marvas:

If what you mean by "vacuum" is the background spacetime without particles, then that probably doesn't exist, as far as can we can observe.

Dark energy, the repulsive force that is the dominant component (69.4 percent) of the

universe. The remaining portion of the universe consists of ordinary

matter and

dark matter. Dark

energy, in contrast to both forms of matter, is relatively uniform in time and space and is gravitationally repulsive, not attractive, within the volume it occupies. The nature of dark energy is still not well understood.

A kind of

cosmic repulsive force was first hypothesized by

Albert Einstein in 1917 and was represented by a term, the “

cosmological constant,” that Einstein reluctantly introduced into his theory of general

relativity in order to counteract the attractive force of

gravity and account for a universe that was assumed to be static (neither expanding nor contracting). After the discovery in the 1920s by American astronomer

Edwin Hubble that the universe is not static but is in fact expanding, Einstein referred to the addition of this constant as his “greatest blunder.” However, the measured amount of matter in the mass-energy budget of the universe was improbably low, and thus some unknown “missing component,” much like the

cosmological constant, was required to make up the

deficit. Direct evidence for the existence of this component, which was dubbed dark energy, was first presented in 1998.

Dark energy is detected by its effect on the rate at which the

universe expands and its effect on the rate at which large-scale structures such as

galaxies and

clusters of galaxies form through gravitational instabilities. The measurement of the expansion rate requires the use of

telescopes to measure the distance (or light travel time) of objects seen at different size scales (or

redshifts) in the history of the universe. These efforts are generally limited by the difficulty in accurately measuring astronomical distances. Since dark energy works against gravity, more dark energy

accelerates the universe’s expansion and retards the formation of large-scale structure. One technique for measuring the expansion rate is to observe the apparent brightness of objects of known luminosity like

Type Ia supernovas. Dark energy was discovered in 1998 with this method by two international teams that included American astronomers

Adam Riess (the author of this article) and

Saul Perlmutter and Australian astronomer

Brian Schmidt. The two teams used eight telescopes including those of the

Keck Observatoryand the

MMT Observatory. Type Ia supernovas that exploded when the universe was only two-thirds of its present size were fainter and thus farther away than they would be in a universe without dark energy. This implied the expansion rate of the universe is faster now than it was in the past, a result of the current dominance of dark energy. (Dark energy was

negligible in the early universe.)

Studying the effect of dark energy on large-scale structure involves measuring subtle distortions in the shapes of galaxies arising from the bending of space by intervening matter, a phenomenon known as “weak lensing.” At some point in the last few billion years, dark energy became dominant in the universe and thus prevented more galaxies and clusters of galaxies from forming. This change in the structure of the universe is revealed by weak lensing. Another measure comes from counting the number of clusters of galaxies in the universe to measure the volume of space and the rate at which that volume is increasing. The goals of most observational studies of dark energy are to measure its

equation of state (the ratio of its pressure to its energy density), variations in its properties, and the degree to which dark energy provides a complete description of gravitational physics.

matter-energy content of the universe
In cosmological theory, dark energy is a general class of components in the stress-energy tensor of the field equations in

Einstein’s theory of

general relativity. In this theory, there is a direct correspondence between the matter-energy of the universe (expressed in the tensor) and the shape of

space-time. Both the matter (or energy)

density (a positive quantity) and the internal pressure contribute to a component’s gravitational field. While familiar components of the stress-energy tensor such as matter and radiation provide attractive gravity by bending space-time, dark energy causes repulsive gravity through negative internal pressure. If the ratio of the pressure to the energy density is less than −1/3, a possibility for a component with negative pressure, that component will be gravitationally self-repulsive. If such a component dominates the universe, it will accelerate the universe’s expansion.

The simplest and oldest explanation for dark energy is that it is an energy density

inherent to empty space, or a “vacuum energy.” Mathematically,

vacuum energy is equivalent to Einstein’s cosmological constant. Despite the rejection of the cosmological constant by Einstein and others, the modern understanding of the vacuum, based on

quantum field theory, is that vacuum energy arises naturally from the totality of

quantum fluctuations (i.e., virtual particle-antiparticle pairs that come into existence and then

annihilate each other shortly thereafter) in empty space. However, the observed density of the cosmological vacuum energy density is ~10−10ergs per cubic centimetre; the value predicted from quantum field theory is ~10110 ergs per cubic centimetre. This discrepancy of 10120 was known even before the discovery of the far weaker dark energy. While a fundamental solution to this problem has not yet been found, probabilistic solutions have been posited, motivated by

string theory and the possible existence of a large number of disconnected universes. In this

paradigmthe unexpectedly low value of the constant is understood as a result of an even greater number of opportunities (i.e., universes) for the occurrence of different values of the constant and the random selection of a value small enough to allow for the formation of galaxies (and thus stars and life).

Another popular theory for dark energy is that it is a

transient vacuum energy resulting from the

potential energy of a

dynamical field. Known as “quintessence,” this form of dark energy would vary in space and time, thus providing a possible way to distinguish it from a cosmological constant. It is also similar in mechanism (though vastly different in scale) to the scalar field energy

invoked in the inflationary theory of the

big bang.

Another possible explanation for dark energy is topological defects in the fabric of the universe. In the case of

intrinsic defects in space-time (e.g., cosmic strings or walls), the production of new defects as the universe expands is mathematically similar to a cosmological constant, although the value of the equation of state for the defects depends on whether the defects are strings (one-dimensional) or walls (two-dimensional).

There have also been attempts to modify gravity to explain both cosmological and local observations without the need for dark energy. These attempts

invoke departures from general relativity on scales of the entire

observable universe.

A major challenge to understanding accelerated expansion with or without dark energy is to explain the relatively recent occurrence (in the past few billion years) of near-equality between the density of dark energy and

dark matter even though they must have evolved differently. (For cosmic structures to have formed in the early universe, dark energy must have been an insignificant component.) This problem is known as the “coincidence problem” or the “fine-tuning problem.” Understanding the nature of dark energy and its many related problems is one of the most

formidablechallenges in modern physics.

Adam Riess
See:

https://www.britannica.com/science/dark-energy#ref1025334
However, there is something called a metric field

** 𝑔𝜇𝜈**. At the level of quantum field theory, this field is generated by particles, or quanta (gravitons), which may in fact have a mass, if we could actually observe them. At this point, we have only indirect evidence of gravitons, and have not observed any at a particle collider, because gravitational interactions are quite weak. Another issue is that this view is only correct if you believe gravity is a gauge theory, which in physics pretty much means that the theory can be specified by establishing mathematical constraints on the fields. We really don't have a solid grasp on what a quantum theory of gravity should look like. For other fundamental forces, it's been possible to take the corresponding theory in the classical regime and "quantize" it (make it a quantum theory by using a strict set of rules). For gravity, this doesn't work, for a number of reasons.

Of course someone who studies something like non-equilibrium quantum field theory will probably say you can "excite" your vacuum -- meaning you can add energy to the natural background -- without necessarily creating massive particles. Then, the mass of these vacuum excitations is effectively zero because these excitations are purely the kinetic energy of the background field.

A second consequence of this formulation of the Heisenberg Uncertainty Principle is the possibility of vacuum energy. Consider a small region of space. Suppose that it’s empty; that is, you’ve taken out everything you can take out of it, including atoms, light (photons), dark matter, and so forth. Make sure that there are no quantum systems anywhere with non-negligible probability for being found in this region of space. Over a finite time interval Δ𝑡, you can’t be sure exactly how much energy there is in this region of space; your uncertainty in the amount of energy must be at least Δ𝐸=ℏ2Δ𝑡. As a result, there may be energy in the vacuum.

What is the expectation value of this energy? You might predict that the expectation should be 0, even though the uncertainty has to be greater than zero. Figuring it out requires going into relativistic quantum mechanics, called quantum field theory. Unfortunately, even quantum field theory can’t calculate that right, for naive estimates of what you’d get (the best we can really do) gives a value of the vacuum energy density that is so high that it would prevent galaxies from ever having formed in our Universe. The fact that you are reading this indicates that this estimate cannot be right. Indeed, quantum field theory estimates a value for the vacuum energy density that is 120 orders of magnitude too big! That’s pretty far off. As such, we have to say that we don’t completely understand the nature of vacuum energy.

What form would this vacuum energy take? We’ve already seen that in a finite time interval Δ𝑡, we can’t say with certainty that the vacuum has zero energy. In quantum field theory, it becomes possible to create and destroy particles, as long as you obey all of the conservation laws. For example, two photons can interact and create an electron/positron pair, where a positron is the antimatter partner to an electron. If you don’t have to worry about conserving energy, however, you can create a positron/electron pair out of absolutely nothing. . . as long as they re-annihilate back to absolutely nothing fast enough. For every fundamental particle that exists, this sort of thing is going on around us all the time.

What is the net energy density of the vacuum as a result of all of this?

See:

https://cds.cern.ch/record/582156/files/p1.pdf
For a long time, many physicists assumed that a various terms would cancel out to zero; the naive calculations indicated something absurd, and the most natural result if those calculations are wrong is that things would cancel out. However, in the last ten years, observations of the expansion of the Universe have shown that the expansion is accelerating; indeed, these astronomical observations were the source of the 2011 Nobel Prize in Physics. We don’t know what is causing this, and have given the name “dark energy” to whatever it is that is causing it. The simplest explanation for dark energy is that it is vacuum energy. Measurements from cosmology indicate a vacuum energy density corresponding to about 10−29 grams per cubic centimeter. That is, the energy density of vacuum energy is 29 orders of magnitude less than the mass-energy density of water. Obviously, we can ignore this in our every day life. However, if you look at the Universe as a whole, most of it is empty; our planet is a very special place that is, compared to most of the Universe, extremely dense with regular atoms. In the Universe as a whole, dark energy makes up three quarters of the energy density. Even though this density may be 120 orders of magnitude smaller than what naive estimates from our theory would suggest, it is coming to dominate the evolution of our Universe.

Hartmann352