In
cosmology
Cosmology () is a branch of physics and metaphysics dealing with the nature of the universe. The term ''cosmology'' was first used in English in 1656 in Thomas Blount (lexicographer), Thomas Blount's ''Glossographia'', and in 1731 taken up in ...
, the cosmological constant problem or vacuum catastrophe is the disagreement between the observed values of
vacuum energy
Vacuum energy is an underlying background energy that exists in space throughout the entire Universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.
The effects of vacuum energy can be experimental ...
density
Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...
(the small value of the
cosmological constant
In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant,
is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...
) and theoretical large value of
zero-point energy
Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly Quantum fluctuation, fluctuate in their lowest energy state as described by the Heisen ...
suggested by
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
.
Depending on the
Planck energy cutoff and other factors, the quantum vacuum energy contribution to the effective cosmological constant is calculated to be as little as 50 and as much as 120 orders of magnitude greater than observed,
a state of affairs described by physicists as "the largest discrepancy between theory and experiment in all of science"
and "the worst theoretical prediction in the history of physics".
History
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,
W. 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/c
2~10
6), 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."
[
]
.
[
With the development of ]inflationary cosmology
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of the universe, expansion of space in the early universe. The inflationary epoch lasted from seconds after the conje ...
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
The expansion of the universe is the increase in distance between any two given gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion whereby the scale of space itself changes. The universe does not exp ...
would not accelerate
In mechanics, acceleration is the rate of change of the velocity of an object with respect to time. Accelerations are vector quantities (in that they have magnitude and direction). The orientation of an object's acceleration is given by the ...
as observed, according to the standard Λ-CDM model.
Quantum description
After the development of quantum field theory in the 1940s, the first to address contributions of quantum fluctuations to the cosmological constant was Yakov Zel'dovich. 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 orders of magnitude; however, modern research suggests that, when Lorentz invariance
In a relativistic theory of physics, a Lorentz scalar is an expression, formed from items of the theory, which evaluates to a scalar, invariant under any Lorentz transformation. A Lorentz scalar may be generated from e.g., the scalar product of ...
is taken into account, the degree of mismatch is closer to 60 orders of magnitude.
The calculated vacuum energy is a positive, rather than negative, contributing 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
In the Standard Model of particle physics, the Higgs mechanism is essential to explain the generation mechanism of the property "mass" for gauge bosons. Without the Higgs mechanism, all bosons (one of the two classes of particles, the other bein ...
during the quark epoch
In physical cosmology, the Quark epoch was the period in the evolution of the early universe when the fundamental interactions of gravitation, electromagnetism, the strong interaction and the weak interaction had taken their present forms, but th ...
.
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. 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.
Estimated values
Proposed solutions
Some physicists propose an anthropic solution, and argue that we live in one region of a vast multiverse
The multiverse is a hypothetical group of multiple universes. Together, these universes comprise everything that exists: the entirety of space, time, matter, energy, information, and the physical laws and constants that describe them. The di ...
that has different regions with different vacuum energies. These anthropic arguments posit that only regions of small vacuum energy such as the one in which we live are reasonably capable of supporting intelligent life. Such arguments have existed in some form since at least 1981. Around 1987, Steven Weinberg
Steven Weinberg (; May 3, 1933 – July 23, 2021) was an American theoretical physicist and Nobel laureate in physics for his contributions with Abdus Salam and Sheldon Glashow to the unification of the weak force and electromagnetic interactio ...
estimated that the maximum allowable vacuum energy for gravitationally-bound structures to form is problematically large, even given the observational data available in 1987, and concluded the anthropic explanation appears to fail; however, more recent estimates by Weinberg and others, based on other considerations, find the bound to be closer to the actual observed level of dark energy.[ Anthropic arguments gradually gained credibility among many physicists after the discovery of dark energy and the development of the theoretical ]string theory landscape
The string theory landscape or landscape of vacua refers to the collection of possible false vacua in string theory,The number of metastable vacua is not known exactly, but commonly quoted estimates are of the order 10500. See M. Douglas, "The ...
, but are still derided by a substantial skeptical portion of the scientific community as being problematic to verify. Proponents of anthropic solutions are themselves divided on multiple technical questions surrounding how to calculate the proportion of regions of the universe with various dark energy constants.
Other proposals involve modifying gravity to diverge from general relativity
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
. 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
The ΛCDM (Lambda cold dark matter) or Lambda-CDM model is a Parameter#Modelization, parameterization of the Big Bang physical cosmology, cosmological model in which the universe contains three major components: first, a cosmological constant de ...
, 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.
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. Going in a different direction, George F. R. Ellis
George Francis Rayner Ellis, FRS, Hon. FRSSAf (born 11 August 1939), is the emeritus distinguished professor of complex systems in the Department of Mathematics and Applied Mathematics at the University of Cape Town in South Africa. He co-auth ...
and others have suggested that in unimodular gravity In mathematics, unimodular may refer to any of the following:
* Unimodular lattice
* Unimodular matrix
* Unimodular polynomial matrix
* Unimodular form
* Unimodular group In mathematical analysis, the Haar measure assigns an "invariant volume" to ...
, the troublesome contributions simply do not gravitate.
Another argument, due to Stanley Brodsky and Robert Shrock, is that in light front quantization, the quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
vacuum becomes essentially trivial. In the absence of vacuum expectation values, there is no contribution from QED, weak interactions
In nuclear physics and particle physics, the weak interaction, which is also often called the weak force or weak nuclear force, is one of the four known fundamental interactions, with the others being electromagnetism, the strong interaction ...
and QCD
In theoretical physics, quantum chromodynamics (QCD) is the theory of the strong interaction between quarks mediated by gluons. Quarks are fundamental particles that make up composite hadrons such as the proton, neutron and pion. QCD is a ty ...
to the cosmological constant. It is thus predicted to be zero in a flat space-time
In physics, spacetime is a mathematical model that combines the three-dimensional space, three dimensions of space and one dimension of time into a single four-dimensional manifold. Minkowski diagram, Spacetime diagrams can be used to visualize S ...
.
In 2018, a mechanism for cancelling Λ out has been proposed through the use of a symmetry breaking
In physics, symmetry breaking is a phenomenon in which (infinitesimally) small fluctuations acting on a system crossing a critical point decide the system's fate, by determining which branch of a bifurcation is taken. To an outside observe ...
potential in a Lagrangian formalism in which matter shows a non-vanishing pressure. The model assumes that standard matter provides a pressure which counterbalances the action due to the cosmological constant. Luongo and Muccino have shown that this mechanism permits to take vacuum energy as quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
predicts, but removing the huge magnitude through a counterbalance term due to baryons
In particle physics, a baryon is a type of composite subatomic particle which contains an odd number of valence quarks (at least 3). Baryons belong to the hadron family of particles; hadrons are composed of quarks. Baryons are also classified ...
and cold dark matter
In cosmology and physics, cold dark matter (CDM) is a hypothetical type of dark matter. According to the current standard model of cosmology, Lambda-CDM model, approximately 27% of the universe is dark matter and 68% is dark energy, with only a sm ...
only.
In 1999, Andrew Cohen, David B. Kaplan and Ann Nelson
Ann Elizabeth Nelson (April 29, 1958 – August 4, 2019) was a particle physicist and professor of physics in the Particle Theory Group at the University of Washington from 1994 until her death. Nelson received a Guggenheim Fellowship in 200 ...
proposed that correlations between the UV and IR cutoffs in effective
Effectiveness is the capability of producing a desired result or the ability to produce desired output. When something is deemed effective, it means it has an intended or expected outcome, or produces a deep, vivid impression.
Etymology
The ori ...
quantum field theory
In theoretical physics, quantum field theory (QFT) is a theoretical framework that combines classical field theory, special relativity, and quantum mechanics. QFT is used in particle physics to construct physical models of subatomic particles and ...
are enough to reduce the theoretical cosmological constant down to the measured cosmological constant due to the CKN bound. In 2021, Nikita Blinov and Patrick Draper confirmed through the holographic principle
The holographic principle is an axiom in string theories and a supposed property of quantum gravity that states that the description of a volume of space can be thought of as encoded on a lower-dimensional boundary to the region — such as a ...
that the CKN bound predicts the measured cosmological constant, all while maintaining the predictions of effective field theory in less extreme conditions.
See also
* List of unsolved problems in physics
*Ultraviolet catastrophe
The ultraviolet catastrophe, also called the Rayleigh–Jeans catastrophe, was the prediction of late 19th century/early 20th century classical physics that an ideal black body at thermal equilibrium would emit an unbounded quantity of energy ...
* Weak gravity conjecture
References
External links
*
{{Portal bar, Physics, Astronomy, Stars, Spaceflight, Outer space, Solar System
Physical cosmology
Physics beyond the Standard Model