In cosmology, the cosmological constant problem
or vacuum catastrophe is the disagreement
between the observed values of vacuum energy
density (the small value of the cosmological
constant) and theoretical large value of zero-point
energy suggested by quantum field theory.
Depending on the Planck energy cutoff and
other factors, the discrepancy is as high
as 120 orders of magnitude, 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."
== Overview ==
The basic problem of a vacuum energy producing
a gravitational effect was identified as early
as 1916 by Walther Nernst.
The value was predicted to be either zero
or very small, so that the theoretical problem
was already apparent, and began to be actively
discussed in the 1970s.
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 leads to huge differences in the resulting
cosmologies.
== 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 Zel’dovich (1967, 1968).
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 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, contribution to the cosmological
constant because the existing vacuum has negative
quantum-mechanical pressure, and 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.
=== 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.
== Proposed solutions ==
Some physicists propose an anthropic solution,
and argue that we live in one region of a
vast multiverse that has different regions
with different vacuum energies.
These anthropic arguments posit that only
regions of small vacuum energy such as the
one we live in are reasonably capable of supporting
intelligent life.
Such arguments have existed in some form since
at least 1981.
Around 1987, Steven Weinberg 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, 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 involving modifying gravity to diverge
from the 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.
=== Quantum field theory prediction based
on light front quantization ===
Light front quantization is a rigorous alternative
due to Paul Dirac to the usual second quantization
method (instant-form method).
causality and frame-independence (Poincaré
invariance) are explicit, contrary to quantization
in the instant-form method.
The light-front quantization shows that a
properly defined (i.e. causal and Poincaré
invariant) vacuum state has no Vacuum fluctuations.
Technically, this is because in the Light-Front
vacuum, all particles have positive momenta
p+= p0+p3.
Since momentum is conserved, particles cannot
couple to the light front vacuum since it
has p+=0.
These features make the quantum field theory
vacuum essentially trivial, with no vacuum
dynamics such as condensate (i.e. vacuum expectation
value).
In contrast, vacuum fluctuations appear in
the vacuum of the ordinary instant-form (the
lowest energy eigenstate of the instant-form
Hamiltonian), but the physical effects depend
on the arbitrary choice of Lorentz frame.
This fact and the violation of causality indicate
that the instant-form vacuum cannot represent
of the physical vacuum.
While the features of the LF vacuum have been
known for a long time, in 2011, Stanley Brodsky
and Robert Shrock showed that the absence
of condensates implies that in the Standard
Model of Particle Physics, there is no contribution
from QED, Weak interactions and QCD to the
cosmological constant.
It is thus predicted to be zero in a flat
space-time.
This was later validated and developed, by
other prominent QCD theorists.
In the case of the Higgs mechanism, the usual
Higgs vacuum expectation value in the instant-form
vacuum is replaced by a constant scalar background
field - a "zero mode" with kμ=0.
The phenomenological predictions are unchanged
using the LF formalism.
Since the Higgs zero mode has no energy or
momentum density, it does not contribute to
the cosmological constant.
The necessity of performing the Quantum Field
Theory vacuum calculations using the LF form
can be understood using the following analogy
with classical mechanics.
First, one needs to recall that the LF form
enforces essential features of general physics:
causality, Poincaré invariance and Lorentz
boosts that are purely kinematical.
In contrast, calculations using the Instant
Form violate causality, break Poincaré invariance
and require Lorentz boosts that introduce
uncontrolled dynamical corrections.
These properties of the instant form means
that the boosts mix the well-controlled kinematics
of the problem with complex dynamics arising
from the force fields.
As Paul Dirac emphasized, boosts are dynamical
in instant form, and thus require as complicated
an analysis as solving the dynamical (bound-state)
problem itself.
The analogy with classical mechanics would
be that doing LF calculation is analogous
to classical calculations in inertial frames,
which keep force and kinematics separated.
In contrast, using the Instant-Form is analogous
of using non-inertial frames in classical
mechanics.
Non-inertial frames produce fictitious forces
which thereby mixes dynamics and kinematics.
These fictitious forces are typically irrelevant
to the internal dynamics of the system and
complicate its study.
In term of energies, the mixing of dynamics
and kinematics results in mixing potential
and kinematical energies (see e.g. Fictitious_force#Fictitious_forces_and_work)
Thus, the Lorentz-dependent and acausal determination
of the vacuum energy by Instant-form calculations
may be thought as similar to generating fictitious
potential energies in classical mechanics
when non-inertial frames are used.
The small non-zero value of the cosmological
constant must then be attributed to other
mechanisms; for example a slight curvature
of the shape of the universe (which is not
excluded within 0.4% (as of 2017)) could modify
the Higgs field zero-mode, thereby possibly
producing a non-zero contribution to the cosmological
constant.
== See also ==
List of unsolved problems in physics
Ultraviolet catastrophe
