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Cosmological constant problem
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Cosmological constant problem
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 Planck energy cutoff and other factors, the quantum vacuum energy contribution to the effective cosmological constant is calculated to be between 50 and as many as 120 orders of magnitude greater than has actually been observed, a state of affairs described by physicists as "the largest discrepancy between theory and experiment in all of science" and "probably the worst theoretical prediction in the history of physics".
The basic problem of a vacuum energy producing a gravitational effect was identified as early as 1916 by Walther Nernst. 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."
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. 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. Original estimates of the degree of mismatch were as high as 120 to 122 orders of magnitude; however, modern research suggests that, when Lorentz invariance is taken into account, the degree of mismatch is closer to 60 orders of magnitude.
With the development of inflationary cosmology in the 1980s, the problem became much more important: as cosmic inflation is driven by vacuum energy, differences in modeling vacuum energy lead to huge differences in the resulting cosmologies. Were the vacuum energy precisely zero, as was once believed, then the expansion of the universe would not accelerate as observed, according to the standard Λ-CDM model.
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 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.
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.
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Cosmological constant problem
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 Planck energy cutoff and other factors, the quantum vacuum energy contribution to the effective cosmological constant is calculated to be between 50 and as many as 120 orders of magnitude greater than has actually been observed, a state of affairs described by physicists as "the largest discrepancy between theory and experiment in all of science" and "probably the worst theoretical prediction in the history of physics".
The basic problem of a vacuum energy producing a gravitational effect was identified as early as 1916 by Walther Nernst. 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."
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. 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. Original estimates of the degree of mismatch were as high as 120 to 122 orders of magnitude; however, modern research suggests that, when Lorentz invariance is taken into account, the degree of mismatch is closer to 60 orders of magnitude.
With the development of inflationary cosmology in the 1980s, the problem became much more important: as cosmic inflation is driven by vacuum energy, differences in modeling vacuum energy lead to huge differences in the resulting cosmologies. Were the vacuum energy precisely zero, as was once believed, then the expansion of the universe would not accelerate as observed, according to the standard Λ-CDM model.
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 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.
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.
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