What is the relationship between vacuum energy and gravity, particularly in terms of gravitational effects and its contribution to the overall cosmological constant? Does vacuum energy possess gravitational properties that affect the cosmological constant, and if so, how? Some sources argue that vacuum energy does not gravitate (see https://arxiv.org/abs/2005.07017). Could anyone provide insights on whether vacuum energy can or cannot gravitate and elaborate on the interplay between vacuum energy and gravity?
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$\begingroup$ In his 2011 pop-sci book titled "The 4% Universe", Panek makes an interesting comment saying that Newton saw gravity as a "force acting across space", whereas Einstein saw it as "a feature or characteristic [I forget which term Panek used] of space", so you might want to be aware that some physicists (Panek interviewed several) do not consider gravity to be a "force" at all. I think that that same consideration is implicit in some of the "energy conditions" formulated by Hawking & Penrose. $\endgroup$– EdouardCommented Jul 10, 2023 at 6:17
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2 Answers
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We don't know at the current state whether vacuum energy gravitate or not. An Experiment (Archimedes) in which i took a very very little part is proposed to investigate such a possibility. The key idea is to turn on and off the Casimir effect between a set of plates and use an equivalent of a two plates scale to measure via interferometry whether the vacuum fluctuations gravitate or not.
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Pertubation fields, that are introduced to correct the ill adapted, nearly free Lagrangians for interacting fields, are no invariant parts of the energy-momentum tensor.
Generally, the perturbation approximations are supposed to be translated in momentum space, renormmalized, in such a way, that their gound state has energy zero.
Vacuum electromagnetic fields e.g. in a capacitor are another expression of the corrrelated fluctuations of the electron field in the plates, in its Fermi distribtion of the free electron gas at 10^4 eV at T=0, so any energy-momentum is probably accounted for already in the matter field.
See Arthur Jaffes disillusioning work on the Casimir effect and its dependence on the geometry of the boundary conditions and its interpretation as the mirror effect of charge density fluctuations in the ground state of a partial filled conduction band.
