Sequestering the Standard Model Vacuum Energy
Nemanja Kaloper · Antonio Padilla
Abstract and summary · read the original at the source · none found
In one page
Quantum field theory says empty space carries an enormous energy density. General relativity says every form of energy curves spacetime. Put the two together and the universe should have curled up long ago. Nemanja Kaloper, at UC Davis, and Antonio Padilla, at Nottingham, propose a minimal change to general relativity that lets both statements stand. They make every mass scale in the matter sector depend on the total four-volume of spacetime, and add two global quantities varied like constants rather than like fields. What comes out is Einstein’s equation with one extra term: the whole-history average of the trace of the matter stress tensor, subtracted from the source. That subtraction removes the vacuum energy exactly — the classical piece and every quantum loop correction — so it never curves anything. Nothing new propagates, and local physics is untouched. The price is a prediction: for those averages to be finite the universe must be finite in time, so today’s steady dark energy is a passing phase and a collapse lies ahead.
Why it matters hereChapter 2 has to answer the obvious objection to a vacuum holding some 10¹¹³ joules per cubic metre — why is the sky not violently curved? Kaloper and Padilla give one clean answer: the energy is entirely real, it simply does not source curvature, and what is left over is small for a reason rather than by a tuning. Chapter 13 needs exactly that separation between how much energy the vacuum holds and how much of it gravitates.
What it claims
01A minimal reformulation of general relativity sequesters all of a matter sector’s vacuum energy from gravity. Every dimensional parameter in that sector is made a functional of the four-volume element of the universe, by coupling matter to a rescaled metric and treating the rescaling and the cosmological term as global auxiliary variables, with an external function placed outside the integral.Abstract; Eqs. (1) and (2)
Published and peer-reviewed02The resulting field equations are Einstein’s with the four-volume historic average of the trace of the matter stress tensor subtracted from the source. Because that average of a constant is the constant itself, the hard cosmological constant — the classical piece plus vacuum loop corrections to any order — drops out of the equations completely and never contributes to curvature.Eq. (3), and Eq. (4) with the paragraph preceding it
Published and peer-reviewed03The mechanism adds no new propagating degrees of freedom. All propagating fields obey standard second-order equations, the spectrum of fluctuations is that of conventional general relativity with minimally coupled matter, and the dependence of the matter scales on the four-volume is invisible to any non-gravitational local experiment by diffeomorphism invariance.Paragraph 4 of the Letter; closing discussion, penultimate paragraph
Published and peer-reviewed04A residual cosmological constant survives — the historic average of the non-constant sources — and it is automatically small rather than tuned. Its size is set by the lifetime of the universe rather than by any ultraviolet cutoff, and two approximate symmetries, a scaling and a shift, make that smallness technically natural.Eq. (4) and the following two paragraphs; footnote 8
Published and peer-reviewed05Vacuum energy released by early-universe phase transitions does not drop out of the field equations, but is automatically suppressed at late times: the leftover is smaller than today’s critical density by a power of the ratio of the transition’s curvature scale to the universe’s lifetime scale, which for the Standard Model is a very large ratio.Eq. (6) and the paragraph after it
Published and peer-reviewed06Three observational consequences follow, and each is a test. The universe must be compact in spacetime — spatially closed, ending in a crunch, plausibly in around a hundred billion years — the vacuum curvature of a large old universe is small but not zero, and the measured dark-energy equation of state near minus one is a transient rather than a permanent state.Abstract; closing discussion, final two paragraphs
What to watch
Read it · abstract
Abstract
We propose a very simple reformulation of General Relativity, which completely sequesters from gravity all of the vacuum energy from a matter sector, including all loop corrections and renders all contributions from phase transitions automatically small. The idea is to make the dimensional parameters in the matter sector functionals of the 4-volume element of the universe. For them to be nonzero, the universe should be finite in spacetime. If this matter is the Standard Model of particle physics, our mechanism prevents any of its vacuum energy, classical or quantum, from sourcing the curvature of the universe. The mechanism is consistent with the large hierarchy between the Planck scale, electroweak scale and curvature scale, and early universe cosmology, including inflation. Consequences of our proposal are that the vacuum curvature of an old and large universe is not zero, but very small, that w_DE ≃ −1 is a transient, and that the universe will collapse in the future.
The way in
https://arxiv.org/abs/1309.6562LICENCE CHECK, 2026-09-08. The preprint arXiv:1309.6562v2, dated 30 April 2014, carries the arXiv.org perpetual non-exclusive distribution licence version 1.0 — read from the arXiv abstract page and confirmed in the INSPIRE-HEP record — which is not a Creative Commons grant. The version of record is Physical Review Letters 112, 091304, published 6 March 2014, under the APS default licence, and it drew a Physics Synopsis. No Creative Commons statement appears in the text. So this sheet carries the summary, the claims and the authors’ own abstract, and sends the reader to the source, where the nine-page Letter is free to read. The abstract below is the one printed on the preprint; the registry copy had picked up TeX markup, which is cleared here without changing a word. Section, equation and footnote numbers in the claims are the preprint’s. Kaloper writes from the Department of Physics, University of California, Davis; Padilla from the School of Physics and Astronomy, University of Nottingham. Read with Steven Weinberg’s statement of the problem at /library/stm-5610822bc8 and Jérôme Martin’s survey of the proposed answers at /library/stm-568da33759.
How to cite it
Nemanja Kaloper, Antonio Padilla (2013) Sequestering the Standard Model Vacuum Energy. doi:10.1103/PhysRevLett.112.091304
Where it sits in the curriculum
What the vacuum isInertia and gravity from the vacuumThe unified picture