now}) = 1$ and $\Omega_{tot} = \Omega_{m,0} + \Omega_{r,0} + \Omega_{\Lambda,0}$

In this case we can also write

$$\Omega_K = 1 - \Omega_{tot}$$

Thus, $\Omega_K < 0$ represents a universe with positive curvature (e.g., the density of the universe is larger than the critical density)