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Mar 21, 2012 at 8:44 comment added kleingordon @metzgeer And then there is also the perspective in the paper linked from the comments below your question: our current understanding of QFT can't predict the measured value of $10^{-9}$ Joules / m$^3$, but there's no "grand mystery" because the existence of $\Lambda$ in Einstein's equations can be considered to be a fundamental law in its own right. The key quote, however, is "there is no known natural way to derive the tiny cosmological constant that plays a role in cosmology from particle physics. And there is no known understanding of why this constant is not renormalized to a high value."
Mar 21, 2012 at 6:17 comment added kleingordon @metzgeer, there simply is no consensus for how to derive the vacuum energy from first principles. It is one of the biggest outstanding puzzles in physics, and a first principles derivation would revolutionize the field. Prior to the measurements of the CMB and type Ia supernovae, there was no clear indication that it would turn out to be $10^{-9}$ Joules per cubic meter. That's just what we measure. Its exceedingly small value (compared to the Planck scale) causes many physicists to invoke anthropic explanations.
Mar 21, 2012 at 2:28 comment added metzgeer Again, the question I'm asking about isn't about the cosmological constant, it's the Quantum Field Theory derivation. I have tried to be clear about this, see the question in the bounty. All the same, thanks for your replies.
Mar 20, 2012 at 22:51 comment added Henry You If is important: the Planck mass is neither large nor very small: it is roughly the amount of Vitamin D you should consume a day, and many living things are smaller, so it is not obviously fundamental, except as a indicator of where general relativistic effects and quantum mechanical effects start to confuse each other.
Mar 20, 2012 at 19:59 history answered kleingordon CC BY-SA 3.0