This insert explicates cosmological constant and dark energy.
The two quantities are NOT the same thing, but 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.
Note that when we say dark energy we usually mean dark energy constant in cosmic time and space. There are theories where dark energy varies in cosmic time and we refer to that varying dark energy we usually say dynamical dark energy---which we do NOT refer to often.
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 of galaxies at that time. 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 are the standard cosmological models ever since the 1920s, when Alexander Friedmann (1888--1925), and Georges Lemaitre (1894--1966) derived the Friedmann equation from on 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).
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
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.
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The cosmological constant as a mathematical
symbol is the capital Greek Lambda Λ:
see the figure below
(local link /
general link: greek_letter_lambda.html).
php require("/home/jeffery/public_html/astro/hellas/greek_letter_lambda.html");?>
How do the
Einstein field equations change
with the insertation of the
cosmological constant?
8*π*G 8*π*G
G_{ik} = ----- T_{ik} to G_{ik} + Λ*g_{ik} = ----- T_{ik} ,
c**4 c**4
where Λ is the cosmological constant, of course,
and
g_{ik} is the metric tensor of general relativity
which describes the geometry of spacetime.
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An especially egregious
kind of ad hoc hypothesis is
a fudge factor.
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.
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.
For for slightly out-of-date values, the figure below
(local link /
general link: cosmos_energy_pie_chart_images.html).
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.
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Question: Density
parameter Omega is:
From the analysis of the
CMB data, galaxy cluster data, and
Type Ia supernovae ASSUMING the dark energy
is a cosmological-constant dark energy,
one finds
Omega_Lambda=0.6853(74)
(see Planck 2018 results. I. Overview and the cosmological legacy
of Planck 2018).
Answer 2 and 3 are right. But answer 3 is best in this context.
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Is there any reason for believing there could be
just a
cosmological-constant dark energy
from physical theory?
php require("/home/jeffery/public_html/astro/cosmol/cosmos_energy_pie_chart_images.html");?>
There may be some deep reason why the
dark energy
and matter should be connected in which case the
dark energy
CANNOT be simply a
cosmological-constant dark energy.