# The units of the cosmological constant

• I
Safinaz
TL;DR Summary
A question about the unit and the value of the cosmological constant
In natural units, it’s known that the unit of the cosmological constant is ##eV^2##.
I don‘t get why in this paper :

https://arxiv.org/pdf/2201.09016.pdf

page (1), it says the value of ##\Lambda \sim meV^4##, this means ##\Lambda \sim (10^6 ~ eV)^4 \sim 10^{24} eV^4 ##, shoud not the unit ##eV ^2 ## instead ?

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Because in natural units the dimension of the cosmological constant is energy^4 and it is not known that the dimension is energy^2.

Safinaz
Staff Emeritus
Homework Helper
Gold Member
Summary: A question about the unit and the value of the cosmological constant

In natural units, it’s known that the unit of the cosmological constant is ##eV^2##.
I don‘t get why in this paper :

https://arxiv.org/pdf/2201.09016.pdf

page (1), it says the value of ##\Lambda \sim meV^4##, this means ##\Lambda \sim (10^6 ~ eV)^4 \sim 10^{24} eV^4 ##, shoud not the unit ##eV ^2 ## instead ?

### ​

See for instance the discussion here:

https://www.quora.com/Why-is-the-cosmological-constant-without-units

Or this paper : https://arxiv.org/pdf/hep-th/0012253.pdf, equation (2)

They say the units of ##\Lambda## is ##eV^2 ## or equivalently in natural units ##cm^{-2} ## or ##sec^{-2}##
Ok, so the confusion is regarding ##\Lambda## vs ##\rho_\Lambda##. I was referring to ##\rho_\Lambda##, the energy density of the cosmological constant. The first paper you cite in the OP is discussing the scale of the energy density, the others discuss the constant appearing in front of the metric in the Einstein field equations. These differ by a constant ##8\pi G## and ##G## has dimensions energy^-2 in natural units.

Ibix and Safinaz