# Thread: dark energy accelerated expansion of the universeI

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## dark energy accelerated expansion of the universeI

I've been thinking about the expansion of the universe. Is dark energy necessary for expansion of the universe or only necessary for the accelerated expansion of the universe. How is this quantified?

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Expansion without acceleration can be everything just "coasting"
from an initial event that got it started. In that case, the expansion
would be slowing due to self-gravitation. It would either slow to a
stop and then fall back together, or slow asymptotically toward a
final expansion rate.

-- Jeff, in Minneapolis

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Originally Posted by Copernicus
Is dark energy necessary for expansion of the universe or only necessary for the accelerated expansion of the universe.
The latter, the expansion itself is not caused by anything we know about, it's just an initial condition to the origin of the universe.
How is this quantified?
What we can observe, in principle, is the history of the expansion. By that I mean, the function a(t), where a is the "scale parameter" (the degree of stretch compared to today), and t is the age of the universe (in coordinates that move with the matter). We observe this by connecting the degree of redshift to the distance away of the various sources we can see. Then we compare a(t) to our best dynamical theory, general relativity with the cosmological principle, and see how well it works based on what we think is out there. The need for dark energy comes from the disconnect between a(t) observed and a(t) expected. The difference is an unexpected acceleration, so we can say the acceleration is caused by dark energy, but we cannot say the expansion is caused by dark energy.

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Originally Posted by Ken G
The latter, the expansion itself is not caused by anything we know about, it's just an initial condition to the origin of the universe.What we can observe, in principle, is the history of the expansion. By that I mean, the function a(t), where a is the "scale parameter" (the degree of stretch compared to today), and t is the age of the universe (in coordinates that move with the matter). We observe this by connecting the degree of redshift to the distance away of the various sources we can see. Then we compare a(t) to our best dynamical theory, general relativity with the cosmological principle, and see how well it works based on what we think is out there. The need for dark energy comes from the disconnect between a(t) observed and a(t) expected. The difference is an unexpected acceleration, so we can say the acceleration is caused by dark energy, but we cannot say the expansion is caused by dark energy.
Interesting distinction!

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Originally Posted by Jeff Root
Expansion without acceleration can be everything just "coasting"
from an initial event that got it started. In that case, the expansion
would be slowing due to self-gravitation. It would either slow to a
stop and then fall back together, or slow asymptotically toward a
final expansion rate.

-- Jeff, in Minneapolis
The slowing would then be negative acceleration?

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Originally Posted by Copernicus
The slowing would then be negative acceleration?
In this context, and the way the expansion (rate of expansion and
changes in the rate of expansion) is defined, the slowing does not
constitute an acceleration. Since it is due to gravity -- the pull of
everything in the Universe on everything else in the Universe -- it
could be defined as an acceleration if you wanted to go that way,
but the more consistent way is to define it as not an acceleration,
but just a contraction, or a reduction in the scale factor. Gravity
is the cause, either way, so dark energy isn't involved.

-- Jeff, in Minneapolis

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Originally Posted by Jeff Root
In this context, and the way the expansion (rate of expansion and
changes in the rate of expansion) is defined, the slowing does not
constitute an acceleration. Since it is due to gravity -- the pull of
everything in the Universe on everything else in the Universe -- it
could be defined as an acceleration if you wanted to go that way,
but the more consistent way is to define it as not an acceleration,
but just a contraction, or a reduction in the scale factor. Gravity
is the cause, either way, so dark energy isn't involved.

-- Jeff, in Minneapolis
I would think dark energy would contribute to the slowing.

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Dark energy is defined as what is causing the speeding up, so
obviously it can't contribute to the slowing.

You say that because energy is the cause of gravity, right?

All known forms of energy contribute to the curvature of spacetime,
which is what gravity is. This unknown form of energy apparently
has the opposite effect.

-- Jeff, in Minneapolis

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Originally Posted by Jeff Root
Dark energy is defined as what is causing the speeding up, so
obviously it can't contribute to the slowing.

You say that because energy is the cause of gravity, right?

All known forms of energy contribute to the curvature of spacetime,
which is what gravity is. This unknown form of energy apparently
has the opposite effect.

-- Jeff, in Minneapolis
Right. I thought that dark energy contributed to the critical density.

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Originally Posted by Copernicus
Right. I thought that dark energy contributed to the critical density.
It does, but it's not just energy that contributes to gravity, so does pressure. For normal mass, the pressure contribution is negligible. For a cosmological constant (the usual way to treat dark energy), the pressure is both negative and a larger contribution (by a factor of 2) than the energy. So you could say that dark energy contributes to both the slowing and the speeding up, but that's like saying if I give you 1 dollar back after stealing 2 from you, I am contributing both to your wealth and to your poverty!

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Originally Posted by Ken G
It does, but it's not just energy that contributes to gravity, so does pressure. For normal mass, the pressure contribution is negligible. For a cosmological constant (the usual way to treat dark energy), the pressure is both negative and a larger contribution (by a factor of 2) than the energy. So you could say that dark energy contributes to both the slowing and the speeding up, but that's like saying if I give you 1 dollar back after stealing 2 from you, I am contributing both to your wealth and to your poverty!
Thanks Ken, So by a factor of 2. Are there equations for this?

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Here: https://en.wikipedia.org/wiki/Equati...te_(cosmology)
Look at the last equation in the section "FLRW equations and the equation of state", noting that w'=-1 for pure dark energy, and w'=0 for pure nonrelativistic matter. So 1+3w' = +1 for normal matter, and -1 for dark energy. That term comes from (rho+3p)/rho, so normal matter is like p=0 and dark energy is like p=-rho, but since pressure counts three times as much, it acts like p-3p= -2p. So that's the factor of 2 I referred to, though I should have said it's a factor of 3 that ends up a factor of 2 after you combine the energy and pressure.

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Originally Posted by Ken G
Here: https://en.wikipedia.org/wiki/Equati...te_(cosmology)
Look at the last equation in the section "FLRW equations and the equation of state", noting that w'=-1 for pure dark energy, and w'=0 for pure nonrelativistic matter. So 1+3w' = +1 for normal matter, and -1 for dark energy. That term comes from (rho+3p)/rho, so normal matter is like p=0 and dark energy is like p=-rho, but since pressure counts three times as much, it acts like p-3p= -2p. So that's the factor of 2 I referred to, though I should have said it's a factor of 3 that ends up a factor of 2 after you combine the energy and pressure.
Doesn't that seem enormous?

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Originally Posted by Copernicus
Thanks Ken, So by a factor of 2. Are there equations for this?
Ken, when they talk about the energy density in the wikipedia article, are they referring to including visible matter, dark matter, and dark energy, or is it referring to just dark energy?

In cosmology, the equation of state of a perfect fluid is characterized by a dimensionless number {\displaystyle w} w, equal to the ratio of its pressure {\displaystyle p} p to its energy density {\displaystyle \rho } \rho :

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Originally Posted by Copernicus
I thought that dark energy contributed to the critical density.
Originally Posted by Ken G
It does, but it's not just energy that contributes to gravity, so does
pressure. For normal mass, the pressure contribution is negligible.
For a cosmological constant (the usual way to treat dark energy),
the pressure is both negative and a larger contribution (by a factor
of 2) than the energy. So you could say that dark energy contributes
to both the slowing and the speeding up, but that's like saying if I
give you 1 dollar back after stealing 2 from you, I am contributing
What is the reason for thinking that dark energy has pressure?

What is the reason for thinking that the pressure is negative?

What is negative pressure?

Is dark energy unique in having negative pressure?

What is the reason for thinking that negative pressure would
cause an acceleration of the expansion rather than adding to
the total gravitation just like all other forms of pressure and
energy?

What determines the ratio of dark energy to the amount of
negative pressure it has?

-- Jeff, in Minneapolis

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Originally Posted by Copernicus
Ken, when they talk about the energy density in the wikipedia article, are they referring to including visible matter, dark matter, and dark energy, or is it referring to just dark energy?
All of them, you just combine their equations of state, i.e., combine their w factors.

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Originally Posted by Ken G
All of them, you just combine their equations of state, i.e., combine their w factors.
So is there any embarrassment to this theory among scientists. I'm just wondering if the pressure drop decreases to the 4th power with expansion, how would the w factor equal -1 wouldn't the w factor have been less than -1 and thus cause the rip? Is that a guess. How does the dissipation factor go from to the -fourth power to the -third power, is that a guess?

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Originally Posted by Jeff Root
What is the reason for thinking that dark energy has pressure?
Loosely, if you think there is energy associated with "dark energy", and that energy is intrinsic to the vacuum, then it must have negative pressure. Pressure can be defined as the negative rate of change of energy with volume, because usually energy increases when volume drops (like compressing a gas). But if the energy comes from the volume, then energy increases when volume increases, so that's negative pressure.
Is dark energy unique in having negative pressure?
I don't know of any other example of an energy that increases on expansion.
What is the reason for thinking that negative pressure would
cause an acceleration of the expansion rather than adding to
the total gravitation just like all other forms of pressure and
energy?
It does add to the total gravitation, but it adds a negative amount. It is essentially antigravity.
What determines the ratio of dark energy to the amount of
negative pressure it has?
If you assume it is a "cosmological constant," this determines the ratio of energy to pressure, as the pressure is the derivative of the energy with respect to increases in volume. The reason that creates antigravity is due to the needs of relativity to be coordinate independent, that's why pressure has to contribute to gravity.

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Originally Posted by Copernicus
So is there any embarrassment to this theory among scientists. I'm just wondering if the pressure drop decreases to the 4th power with expansion, how would the w factor equal -1 wouldn't the w factor have been less than -1 and thus cause the rip?
The pressure stays constant with expansion, because the vacuum is the same vacuum. It's weird pressure-- both negative and constant with time-- if it's a cosmological constant. (And if anyone is wondering how negative pressure can allow expansion since we normally think of positive pressure doing that, remember that it is not pressure that causes explosions, but differences in pressure. A cosmological constant is not a difference in pressure.)
Last edited by Ken G; 2018-Jan-06 at 02:51 PM.

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To clarify only the points that are already closest to being clear:
Dark energy causes positive gravity because it is energy, and also
causes negative gravity because it has negative pressure, and
the gravitational effect of the negative pressure is 3 times the
gravitational effect of the energy?

Is the idea of negative energy essential to this picture, or no?

-- Jeff, in Minneapolis

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Originally Posted by Jeff Root
To clarify only the points that are already closest to being clear:
Dark energy causes positive gravity because it is energy, and also
causes negative gravity because it has negative pressure, and
the gravitational effect of the negative pressure is 3 times the
gravitational effect of the energy?
Correct.
Is the idea of negative energy essential to this picture, or no?
There's no negative energy, only the pressure is negative.

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Originally Posted by Ken G
There's no negative energy, only the pressure is negative.
Okay. But gravitational potential energy is negative energy, isn't it?
And gravitational potential energy figures in somehow. So... ?

-- Jeff, in Minneapolis

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Gravitational potential energy is tricky in general relativity, since the motion is already inertial and all gravity does is change the meaning of a straight line, so one does not normally even invoke the concept of potential energy there. So that's all dark energy does, it means that vacuum itself has its own idea of what a straight line is, and it involves accelerating expansion.

However, it is true that we seem to have a spatially flat universe, which is a special case we might be tempted to elevate to its own physical principle. If we do that, we find we have a special case where the Friedmann equation (the key equation for the dynamics of the scale parameter in general relativity under the cosmological principle) works exactly like Newtonian dynamics in the case of zero total energy, if we simply interpret the energy density as an effective mass density times c2. But if you take that view instead of the "negative pressure" view, then the picture of what dark energy is doing is quite a bit different, because it acts like a constant mass density in a universe that is constrained to keep its total energy zero in any arbitrarily chosen sphere of material, including an effective Newtonian gravitational potential energy. In the case of pure dark energy, the effective Newtonian potential energy is that of an expanding sphere of fixed effective density but rising volume, so that's a gravitational potential that rises with time. To keep the total energy zero, the kinetic energy of that sphere of material must also rise as the sphere grows in size, and that's where the acceleration comes from. One could say, in this quasi-Newtonian picture, that the appearance of new vacuum within the sphere of material generates negative gravitational potential energy much like two objects falling together does, but the antigravity element derives from the fact that with cosmological expansion the "falling" is apart and the net "gravity" is negative. The negative potential energy derives from a positive dark energy producing a positive effective mass density times c2.

So it's not the sign of the effective mass density that is negative with dark energy, nor is it unusual for a positive mass density to generate a negative gravitational potential energy. What is unusual here is only how that negative gravitational potential energy changes as the universe falls apart, and that's what makes dark energy produce acceleration if one wishes to use a quasi-Newtonian picture that invokes gravitational potential energy. In this picture, one does not associate any energy with dark energy when one makes the total energy zero, one only takes into account the kinetic energy of the effective mass density of dark energy, and the potential energy of the effective mass density of dark energy, and adds them to zero without any "dark energy" at all.

Ironically, this turns a universe of pure dark energy into the steady-state picture where new vacuum is being "created" all the time to "fill in" behind what has expanded away, so you get precisely Hoyle's picture going forward in time (though not backward) once all the matter is so expanded that you don't notice it any more except for test particles to trace the dynamics. Of course, it is the situation going backward in time (involving the CMB and distant galaxy clusters and so on) that is what we actually need to predict (or postdict, if you prefer), so the Hoyle picture is still not very useful even in a dark-energy dominated universe.
Last edited by Ken G; 2018-Jan-07 at 12:53 PM.

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Whew! A lot to absorb.

At the moment, I'll just ask for confirmation of another very basic
point that also seems pretty clear, but I want to be sure about.

Is dark energy a property of spacetime?

The way I interpret your descriptions, it seems pretty definite that
dark energy is an intrinsic property of spacetime. My own ATM
hypothesis about the acceleration of the expansion is not so clear
on that point. It posits a gravitational repulsion between ordinary
matter and antimatter, with equal amounts of the two distributed
throughout the Universe, thoroughly separated from each other
by their mutual repulsion. That might still be considered to be a
property of spacetime, and might still take the label "dark energy".

So are descriptions of negative pressure pervading the Universe
and of mutually repelling regions of ordinary matter and antimatter
both descriptions of "dark energy", or is there reason not to use
that label in the latter case? Can the label be used for *any* cause
of the accelerated expansion?

-- Jeff, in Minneapolis

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Originally Posted by Jeff Root
Is dark energy a property of spacetime?
There's not going to be any way to be sure about that one! In fact, you could break that question down into two parts, neither of which are we sure about. First, ask if dark energy is purely an effect of gravity. If it's a cosmological constant, then it's purely gravity, but maybe it's more than that. Then, ask if gravity itself is a property of spacetime! In general relativity, it is, but most particle theorists don't like general relativity as their fundamental theory of gravity because it seems inconsistent with quantum mechanics and can't seem to work at the Planck scale. So I think the best answer you'll get to that one, for centuries most likely, is that our best model of dark energy is to make it a property of spacetime, without actually believing that it is. As you know, that's also the flavor that I feel all our theories should have, it's scientific.[quote]
It posits a gravitational repulsion between ordinary
matter and antimatter, with equal amounts of the two distributed
throughout the Universe, thoroughly separated from each other
by their mutual repulsion.
An interesting idea, though of course it needs to be taken to the next level, where it makes a set of testable predictions and all its ramifications can be tested. Without going into detail as this is not the ATM section, your idea seems to suffer from the problem that repulsion between matter and antimatter should decrease as the universe expands, but dark energy is only needed to explain the recent history of that expansion.
Can the label be used for *any* cause
of the accelerated expansion?
Yes, any cause of acceleration that fits the required behavior (recent acceleration) would qualify as "dark energy," as that is all the term currently means.

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I have asked something similar before, but could not all this dark energy not cause the redshift itself, or would that only be if the earth was at the center of the universe?

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Thanks, Ken!

-- Jeff, in Minneapolis

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Originally Posted by Copernicus
I have asked something similar before, but could not all this dark energy not cause the redshift itself, or would that only be if the earth was at the center of the universe?
I'am not sure what you are asking, dark energy is a contributing factor to the redshift we see in anything in which we see cosmological redshift.

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Originally Posted by Ken G
I'am not sure what you are asking, dark energy is a contributing factor to the redshift we see in anything in which we see cosmological redshift.

Hi Ken, what I meant was does the dark energy, forget the term dark energy, and just call it energy, and mass of the universe, cause the red-shift without any expansion of the universe, or could it only be cause if earth was near the center of the universe?

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All cosmological redshift is due to expansion, there simply is no other contributing factor regardless of dark energy's contribution.

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