## Wednesday, July 2, 2014

### a much smaller Planck-mass

could you define a set of Planck-units based on the speed of light $c$, the Planck-constant $\hbar$ and instead of the gravitational constant $G$ the cosmological constant $\Lambda$? what would the numerical values be?

#### 1 comment:

1. well, I hope that this works out: a dimensional analysis for constructing a mass-scale $m$ from the ansatz $c^\alpha\hbar^\beta\Lambda^\gamma=m$ yields the solution $\alpha=-1$, $\beta=1$ and $\gamma=1/2$, implying for the mass scale $m=\hbar/c\times\sqrt{\Lambda}$. for a FLRW-universe $\Lambda$ can be expressed with the density parameter $\Lambda=3\Omega_\Lambda/\chi_H^2$ with the Hubble distance $\chi_H=c/H_0$, meaning $m=\hbar/c\times\sqrt{3\Omega_\Lambda}/\chi_H$ with the numerical value $\sim2\times10^{-64}$ grams.