I'm trying to understand the connection between the $\Lambda$ from cosmology and the $\Lambda$ from QFT.

Cosmology: The cosmological constant enters the Einstein equations. In the special case of the Friedman universe it enters the Friedman equations. If we consider a spatially flat de Sitter universe, we get that

$$H_\Lambda^2=\frac{\Lambda c^2}{3}$$

therefore $\Lambda$ has the mass dimension of 2 ($[c]=0$, $[H_\Lambda]=1$).

QFT: The cut-off parameter $\Lambda$ in momentum space is such that the integration goes till $k\leq\Lambda$. Therefore $\Lambda$ has the mass dimension 1 ([k]=1).

On the other hand, both scales seem to be used interchangeably, for example here: http://www.perimeterinstitute.ca/videos/cosmological-constant To quote:

If we take the idea of the Planck length as a fundamental (minimum) scale and if additionally we impose the Cosmological Constant ($\Lambda$) as and infrared (IR) cut-off parameter.

But how can this work if the cosmological constant and the cut-off parameter have different mass dimensions?


Trying to answer my old question myself: The cited piece is talking about an infrared cutoff, which basically amounts to giving the propagating particle a mass which appears squared in a propagator. So I think, what is meant is considering

$$\lim_{\Lambda\to 0}\int \frac{d^4p}{p^2+\Lambda}$$

and this $\Lambda$ of course has a mass dimension of 2.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.