W-Z-Unruh's Solution To The Cosmological Constant Employment Is Intriguing

Several folks accept asked me how I reacted to the paper

How the huge issue energy of quantum vacuum gravitates to drive the tedious accelerating expansion of the Universe (March 2017)

by Qingdi Wang, Zhen Zhu, William G. Unruh (who is famous for the Unruh radiations i.e. the simpler Hawking radiations inwards the apartment Rindler space). They claim that the Hubble constant implied past times only about vacuum issue energy density – which arises thank you lot to the quantum fluctuations inwards the vacuum – isn't the usual\[

H \sim \frac{\Lambda^2}{M_{Pl}}

\] but instead, it contains only about shocking exponentially decreasing factor\[

H \sim \Lambda \exp(-c \Lambda / M_{Pl} ), \quad c\sim O(1).

\] If true, the decreasing exponential could survive identified alongside the tiny factor of \(\exp(-123)\) as well as this machinery could explicate at to the lowest degree the "old" cosmological constant problem. My starting fourth dimension reactions were skeptical or "incomplete" but the to a greater extent than I human face into the paper, the to a greater extent than it reminds me of an endeavour of mine that I starting fourth dimension invented only about fifteen years ago. And that's an encouraging sign. ;-)




I practice believe that the contention well-nigh the "totally dissimilar formula for the Hubble constant" inwards a theory alongside the vacuum issue energy contradicts only about full general relationships betwixt the spacetime geometry as well as the quantum fluctuations e.g. inwards SUGRA. But the vacuum diagrams are "different" than all other Feynman diagrams, at that spot could survive an overlooked exception, as well as they're arguably to the lowest degree tested. To enjoin the least, the vacuum diagrams are the to the lowest degree successfully tested Feynman diagrams.

Even though they instruct an exponentially suppressed Ansatz for the Hubble constant, their endeavour really reminds me of only about efforts of mine to derive a "seesaw formula" for the cosmological constant,\[

\rho \sim \frac{M_{SUSY}^8}{M_{Planck}^4}

\] past times arguing that there's something incorrect alongside the vacuum energy's one-point component division as well as that alone its two-point component division is nicely calculable as well as the leading term is of the lodge written above. Why? Because after SUSY breaking, \(\rho\) is estimated to survive of lodge \(m_{SUSY}^4\), the 4th ability of the superpartner masses' differences, but nosotros demand to calculate \(\langle\rho^2\rangle\), which is why nosotros instruct the 8th power, but that has to survive divided past times the genuinely substitution scale, the 4th ability of the Planck scale, for dimensional reasons.

Just to survive sure, the formula inwards a higher house gives you lot a pretty goodness approximate for the observed vacuum issue energy for the same argue why a similar seesaw formula gives you lot a goodness approximate for the neutrino masses: \(M_{SUSY}\) is comparable to \(M_{EW}\) patch \(M_{Planck}\) is comparable to \(M_{GUT}\). And yes, the vacuum issue energy density is comparable to the 4th ability of the neutrino masses. I guess that the experts inwards the cosmological constant work are aware of all these coincidences.




Similarly, Unruh as well as his Asian pals claim that the commons formula for the Hubble constant is also classical as well as naive. The commons ability constabulary formula for the Hubble constant starts alongside imagining the zero-point oscillators of the quantum fields that add together only about issue energy density. It has the quantum source but it's understood to survive a classical constant inwards the spacetime as well as it's inserted to the classical Einstein equations that are basically trusted at all scales.

Instead, Unruh et al. claim that it's of import to process the consequence of the vacuum issue energy density on the spacetime geometry quantum mechanically, too. In particular, they believe that it's of import to stress that the vacuum issue energy density isn't really a constant equally a component division of the spacetime. Instead, \(\rho(x,y,z,t)\) is profoundly oscillating equally a component division of the spacetime coordinates – much similar all quantum fields, simple or composite, are quantum fluctuating inwards whatever quantum plain theory.

It follows that inwards only about regions, the vacuum issue energy volition survive negative, inwards others, it volition survive positive. If you lot human face at regions that are smaller than the regions of the size where \(\rho(x,y,z,t)\) likes to alter the sign, the commons intuition is said to survive basically right as well as the effects of the cosmological constant are huge. However, most of these effects are claimed to cancel out. On laissez passer on of that, they desire to believe that due to the asymmetric geometry of the positive as well as negative \(\rho\), the expanding geometry wins a footling flake when you lot human face at real long scales comparable to the size of the Universe as well as that's why nosotros instruct only about leftover accelerating expansion.

It's cool that they verbalize well-nigh the fluctuations of the stress-energy tensor, particularly because of e.g. the equation 29\[

\langle T_{ij}^2 \rangle \sim \langle T_{00}^2 \rangle

\] The expectation values of the squared stress-energy tensor is clearly relevant for the quantification of the quantum oscillations. But inwards my picture, it was also helpful because I wanted to justify or rationalize a seesaw formula for the vacuum energy. That would survive small. They enjoin that the Ansatz for the effective cosmological constant is exponentially pocket-size as well as so the parameteric dependence is dissimilar but at that spot is at to the lowest degree i shared take in betwixt me as well as Unruh et al.: To bargain alongside the effects of the vacuum issue energy density properly, you lot demand to consider non only the one-point component division of the stress-energy tensor but the two-point function, too.

The reasons why their Hubble expansion charge per unit of measurement has the exponentially pocket-size slice remains incomprehensible to me. The newspaper is based on sort of simple physics; but it nevertheless talks well-nigh many things. It sure contains lots of "curved complexities" that don't seem essential to sympathise why they instruct the exponential decrease. This sounds real non-Unruhy: Unruh has constitute the thermal radiations seen past times an accelerating observer which was really a simplified cousin of Hawking's derivation of his radiation. All the curved shape problems accept been removed. It would accept been to a greater extent than logical for the Unruh radiations to survive discovered first, as well as the Hawking radiations of an actual dark hole afterwards. History has proceeded illogically: Hawking belike constitute "his" radiations starting fourth dimension because of his excessive encephalon power. Excessive encephalon ability sometimes makes the people solve harder problems earlier they solve the to a greater extent than simple ones. Just to survive sure, these compliments aren't meant to contradict the observation that Hawking is an idiot if he believes that the mankind must as well as volition leave of absence public inwards 100 years.

Here, Unruh et al. are deriving something rather complicated to start alongside but I experience that nosotros don't demand all the complicated things as well as tangents etc.

I am open-minded to the possibility that the newspaper contains a grain of the truth which would survive wonderful. It would survive shocking if it were truthful as well as if the solution to the one-time cosmological constant would survive constitute only about 17 years after the enthusiasm well-nigh the cosmological constant work peaked. (I accept ever stressed that I constitute the claims that "the cosmological constant work is the deepest mystery of physics" to survive exaggerated – as well as it was ever conceivable that the work was rather pocket-size as well as isolated from the genuinely deep as well as universal wisdom of physics.) But it's possible. Even if the toad of truth squatteth inwards this swamp of unbalanced formulas of the Unruh et al. newspaper (thanks, Sheldon Cooper), I would dearest to run across that these unorthodox formulae may survive compatible alongside to a greater extent than consummate theories of quantum gravity such equally string/M-theory, or at to the lowest degree instruct only about "excuse" inwards supergravity.