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According to Sean Carroll's The Cosmological constant (Eqn.20) cosmological observations imply that the magnitude of the vacuum energy density in natural units is given by $$|\rho^{(obs)}_\Lambda|\le (10^{-12}\ \rm{GeV})^4.$$ Does this imply that the minimum length scale of modes of the vacuum are of the order of $\lambda \sim (\rm{meV})^{-1}\sim \rm{mm}$ ?

If this is true then would this millimeter cutoff length be detectable by Casimir effect-type experiments?

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  • $\begingroup$ What is a "mode of the vacuum"? $\endgroup$ – ACuriousMind Apr 7 at 19:17
  • $\begingroup$ I assume that there are quantum fields in the vacuum with zero-point energy normal modes down to some cutoff wavelength $\lambda$. $\endgroup$ – John Eastmond Apr 8 at 7:50
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No, it doesn’t imply this. Physicists do not think that there is a macroscopic millimeter-scale cutoff for the wavelength of virtual particles. If there were, all sorts of QED calculations would not agree with experiment.

The cutoff has to be at much smaller length scales, which means the value of the cosmological constant remains mysterious.

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