This insert explicates the cosmological constant and dark energy which are alternative theories used to reproduce the observed acceleration of the universe.
However, cosmological constant has been used since the beginning of modern cosmology 1917 for many reasons after having been introduced by Albert Einstein (1879--1955) who used to give his static Einstein universe (1917).
Despite being different intrinsically, cosmological constant and dark energy both have the same effect in the Friedmann equation and (so far as we know) in cosmology in general. They are different in other respects though those other effects are so far unobservable directly and indirectly.
It seems the vast majority of cosmologists favor the theory of dark energy over the cosmological constant because of the quantum field theory argument for it. And so cosmologists tend to just refer to dark energy with the usually unspoken qualification that the cosmological constant is also a viable theory. But there is a horrible ambiguity in discussions of the cause of the acceleration of the universe because of having two viable theories.
In fact, both cosmological constant and (constant) dark energy are symbolized the Greek upper case letter Λ.
For example, the Λ-CDM model uses Λ to mean either of cosmological constant or dark energy with most cosmologists favoring the latter in agreement with the above discussion.
Historically, however, Λ just meant the cosmological constant.
Yours truly uses either cosmological constant, dark energy, or conflates them as Λ as appropiate to the context.
Hopefully, one day one or other of the cosmological constant, constant dark energy, or non-constant dynamical dark energy (see below section Dynamical Dark Energy) will win out and end the ambiguity cosmological constant and dark energy
Of course, all three theories could be wrong or all three could be right, but this disfavored by Occam's razor.
However, for various reasons of historical interest,
Einstein wanted
a STATIC cosmological model---one
that was full of stars distributed
uniformly on average throughout
space.
Note, stars NOT
galaxies since no one
knew for sure about galaxies
in 1917 and
Einstein may have known nothing.
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).
As Einstein
used it, the cosmological constant
is NOT a form of energy
at all
in a strict general relativity sense.
It is a quantity 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.
In fact, Einstein had NO
accurate value for the fine tuning.
So Einstein's STATIC MODEL
had, in fact, an undetermined free parameter.
What if the cosmological constant
was NOT fine tuned for a STATIC MODEL.
The model would evolve in time, but Einstein
did NOT investigate that evolution
in 1917.
We call Einstein's STATIC MODEL
the Einstein universe (1917).
If he had derived it, then the
Einstein universe (1917)
and all simple
general relativistic
cosmological models
including the
Einstein universe (1917)
would have been easy to find.
In fact, the
Einstein universe (1917)
is the only STATIC MODEL among the simple
general relativistic
cosmological models.
All others are in general expansion or contraction.
Alexander Friedmann (1888--1925)
and, independantly,
Georges Lemaitre (1894--1966)
derived the Friedmann equation
in the 1920s.
You must understand that
Einstein's
research in 1917
was a pioneering effort before all the mathematical tricks for dealing with
general relativity had
been developed by Einstein
and many others in the decades after
1917.
Einstein described his
search for the
Einstein universe (1917)
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).
The cosmological constant,
whether true or NOT,
has a definite singular meaning as discussed in the figure above
(local link /
general link: general_relativity_field_equations.html).
Dark energy, however,
is a word for our ignorance since there are many possible
versions of dark energy
and which if any are true we do NOT know.
However, when people say
dark energy without qualification,
they mean the simplest version of
dark energy unless context
says they mean something else: e.g.,
any kind of dark energy.
Note, we call the
dark energy
by that name
because we do NOT 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).
The simplest version of dark energy
(hereafter in this subsection usually just
dark energy)
is a sort of stuff that is
CONSTANT in
space
(NO matter how that expands/contracts
via general relativity)
and time
(most especially
cosmic time).
And it has formally NEGATIVE pressure which
we will explicate shortly.
The simplest theory of what the
dark energy is is that it is
vacuum energy
which is a special case of
zero-point energy
in quantum field theory.
However, the most natural estimate of
vacuum energy is 50 to 120
orders of magnitude
larger than what the
dark energy has to be to
match observations: i.e., be replacement for
the cosmological constant.
This profound discrepancy between theory
and observation is the
cosmological constant problem.
OK, what is
NEGATIVE pressure?
Well, it's a
pressure that pulls in rather than pushes out.
This means that as a universe expands,
you need to put mass-energy
into it in order to expand it against the pulling in
NEGATIVE pressure.
In order to keep the
density
of the dark energy
constant in space
and time
as the universe expands,
the dark energy
pressure has to be constant
in space
and time also.
This means there is NEVER any imbalance and the
dark energy
pressure
NEVER actually pulls on itself or anything.
Nothing feels it in theory, and therefore
it seems to yours truly that
NEGATIVE pressure is
just a formal pressure: some may disagree.
In fact, this mysterious
dark energy
pressure p_dark must
obey the
formula p_dark = - ρ_dark/c**2,
where the density of the
dark energy is ρ_dark.
So we have some requirements for simplest version
the dark energy, but
we still do NOT know what it is.
The expression
dynamical dark energy
is a catchall expression for
all versions of dark energy
that are NOT simplest version where
dark energy
is constant in space
and time.
There are many theories
of dynamical dark energy,
but which if any are true, we do NOT know.
Theorists keep coming
up with new
theories
of dynamical dark energy
in the hope of solving all problems in
cosmology.
And that is all we need to say
about dynamical dark energy.
From the analysis of the
CMB data,
we find
Omega_Λ
= 0.6853(74)
(i.e., ratio of dark energy
to the critical density = 3H_{0}**2/(8πG) = (9.20387*10**(-27))*h_70**2 kg/m**3 = (1.35989*10**11)*h_70**2 M_☉/Mpc**3)
and
Omega_matter
= 0.3147(74).
The reference for these values is
Planck 2018 results. I. Overview and the cosmological legacy
of Planck 2018.
Note,
0.6853(74) and 0.3147(74) are very COMPARABLE.
There may be some deep reason why the
dark energy
and matter should be COMPARABLE in which case the
dark energy
CANNOT be simply
dark energy: it must have some
relationship to the matter content of the
observable universe
On the other hand, possibly the COMPARABILITY of
the two values 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
a href="http://en.wikipedia.org/wiki/Probability_distribution">probability distribution
Those pocket universes with a
Omega_Λ
to Omega_matter
ratio
NOT somewhat like our own
pocket universe with ratio approximately 2/3 to 1/3
NOT be able to support life as we know it.
Too small a ratio
and the universe may NOT have formed the right
kind of galaxies
and stars.
Too large a ratio
and the universe would have expanded too quickly
ever to form galaxies and
stars.
So the explanation of the ratio of approximately 2/3 to 1/3
in our
pocket universe with ratio approximately 2/3 to 1/3
may just be a lucky-for-us 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
were fine-tuned beyond
the needs (so far as we can tell) of making our
pocket universe
be suitable for life as we know it.
For example, say
Omega_Λ
to Omega_matter
ratio
were exactly 2/3 to 1/3.
That is more exactness than is needed for
our pocket universe
to be suitable life as we know it
and strongly suggests the
Omega_Λ
to Omega_matter
ratio is determined by
fundamental physical law
and NOT by having
multiverse with
parameters
set by a
probability distribution.
But there is NOT such exactness, and
so the multiverse
passes this significant
falsification test.
As noted in the above section
What They Are and a Horrible Ambiguity,
the cosmological constant
and (constant) dark energy
symbol
is the
Greek upper case letter Λ
which display in
the figure below
(local link /
general link: greek_letter_lambda.html).
For simplicity, one often just says Lambda instead
of the cosmological constant
or dark energy.
Is the cosmological constant
an ad hoc hypothesis?
First, what is an ad hoc hypothesis?
An ad hoc hypothesis is a
hypothesis
invented JUST to make a theory give a very specific
result often without any other consequences.
So ad hoc hypotheses
are often just a way to
a wrong theory
look right.
If you need many
ad hoc hypotheses
to make theory general,
the theory is probably wrong.
An especially egregious
kind of ad hoc hypothesis is
a fudge factor.
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 are quite adept at creating
fudge factors on
tests.
For example, leprechauns
are the cause of ...
For leprechauns
see the figure below
(local link /
general link: leprechaun.html).
The argument is
that cosmological constant
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.
It 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 cosmological constant
had some chance of being right if
Einstein's assumption of a
STATIC
universe had been right---which it wasn't, of course.
One could also say
that cosmological constant
is by far the simplest modification of the
Einstein field equations
that one could imagine
and the specific specific effect it was usef for applies to
whole universe.
Thus, the modified
Einstein field equations
are a very interesting alternative to the
original Einstein field equations,
and so cosmological constant
NO matter what one thinks of
STATIC cosmological models.
The upshot is the cosmological constant
is NOT an
ad hoc hypothesis in the
opinion of yours truly.
In fact,
Alexander Friedmann (1888--1925)???
and Georges Lemaitre (1894--1966)
in their work on
expanding universe
cosmological models did NOT
dispense with the
cosmological constant.
This shows that they too thought it was NOT
an ad hoc hypothesis.
For an interesting historical tidbit on dark energy,
see the discussion below
on Erwin Schroedinger (1887--1961)
in the figure below
(local link /
general link: erwin_schroedinger.html).
Yours truly believes that
the
cosmological constant
is NOT an
ad hoc hypothesis
even though it was introduced originally by
Albert Einstein (1879--1955)
to get a specific effect:
that the general relativity
give any kind of
cosmological model.
The kind he actually got was the STATIC
Einstein universe (1917).