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## Homework Statement

Show that, in natural units [itex]h=c=1[/itex], an energy density may be expressed as the fourth power of a mass. If the vacuum energy contributed by a cosmological constant is now of order of the critical density, what is the mass to which this density corresponds?

**2. The attempt at a solution**

For the first part I think that

[tex]\rho_E \propto \frac{m_Pc^2}{l_P^3} = \frac{m_P^4c^5}{h^3}[/tex]

where the index P is for the Planck units.

Then I'm stuck. I'm not sure about how to relate the vacuum energy, the cosmological constant and the critical density. Anyone?