Over in SPR John Baez asked what is the value of the cosmological constant (Lambda) expressed in Planck units.(adsbygoogle = window.adsbygoogle || []).push({});

I posted a reply earlier today, but it contained a mistake

---what I posted on SPR around 10AM today---

I think the current estimate of Lambda in Planck units is

4.0 E-123

The estimated dark energy density would be one third of that, expressed in Planck units, namely

1.3 E-123

....

...

----end quote---

Turns out I was right about the dark energy density----rho_Lambda---which is 1.3 E-123.

But I was wrong about the relation of Lambda itself to this.

I gather from Ted Bunn post that Lamda is 8pi times rho_Lambda. Making it (according to him) about 3.2 E-122. this is all in Planck terms.

I will correct my calculation accordingly to agree with what Ted Bunn says:

First let's calculate the dark energy density from the value of the Hubble parameter 71 km/s per Megaparsec.

This is an inverse time, and in MKS units it would be 2.3 E-18 per second,

or 2.30 E-18, if we postpone rounding off till later.

This MKS value is equivalent to 1.24 E-61 reciprocal Planck time units.

Putting G=c=1,

the critical density, rho_crit, is (3/8pi)H^2

The current estimate of the dark energy density is 73 percent of that.

So in Planck terms the dark energy density is

0.73 (3/8pi)H^2 = 0.73 (3/8pi)(1.24 E-61)^2 = 1.3 E-123

But according to the conventions about Lamda you still have to multiply by 8pi.

Lambda = 8pi x 0.73 (3/8pi)H^2 = 0.73 (3)(1.24 E-61)^2 = 3.4 E-122

Hope this is right. Anyone have suggestions, corrections?

This was Baez original post

What's the cosmological constant in Planck units?

A figure of 10^{-120} is often bandied about, but

I've recently seen 10^{-123}. If we use the WMAP

data and all the current conventional wisdom on

cosmology, what do we actually get? (I don't

really want to hear all the caveats.)

If you give it to me in MKS units, I'll do the rest.

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# The Planck Lambda (Baez question)

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