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Tye, Wong claim that type IIB string theory generically predicts a tiny cosmological constant

...along with very light scalars...

According to the rules of naturalness in quantum field theory, the observed small Higgs mass is unlikely (because unless some special adjustments are made, scalar fields "love" to eat loops and become as fat as the cutoff scales) and therefore deserves an extra explanation, much like the even tinier magnitude of the cosmological constant (the energy density of the vacuum, the dark energy).

However, in the new paper

Linking Light Scalar Modes with A Small Positive Cosmological Constant in String Theory
Henry Tye and Sam Wong claim that string theory dramatically revises (or can revise?) all this reasoning and makes (or can make?) a tiny cosmological constant along with very light scalars very likely as predictions of a randomly chosen type IIB compactification.

This is obviously an incredibly ambitious statement that experts will be skeptical towards at the beginning and the devil may be in the details. Tye and Wong would not only solve the cosmological constant problem in string theory – but the hierarchy problem and most of the similar problems, too. But is it true?

So far, I don't understand their arguments. They claim that the probability distribution \(P(\Lambda)\) for the cosmological constant diverges for \(\Lambda\to 0^+\). In the continuum approximation, \(\Lambda=0\) would be the most likely value but there are cutoffs due to the discrete spectrum of the cosmological constant.

And they say that when the Hodge number of the Calabi-Yau compactifications are something like \(h_{12}\sim O(100)\), then the median value of the cosmological constant is predicted to be close to the observed tiny value. It's clearly not the first paper by Tye and co-authors making this bold claim. A previous 2012 paper already did the same and the new one elaborates upon the old one, among other papers.

But I had to miss or forget the previous Tye papers and I am not actively aware of any explanation why they're right or why they're wrong so I hope to learn something about these matters later.

In the context of a recent PRL paper by Acharya et al., I've mentioned that I don't believe the strongest anthropic arguments. Could I believe that our vacuum is "typical" – that the equal probability distribution for the type IIB vacua is a good enough approximation for these statistical purposes – so that it would be enough to buy the Tye-Wong paper if the mathematics is right?

Well, I think that when the cosmological constant is small enough, its precise size is not immediately obvious (cannot be used for "profiling") in the vacuum selection cosmological epoch. The details may decide whether your Universe will have the radius one inch or 10 miles but it can't be seen immediately when the Universe has the curvature close to the Planck scale.

These comments mean that it's reasonable to assume that the different vacua are comparably likely and the generic or median one could be a good estimate of the cosmological constant according to my "softcore anthropic" rules. But is the Tye-Wong mathematics correct? The 2012 paper only has some 12 or so followups so it has surely not ignited a revolution that most people would appreciate – yet. This is not a safe argument to conclude that their ambitious idea must be wrong, of course.

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