This insert explicates cosmological constant and dark energy.
The two quantities are NOT the same thing: the cosmological constant and dark energy are NOT the same thing, but when dark energy is a CONSTANT dark energy, they have the same effect in Friedmann equation (FE) and the Friedmann equation models, and so they are often conflated in casual discussion and referred to as Lambda the name for the capital Greek letter Λ which is the symbol for the cosmological constant.
Context tells you whether by Lambda you mean one or the other or both or either. In the context of discussion of the Friedmann equation models just in themselves, one usually means either.
Yours truly has come to the idiosyncratic conclusion that yours truly will refer to the cosmological constant as the simplest form of the dark energy even though it is NOT really a form of energy at all in a strict general relativity sense. This is just the best way of dealing the ambiguity in physics and speech between cosmological constant and dark energy in yours truly's opinion.
Note that when we say dark energy without qualification we usually mean dark energy constant in cosmic time and space. There are theories where dark energy varies in cosmic time and probably in space and when we refer to that varying dark energy, we usually say dynamical dark energy---which we do NOT mention often in Introductory Astronomy Lectures (IAL).
However, for various reasons of historical interest, he wanted a static cosmological model---one that was full of stars spread approximately uniformly through space since he did NOT know about or at least not much about galaxies in 1917. For why he wanted these things, see IAL 30: Cosmology: The Static Universe Assumption.
In fact, Einstein could NOT find a static cosmological model with general relativity as he had originally proposed it (No-520).
Also, in fact, he could NOT find any cosmological model with general relativity as he had originally proposed it (Cormac O'Raifeartaigh et al., Einstein's 1917 Static Model of the Universe: A Centennial Review, 2017; Cormac O'Raifeartaigh, Historical and Philosophical Aspects of the Einstein World, 2019). Such cosmological models exist---plenty of them. We call them the Friedmann equation (FE) models and they have been the standard cosmological models ever since the 1920s, when Alexander Friedmann (1888--1925), and Georges Lemaitre (1894--1966) derived the Friedmann equation from general relativity and found the earliest Friedmann equation (FE) models.
But Einstein did NOT find the Friedmann equation, and so could NOT find Friedmann equation (FE) models.
You must understand his search for a cosmological model was a pioneering effort before general relativity had been explored by any other of the great minds.
Einstein describe his search as a "rough and winding road" (Cormac O'Raifeartaigh et al., Einstein's 1917 Static Model of the Universe: A Centennial Review, 2017, p. 18).
As Einstein used it cosmological constant term is NOT a form of energy at all in a strict general relativity sense. It is a term that affects the geometry of spacetime.
However, the geometry of spacetime does encode energy in a non-local way: i.e., in a way that does NOT allow you to say there is so much energy here or there. For a further discussion of this intriguing point, see Non-Local Encoding of Energy in General Relativity in Cosmology file: cosmological_redshift.html.
The repulsion could be considered at kind of anti-gravity, but its NOT what one ordinarily means by that term and no one calls it that.
UNDER CONSTRUCTION BELOW
Dark energy formally has NEGATIVE PRESSURE, but since it does NOT push on anything, in fact, this NEGATIVE PRESSURE is sort of mythical.
Note the name and concept of dark energy only came into general use circa 1998, but the concept of dark energy was actually first introduced (with no apparent historical impact) by Erwin Schroedinger (1887--1961) in 1918 (see Astronomer file: erwin_schroedinger.html).
Actually, the first person to notice the effective equivalence of the cosmological constant and constant dark energy was none other than Erwin Schroedinger (1887--1961) in 1918, but he did NOT use the modern term dark energy (see Cormac O'Raifeartaigh, Historical and Philosophical Aspects of the Einstein World, 2019, p. 13).
For an image of Erwin Schroedinger (1887--1961), see the figure below (local link / general link: erwin_schroedinger.html).
Often one just says Lambda instead of the cosmological constant.
Below we sometime say the cosmological constant Λ for clarity.
They change from
8*π*G 8*π*G G_{ik} = ----- T_{ik} to G_{ik} + Λ*g_{ik} = ----- T_{ik} , c**4 c**4where Λ is the cosmological constant, of course, and g_{ik} is the metric tensor of general relativity which describes the geometry of spacetime.
The cosmological constant was an ad hoc hypothesis to obtain a STATIC MODEL, but at least it was just about the simplest modification of the Einstein field equations that one could imagine and it was sufficiently small that it had NO significant effect on any gravitational phenomena other than that of the universe as a whole.
An ad hoc hypothesis is a hypothesis invented to make a theory give a very specific effect. Because theories are should be general ad hoc hypotheses are likely to be wrong.
For example, leprechauns are the cause of ... For leprechauns see the figure below (local link / general link: leprechaun.html).
A fudge factor is a quantity one just inserts into a calculation to get the answer one expects---fudge factor because one cooks it up.
Students too are quite adept at creating fudge factors on tests.
The cosmological constant is arguably a fudge factor.
But yours truly argues that the cosmological constant is NOT a fudge factor and NOT so bad as ad hoc hypotheses go.
It satisfies Occam's razor in that is the simplest and most natural way of getting a STATIC MODEL of the universe from the Einstein field equations.
The cosmological constant hypothesis is NOT a case of a hodge-podge of hypotheses that have little chance of being right.
So it could be argued that cosmological constant STATIC MODEL had some chance of being right if Einstein's assumption of a static universe had been right---which it wasn't.
But what does the cosmological constant mean physically?
In the Einstein field equations, Lambda just appears as a modification to how gravity affects spacetime. It is a "just-so" modification.
The cosmological constant is sort of an anti-gravity, but we do NOT call it that and it is NOT symmetric with gravity in any simple way.
In modern physics, there is a strong preference to interpret Lambda as representing a constant dark energy. The dark energy just grows with the expansion of space adding a balanced amount of relative kinetic energy and gravitational potential energy such as to keep the space growing at a constant relative rate (a time-constant Hubble constant) if there were no other mass-energy forms in the observable universe.
The dark energy is often said to have NEGATIVE PRESSURE, but this is so far just a formal NEGATIVE PRESSURE since the NEGATIVE PRESSURE does NOT pull on anything. The NEGATIVE PRESSURE is, in fact, a formal thermodynamics effect if you want to think of the dark energy in a certain hypothetical way.
We call the dark energy by that name because we don't see it so far in any other way than through its effect on the universal expansion. It's very "dark". For another thing very dark, see the figure below (local link / general link: vantablack.html).
Now constant dark energy has a constant energy density in time and space. It is about the simplest kind of dark energy imaginable.
That the cosmological-constant dark energy density is constant in time is UNUSUAL. For example, matter density must decrease because of the expansion of the universe. In fact, as cosmic scale factor a(t) increases, volumes increase by a(t)**3, and matter density falls as a(t)**(-3).
The cosmological-constant dark energy density can be treated as a contribution to Omega: we denote this contribution by Omega_Lambda.
Answer 2 and 3 are right. But answer 3 is best in this context.
But the dark energy need NOT have constant density in either time or space and it may interact with other forms of mass-energy in ways we do NOT know.
Until circa 2018, nothing in the observations told us to go beyond the simple theory of cosmological-constant dark energy.
But currently, there is Hubble tension: see the discussion in the figure below (local link / general link: hubble_constant_problem.html).
Yes, quantum field theory (i.e., relativistic quantum mechanics) suggests there could be cosmological-constant dark energy, but alas predicts its density to be 10**120 times bigger than needed to fit the observed acceleration (e.g., Carroll, S. 2003, p. 3, Why is the Universe Accelerating?).
This remarkable OVERESTIMATE suggests that the dark energy is more complex than the simple cosmological-constant dark energy with a density which is constant in time and space.
Another remarkable thing about dark energy is that the cosmological-constant dark energy density from the analysis of the CMB data is Omega_Lambda = 0.6853(74), which is COMPARABLE to the matter density Omega_matter = 0.3147(74). The reference for these values is Planck 2018 results. I. Overview and the cosmological legacy of Planck 2018. There may be some deep reason why the dark energy and matter should be COMPARABLE in which case the dark energy CANNOT be simply a cosmological-constant dark energy.
On the other hand, possibly the COMPARABILITY of Omega_Lambda = 0.6853(74) and Omega_matter = 0.3147(74) (Planck 2018 results. I. Overview and the cosmological legacy of Planck 2018) is explained by the anthropic principle. (See IAL 0: A Philosophical and Historical Introduction to Astronomy: The Anthropic Principle.)
Say there are an infinity or a quasi-infinity of pocket universes in a multiverse with different parameters set by some probability distribution of parameters.
Those NOT somewhat like our own in mass-energy contents may NOT be able to support life.
Too small a cosmological-constant dark energy density and the universe may NOT have formed the right kind of galaxies and stars.
Too large a cosmological-constant dark energy density and the universe would have expanded too quickly ever to form galaxies and stars.
So the ratio of dark energy and matter may just be a roll of the pocket universe parameter dice.
Now it is very hard to prove an argument based on the anthropic principle.
But such an argument could be falsified if the dark energy density and matter density (the sum of dark matter density and baryonic matter density) were fine-tuned beyond the needs (so far as we can tell) of making our pocket universes suitable for us to be here.
For example, the ratio is now of dark energy density to matter density is approximately 2 to 1.
If the ratio were exactly 2 to 1, that is more exactness than is needed for a pocket universe to that can support life like us, and strongly suggests dark energy and matter---NOT just that random throw of the pocket universe parameter dice.
But there is NOT such exactness, and so the multiverse passes this significant falsification test.