Cosmological constant problem
Beyond the Standard Model |
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Standard Model |
Why is the vacuum energy density much smaller than a zero-point energy suggested by quantum field theory?
In cosmology, the cosmological constant problem or vacuum catastrophe is the substantial disagreement between the observed values of vacuum energy density (the small value of the cosmological constant) and the much larger theoretical value of zero-point energy suggested by quantum field theory.
Depending on the
History
The basic problem of a vacuum energy producing a gravitational effect was identified as early as 1916 by Walther Nernst.[4][5][6] He predicted that the value had to be either zero or very small. In 1926, Wilhelm Lenz concluded that "If one allows waves of the shortest observed wavelengths λ ≈ 2 × 10−11 cm, ... and if this radiation, converted to material density (u/c2 ≈ 106), contributed to the curvature of the observable universe – one would obtain a vacuum energy density of such a value that the radius of the observable universe would not reach even to the Moon."[7][6]
After the development of quantum field theory in the 1940s, the first to address contributions of quantum fluctuations to the cosmological constant was Yakov Zeldovich in the 1960s.[8][9] In quantum mechanics, the vacuum itself should experience quantum fluctuations. In general relativity, those quantum fluctuations constitute energy that would add to the cosmological constant. However, this calculated vacuum energy density is many orders of magnitude bigger than the observed cosmological constant.[10] Original estimates of the degree of mismatch were as high as 120 to 122 orders of magnitude;[11][12] however, modern research suggests that, when Lorentz invariance is taken into account, the degree of mismatch is closer to 60 orders of magnitude.[12][13]
With the development of
Cutoff dependence
The calculated vacuum energy is a positive, rather than negative, contribution to the cosmological constant because the existing vacuum has negative quantum-mechanical pressure, while in general relativity, the gravitational effect of negative pressure is a kind of repulsion. (Pressure here is defined as the flux of quantum-mechanical momentum across a surface.) Roughly, the vacuum energy is calculated by summing over all known quantum-mechanical fields, taking into account interactions and self-interactions between the ground states, and then removing all interactions below a minimum "cutoff" wavelength to reflect that existing theories break down and may fail to be applicable around the cutoff scale. Because the energy is dependent on how fields interact within the current vacuum state, the vacuum energy contribution would have been different in the early universe; for example, the vacuum energy would have been significantly different prior to electroweak symmetry breaking during the quark epoch.[12]
Renormalization
The vacuum energy in quantum field theory can be set to any value by renormalization. This view treats the cosmological constant as simply another fundamental physical constant not predicted or explained by theory.[15] Such a renormalization constant must be chosen very accurately because of the many-orders-of-magnitude discrepancy between theory and observation, and many theorists consider this ad-hoc constant as equivalent to ignoring the problem.[1]
Estimated values
The vacuum energy density of the Universe based on 2015 measurements by the Planck collaboration is ρvac = 5.96×10−27 kg/m3 ≘ 5.3566×10−10 J/m3 = 3.35 GeV/m3[16][note 1] or about 2.5×10−47 GeV4 in geometrized units.
One assessment, made by Jérôme Martin of the Institut d'Astrophysique de Paris in 2012, placed the expected theoretical vacuum energy scale around 108 GeV4, for a difference of about 55 orders of magnitude.[12]
Proposed solutions
Some proposals involve modifying gravity to diverge from general relativity. These proposals face the hurdle that the results of observations and experiments so far have tended to be extremely consistent with general relativity and the ΛCDM model, and inconsistent with thus-far proposed modifications. In addition, some of the proposals are arguably incomplete, because they solve the "new" cosmological constant problem by proposing that the actual cosmological constant is exactly zero rather than a tiny number, but fail to solve the "old" cosmological constant problem of why quantum fluctuations seem to fail to produce substantial vacuum energy in the first place. Nevertheless, many physicists argue that, due in part to a lack of better alternatives, proposals to modify gravity should be considered "one of the most promising routes to tackling" the cosmological constant problem.[17]
Bill Unruh and collaborators have argued that when the energy density of the quantum vacuum is modeled more accurately as a fluctuating quantum field, the cosmological constant problem does not arise.[18] Going in a different direction, George F. R. Ellis and others have suggested that in unimodular gravity, the troublesome contributions simply do not gravitate.[19][20]
Another argument, due to
In 2018, a mechanism for cancelling Λ out has been proposed through the use of a
In 1999, Andrew Cohen, David B. Kaplan and Ann Nelson proposed that correlations between the UV and IR cutoffs in effective quantum field theory are enough to reduce the theoretical cosmological constant down to the measured cosmological constant due to the Cohen–Kaplan–Nelson (CKN) bound.[25] In 2021, Nikita Blinov and Patrick Draper confirmed through the holographic principle that the CKN bound predicts the measured cosmological constant, all while maintaining the predictions of effective field theory in less extreme conditions.[26]
Some propose an anthropic solution,
See also
- List of unsolved problems in physics
- Ultraviolet catastrophe – Classical physics prediction that black body radiation grows unbounded with frequency
- Weak gravity conjecture – Conjecture that gravity must be the weakest force
Notes
- ^ Calculated based on the Hubble constant and the dark energy density parameter ΩΛ.
References
- ^ ISSN 0002-9505.
- S2CID 189762342. Retrieved 21 October 2022.
- ISBN 978-0-521-82951-9.
- ^ W Nernst (1916). "Über einen Versuch von quantentheoretischen Betrachtungen zur Annahme stetiger Energieänderungen zurückzukehren". Verhandlungen der Deutschen Physikalischen Gesellschaft (in German). 18: 83–116.
- ^
H Kragh (2011). "Preludes to dark energy: Zero-point energy and vacuum speculations". arXiv:1111.4623 [physics.hist-ph].
- ^ a b H Kragh (2012). "Walther Nernst: grandfather of dark energy?". Astronomy & Geophysics. 53 (1): 1.24–1.26. .
- ^ W Lenz (1926). """". Physikalische Zeitschrift (in German). 27: 642–645.
- ^ Zel'Dovich, Ya. B. (1967). "Cosmological Constant and Elementary Particles". JETP Letters. 6: 316–317.
- .
- .
- S2CID 122259372.
- ^ S2CID 119272967.
- arXiv:gr-qc/0208027.
- S2CID 122259372.
- S2CID 9007190.
- ISSN 0004-6361.
- ^ S2CID 118450389.
- S2CID 119076077.
- S2CID 119000135.
- S2CID 118934871.
- .
- S2CID 118373670.
- .
- S2CID 119346601.
- S2CID 17203575.
- arXiv:2107.03530 [hep-ph].
- S2CID 133086904. Retrieved 21 October 2022.
- ^ S2CID 5221573.
- S2CID 119064782.
External links
- .
- "The worst prediction in physics". YouTube. Fermilab. March 14, 2024. (video by Fermilab's Don "Dr. Don" Lincoln)