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- "The vacuum energy density is treated as a constant in the usual formulation of the cosmological constant problem. While this is true for the expectation value, it is not true for the actual energy density."

Hi all,

Just had a look at the 2016 paper by Wang, Zhu, and Unruh,

"How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe," Qingdi Wang, Zhen Zhu, and William G. Unruh, Phys. Rev. D 95, 103504 – Published 11 May 2017

The paper states (Section III):

"The vacuum energy density is treated as a constant in the usual formulation of the cosmological constant problem. While this is true for the expectation value, it is not true for the actual energy density.

That is because the vacuum is not an eigenstate of the local energy density operator $T_00$, although it is an eigenstate of the global Hamiltonian operator H. This implies that the total vacuum energy all over the space is constant but its density fluctuates at individual points.

...

Furthermore, the energy density of the vacuum is not only not a constant in time at a fixed spatial point, it also varies from place to place. In other words, the energy density of vacuum is varying wildly at every spatial point and the variation is not in phase for different spatial points. This results in an extremely inhomogeneous vacuum."

This seems to patently violate the description of vacuum fluctuations in @A. Neumaier's Insight articles and in his Physics FAQ. Also, since the fields are in the ground state everywhere in spacetime, how can energy density change? Lastly, the authors use a cutoff to recover the slow expansion... doesn't this break Lorentz invariance?

I'm very puzzled, but it's a paper with Unruh, so... clarifications welcome.

p.s., In a 2018 follow on paper, the abstract states that "By treating the fluctuations in the vacuum seriously..." - I'm not clear what this means, either.

Thanks all.

Just had a look at the 2016 paper by Wang, Zhu, and Unruh,

"How the huge energy of quantum vacuum gravitates to drive the slow accelerating expansion of the Universe," Qingdi Wang, Zhen Zhu, and William G. Unruh, Phys. Rev. D 95, 103504 – Published 11 May 2017

The paper states (Section III):

"The vacuum energy density is treated as a constant in the usual formulation of the cosmological constant problem. While this is true for the expectation value, it is not true for the actual energy density.

That is because the vacuum is not an eigenstate of the local energy density operator $T_00$, although it is an eigenstate of the global Hamiltonian operator H. This implies that the total vacuum energy all over the space is constant but its density fluctuates at individual points.

...

Furthermore, the energy density of the vacuum is not only not a constant in time at a fixed spatial point, it also varies from place to place. In other words, the energy density of vacuum is varying wildly at every spatial point and the variation is not in phase for different spatial points. This results in an extremely inhomogeneous vacuum."

This seems to patently violate the description of vacuum fluctuations in @A. Neumaier's Insight articles and in his Physics FAQ. Also, since the fields are in the ground state everywhere in spacetime, how can energy density change? Lastly, the authors use a cutoff to recover the slow expansion... doesn't this break Lorentz invariance?

I'm very puzzled, but it's a paper with Unruh, so... clarifications welcome.

p.s., In a 2018 follow on paper, the abstract states that "By treating the fluctuations in the vacuum seriously..." - I'm not clear what this means, either.

Thanks all.

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