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It is often said that it seems that the Universe is quite close to critical density (for example https://astronomy.swin.edu.au/cosmos/C/Critical+Density).

Does this include Dark Energy as well (apart from Dark matter and Baryonic matter)?

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Yes. Quoting values from wikipedia (which in turn cites Ade et.al. in Astronomy and Astrophyics 517), the contribution of matter (both Dark and visible matter) is $$Ω_\text{mass} ≈ 0.315±0.018$$ The contribution of photons and neutrinos is small, and within the boundaries of error of the other terms: $$Ω_\text{relativistic} ≈ 9.24×10^{−5}$$ And the contribution of Dark Energy is: $$Ω_Λ ≈ 0.6817±0.0018$$

$$Ω_\text{total}= Ω_\text{mass} + Ω_\text{relativistic} + Ω_Λ= 1.00±0.02$$

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