# Question about the Cosmological Constant

• I
• Buzz Bloom
In summary: Lambda has units of 1/m2In summary, the cosmological constant, represented by the constant Λ, has units of 1/m2 and is derived from the Riemann curvature tensor, which has dimensions of 1/L^2. The stress energy tensor, T, has units of M/LT^2 and when multiplied by G and divided by c^4, has units of 1/L^2, resulting in the cosmological constant having units of 1/m2.
Buzz Bloom
Gold Member
TL;DR Summary
Reference:
https://arxiv.org/pdf/1203.4513.pdf
Page 4
Equation [2].
PNG image of [2] in main body text.
Using m,s, kg units, all of the terms in the equation, except one, have dimensions m^2/s^2. In order for the term with the Cosmological Constant,Lambda, to also have these units, Lambda must have units 1/m^2. This seems to me to be an oddity.

I am hoping someone can explain to me why the constant Λ has units 1/m2.

In the article
In the Equations section, the following equation is presented.

Do tensors have dimensions? If so, can someone tell me what the dimensions are for these three tensors: R, g, and T? I know the dimensions for G and c. I am guessing the constant R has the dimension 1/m2 since apparently Λ also does.

Most physical constants have dimensions. G, h, c, ε0, ... all have dimensions. As to the dimensions of R, the metric tensor is dimensionless, as you'll see if you look up its definition. Since the Riemann curvature tensor is derived from second spatial derivatives of the metric tensor, it has units of 1/L^2. Contracting a tensor doesn't change the dimensions, since you are just summing up components. So the Ricci tensor and the curvature scalar also have dimensions of 1/L^2.

Buzz Bloom
Hi @phyzguy:

Thank you @phyzguy. You have been very helpful.

I have now been able to figure out that the T tensor has dimensions L/M or m/kg. Is this correct?

Regards,
Buzz

Buzz Bloom said:
Hi @phyzguy:

Thank you @phyzguy. You have been very helpful.

I have now been able to figure out that the T tensor has dimensions L/M or m/kg. Is this correct?

Regards,
Buzz

No. The stress energy tensor is an energy density, so it has units of Energy/Volume = $\frac{ML^2}{T^2} \frac{1}{L^3} = \frac{M}{L T^2}$. G has units of $\frac{L^3}{M T^2}$, so then GT/c^4 has units of $\frac{L^3}{MT^2} \frac{T^4}{L^4} \frac{M}{L T^2} = \frac{1}{L^2 }$

vanhees71 and Buzz Bloom

## What is the Cosmological Constant?

The Cosmological Constant is a term in Einstein's theory of General Relativity that represents the energy density of the vacuum of space. It is often denoted by the Greek letter lambda (Λ) and is responsible for the expansion of the universe.

## Why is the Cosmological Constant important?

The Cosmological Constant is important because it helps explain the observed expansion of the universe. It also plays a crucial role in the study of dark energy, which is thought to make up about 70% of the total energy in the universe.

## How is the Cosmological Constant calculated?

The Cosmological Constant is calculated using the Einstein Field Equations, which relate the curvature of space-time to the distribution of matter and energy. It can also be estimated through observations of the universe's expansion and the amount of dark energy present.

## What is the current value of the Cosmological Constant?

The current value of the Cosmological Constant is estimated to be around 10^-29 g/cm^3. This is an incredibly small value, but it has a significant impact on the expansion and evolution of the universe.

## What are some implications of the Cosmological Constant?

The Cosmological Constant has many implications, including the accelerated expansion of the universe, the existence of dark energy, and the fate of the universe. It also has implications for theories of gravity and the fundamental laws of physics.

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