Post by: Aeris on 13/12/2021 16:47:29
"Whispers" Huh? What's that you're saying? "Whispers" Real-life is nothing at all like fiction and absolutely no one here is shocked to see me again, nor are they expecting a reintroduction speech from me?
Well alrighty then, let's just get right into it! Today, I wanna learn more about Dark Energy. Hopefully we know just enough about the stuff that not every single one of my questions will be answered with some variation of "We don't know.", or "We theorize that...".
1. So... no one right now currently knows what Dark Energy actually is, but can we say anything at all about what it's probably not? Like, we don't know what Dark Matter is either, but we do know based on simple observations that it isn't traditional matter, antimatter or made up of Black Holes (I'll post a video at the bottom of the page detailing why this is the case). Can we say for example something like "Dark Energy isn't pure energy or a localized Quantum Field because the idea of a form of energy that exists separately from matter or a spatial field that doesn't exist everywhere at once is beyond ludicrous."? Can we drop any ideas about Dark Energy being even slightly related to that of the supposed Aether and Quintessence? Could Dark Energy quite literally be anything?
2. As you most likely already know by now, Dark Energy is the technical name assigned to the mysterious force that's driving the expansion of the Universe, but is that expansion a Thermodynamic process in the sense that energy is entering a system to preform work on it and then exiting that system as a lower form of energy (usually heat and/or sound)? Has anyone ever considered the possibility that Dark Energy may not exist at all and that the space can just expand without any outside force acting on it?
3. Would someone please be so kind as to explain to me why Dark Energy isn't considered to be a violation of the first Law of Thermodynamics, despite the fact that the amount of it is increasing and casing the expansion of the universe to accelerate?
Huh, not as many questions as I originally thought. It's surprisingly difficult to think of and write questions about something that not even professionals know everything about. This may or may not be revisited in the future...
Here's the video I was talking about in relation to my first question. For context, head to 1:33 to hear more about the statement I made in said question
Oh yeah. Merry Christmas everyone :)
Post by: Halc on 13/12/2021 21:13:21
no one right now currently knows what Dark Energy actually isScience isn't really in the business of saying what something actually is. It is concerned with how it behaves. So we might not know what ordinary matter actually is, but we're reasonably familiar with how it behaves.
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Like, we don't know what Dark Matter is either, but we do know based on simple observations that it isn't traditional matter, antimatter or made up of Black HolesRight. All those things interact with EM. Dark matter doesn't. But that is a description of how dark matter behaves, not a description of what it is.
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Can we say for example something like "Dark Energy isn't pure energy or a localized Quantum Field because the idea of a form of energy that exists separately from matter or a spatial field that doesn't exist everywhere at once is beyond ludicrous."? Can we drop any ideas about Dark Energy being even slightly related to that of the supposed Aether and Quintessence? Could Dark Energy quite literally be anything?No comment on 'what it is'. A scalar field (quintessence) and the Aether comment seem quite relatived since both are a function of an absolute time of sorts, and the behavior of dark energy does seem to suggest an absolute ordering of most events in the universe, even if that ordering doesn't correspond to any inertial frame.
Dark energy is the Λ in the ΛCDM model. That isn't what it is, just how it fits into the current accepted standard model. The scalar fell naturally out of Einstein's field equations, contributing to the stress energy tensor, even after it was temporarily dropped due to suspicion that is was zero, until later when it was demonstrated to be otherwise.
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Dark Energy is the technical name assigned to the mysterious force ..Careful about calling it a force, a word typically used to denote a vector change in momentum of an object, and to say a typical reasonably stationary (relative to above mentioned absolute coordinate system) object like a galaxy, dark energy isn't accelerating it in any particular direction, and thus there is no 'force' acting on it, at least not in the usual way. Ditto with the reduction of expansion during times of higher energy density. That also didn't accelerate objects in any particular direction.
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... that's driving the expansion of the Universe, but is that expansion a Thermodynamic process in the sense that energy is entering a system to preform work on it and then exiting that system as a lower form of energy (usually heat and/or sound)?The universe is by definition a closed system, so nothing is acting on it from outside, or exiting.
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Has anyone ever considered the possibility that Dark Energy may not exist at all and that the space can just expand without any outside force acting on it?Dark energy not coming from outside doesn’t mean it doesn’t act. It’s a measurable thing.
There are other models, none which fit the evidence as well, but yes, there are models that do not posit dark energy, so in that sense it might not exist.
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Would someone please be so kind as to explain to me why Dark Energy isn't considered to be a violation of the first Law of Thermodynamics, despite the fact that the amount of it is increasingIs it? The ratio of DE/DM/matter changes over time? That’s not impossible, and there’s not even the usual energy conservation law for the above mentioned cosmological coordinate system. It only works for static coordinate systems where space is constant over time.
Post by: Aeris on 14/12/2021 10:57:25
Thanks. It's good to be back :)
"Right. All those things interact with EM. Dark matter doesn't. But that is a description of how dark matter behaves, not a description of what it is."
I thought Black Holes were just regions of Spacetime where Gravity is so strong that neither particles or electromagnetic radiation could escape it. They aren't even technically made of anything remotely tangible, so why would they interact with the electromagnetic force at all (unless you count sucking in electromagnetic radiation via intense gravity as "interacting" with it)?
Also just for the record, I'm not interested in knowing what specifically dark energy is specifically. That's an unrealistic expectation. I was just curious to know if we could say anything at all on what it's most likely not. You're right in saying that dark matter not exhibiting the properties of traditional matter, antimatter or black holes doesn't tell us what dark matter actually is, but unless dark matter is in direct violation of the law of non-contradiction, it does tell us that dark matter isn't any of those things. I was curious if we could apply the same process to dark energy.
"A scalar field (quintessence) and the Aether comment seem quite relatived since both are a function of an absolute time of sorts, and the behavior of dark energy does seem to suggest an absolute ordering of most events in the universe, even if that ordering doesn't correspond to any inertial frame."
What does this even mean? "A function of an absolute time of sorts", that doesn't make a lick of sense to me.
"Careful about calling it a force, a word typically used to denote a vector change in momentum of an object, and to say a typical reasonably stationary (relative to above mentioned absolute coordinate system) object like a galaxy, dark energy isn't accelerating it in any particular direction, and thus there is no 'force' acting on it, at least not in the usual way. Ditto with the reduction of expansion during times of higher energy density. That also didn't accelerate objects in any particular direction."
Makes sense. I just chose the word force since it honestly seems the most fitting term to assign to something like dark energy. Keep in mind of course, I wasn't referring to force in the Newtonian sense.
"The universe is by definition a closed system, so nothing is acting on it from outside, or exiting."
Yeah, that's my bad. I should've been less vague in my description. Let me elaborate a bit more on what I was actually asking
When you typed out your response to my questions yesterday evening, a chemical reaction in your body took place in which energy was spent thinking of multiple responses to my questions and then using your fingers to type them out on the keyboard. This right here is a thermodynamic process, energy was spent preforming work on the area around you and some of it was wasted as heat and/or noise. My question was is the expansion of the universe a thermodynamic process comparable to that of freezing water or igniting a fire?
Also, this is unrelated to my response, but if the universe really is a closed system, what about all the redshifted light that's disappeared in seemingly nothingness due to the expansion of the universe? What about all those trillions and trillions virtual particles popping in and out of existence every second?
"Dark energy not coming from outside doesn’t mean it doesn’t act. It’s a measurable thing.
There are other models, none which fit the evidence as well, but yes, there are models that do not posit dark energy, so in that sense it might not exist."
If you don't mind me asking, how do we measure something that we can't visibly see with our eyes or detect with our technology? Do we measure it based on it's effects on the universe like dark matter?
"Is it? The ratio of DE/DM/matter changes over time? That’s not impossible, and there’s not even the usual energy conservation law for the above mentioned cosmological coordinate system. It only works for static coordinate systems where space is constant over time."
are you referring to Noether's theorem by any chance? What's so special about dark energy that it's capable of blowing off time translation symmetry and thus the law of conservation of energy?
Post by: Eternal Student on 03/01/2022 01:41:45
What's happened to this thread then? Has it gone quiet? We wish you well Aeris, wherever you are.
Looks like Halc has offered some reasonable discussion. Well done Halc.
Well alrighty then, let's just get right into it! Today, I wanna learn more about Dark Energy.Excellent. Keep studying, either formally or in your own time and best wishes to you.
Post by: Halc on 03/01/2022 02:56:41
What's happened to this thread then? Has it gone quiet?Actually, I totally missed the reply on the 14th. Thanks for the bump.
I thought Black Holes were just regions of Spacetime where Gravity is so strong that neither particles or electromagnetic radiation could escape it.Pretty off topic since dark matter and black holes are quite different things. A black hole is a set of events from which light (or any information) cannot reach null infinity.
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Also just for the record, I'm not interested in knowing what specifically dark energy is specifically. That's an unrealistic expectation. I was just curious to know if we could say anything at all on what it's most likely not.OK. It's not pretty much anything with which you classically interact. Pretty bad answer, I know, but that's almost what physics will say as well. Nobody really has a model for it since it seems to have no properties other than mass, unlike black holes which have at least charge. There seems to be no meaning for instance to a distinction between dark matter and dark antimatter.
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What does this even mean? "A function of an absolute time of sorts", that doesn't make a lick of sense to me.It means that every event in the universe can be assigned, in principle, a value for the age of the universe at that event. This is not entirely true since the time of say (Earth, Y2K) depends on the location (but not speed) of the clock that measures it, and that clock runs at some rate depending on the local gravitational potential. So maybe we need to specify some sort of 'average potential' when saying that (Earth, Y2K) is at absolute time X (approx 13.8 BY). Point is, the time is not frame dependent. It is calculated on a peculiar (absolute) velocity at Earth at Y2K, not the actual peculiar velocity of Earth then, which is not quite 400 km/sec, which messes up our local clocks.
So my statement says that the expansion rate of the universe is a function of this absolute time. It can be thought of as the same everywhere at a given time, but I think actually that the model makes it a function of the local mass density, and not just a flat function of time. So I was probably wrong in simplifying it like that. The universe expands more between galaxies than within them because the mass density is lower way out there. But on the largest scales, mass density is uniform, and thus expansion is constant everywhere at a given moment in time, but not the same at one time as at a different time. It was much faster in the past, slowed down, but is now accelerating and will continue to do so.
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My question was is the expansion of the universe a thermodynamic process comparable to that of freezing water or igniting a fire?I don't really see how either applies. It doesn't seem thermodynamic. It isn't driven by heat (like a freezing process), nor does it consume fuel (like a fire). Any my apologies for the vague answer. I don't know what dark energy is, and am likely to get things wrong if I assert anything.
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if the universe really is a closed system, what about all the redshifted light that's disappeared in seemingly nothingness due to the expansion of the universe?Our observable universe is not closed, so things are free to exit it. Light falling into a black hole also disappears into seeming nothingness, but it hasn't exited the universe, not even in a model where black holes don't exist.
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What about all those trillions and trillions virtual particles popping in and out of existence every second?They have no more eternal existence than does a rock or anything else. If they meaningfully exist (something I question, even for a distant rock), then it is for a finite duration, not all time.
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If you don't mind me asking, how do we measure something that we can't visibly see with our eyes or detect with our technology? Do we measure it based on it's effects on the universe like dark matter?Right. We see galaxies turning too fast, hence dark matter. We see the acceleration of expansion and measure it, hence dark energy. I see the Eggos disappearing, hence Eleven, despite no direct measurement.
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are you referring to Noether's theorem by any chance? What's so special about dark energy that it's capable of blowing off time translation symmetry and thus the law of conservation of energy?Don't know.
Post by: Origin on 03/01/2022 15:27:48
As you most likely already know by now, Dark Energy is the technical name assigned to the mysterious force that's driving the expansion of the UniverseAeris, I am not sure if this was just a slip of the tongue, but I wanted to point out that dark energy is what is causing the expansion of the universe to speed up not the expansion itself.
Post by: Eternal Student on 04/01/2022 00:02:27
I see the Eggos disappearing, hence Eleven, despite no direct measurement.I think we're supposed to laugh but there may be a cultural or national problem here.
What are Eggos ?? Eggos are some type of egg flavoured waffle according to Google, sold only in North America.
I guess people usually eat them for their elevens' (around about 11 am in the morning).
Anyway, that's my best guess.
Post by: Halc on 04/01/2022 05:20:21
Anyway, that's my best guess.It's a stranger thing than that.
Try googling eggos eleven
Mathematically, it can be expressed as:
Reese's Pieces/ET = Eggos/Eleven
Post by: Killed the cat on 05/01/2022 22:34:27
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Aeris, I am not sure if this was just a slip of the tongue, but I wanted to point out that dark energy is what is causing the expansion of the universe to speed up not the expansion itself.
Really ??? I have always believed that the metric expansion of space is an effect of dark energy, which at a local level isn't speeding up. However If each light year of distance in our universe (Metaphorically and strictly for arguments sake.) was expanding by one mile per day and there was a nice straight run of stars spaced at one light year intervals, after one day the first star would have moved one mile away from you the observer, the second star would have moved two miles away from you, the third star three miles etcetera, the effect is cumulative. over cosmic distances these extra one mile per light year increments, add up, to light years, which then also expand by the same amount.. Dark energy is the cause of both effects !!!
Post by: Origin on 05/01/2022 22:45:57
Dark energy is the cause of both effects !!!No that is not correct. The expansion of the universe of course means that objects farther away have a higher recession velocity, but it was discovered that the expansion itself was increasing. That means that the expansion in km/sec*Mpc is increasing over time. Dark energy is theorized to be the cause of the increasing rate of expansion.
Post by: Halc on 06/01/2022 01:06:16
If each light year of distance in our universe (Metaphorically and strictly for arguments sake.) was expanding by one mile per day and there was a nice straight run of stars spaced at one light year intervals, after one day the first star would have moved one mile away from you the observer, the second star would have moved two miles away from you, the third star three miles etcetera, the effect is cumulative. Over cosmic distances these extra one mile per light year increments, add up, to light years, which then also expand by the same amount.This is more or less correct. The recession rate of anything is approximately proportional to the current distance to it. No energy, dark or otherwise, is necessary to maintain this. The energy is only needed if a given object increases its recession rate over time (and not if the recession rate, currently around 70/km/sec/mpc, increases).
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Dark energy is the cause of both effects !!!I only counted one effect in your post, and dark energy doesn't cause it, so no.
The expansion of the universe of course means that objects farther away have a higher recession velocity, but it was discovered that the expansion itself was increasing. That means that the expansion in km/sec*Mpc is increasing over time.The last statement is wrong. Flat expansion (neither increasing nor decreasing) would be proportional to the inverse of time, or 1/<age-of-universe>. The current rate is almost exactly that, evident if you cancel terms of 70 km/sec/mpc.
That rate (of 70) is going down, just not as much as expected. What is increasing is the recession rate of any given object. So take a rock that is a mpc away. It is currently receding at 70 km/sec. If expansion is flat, it will, per Newton, still be receding at 70 km/sec in 14 billion years at which point it will be 2mpc away for an expansion rate of 35 km/sec/mpc. But due to dark energy, it will be receding at more like 140 km/sec in 2 billion years for an expansion rate of 60 km/sec/mpc, lower than 70 (so that rate is going down, not up), but still faster than 35 for linear. It is predicted to level out at around 57 km/sec/mpc in the long run, which is exponential expansion. This expansion will eventually put every pair of non-gravitationally-bound glowing objects beyond their respective event horizons and light from one object will never reach another. Given linear expansion, light will get from anywhere to anywhere else given enough time. There would be no event horizon.
Numbers are not well computed, just off the top of my head. The 57 part is not made up.
Post by: Origin on 06/01/2022 02:59:03
The last statement is wrong. Flat expansion (neither increasing nor decreasing) would be proportional to the inverse of time, or 1/<age-of-universe>. The current rate is almost exactly that, evident if you cancel terms of 70 km/sec/mpc.Thanks for pointing out my misconception and taking the time to explain it to me. I don't quite get it, but I'm getting there.
That rate (of 70) is going down, just not as much as expected. What is increasing is the recession rate of any given object. So take a rock that is a mpc away. It is currently receding at 70 km/sec. If expansion is flat, it will, per Newton, still be receding at 70 km/sec in 14 billion years at which point it will be 2mpc away for an expansion rate of 35 km/sec/mpc. But due to dark energy, it will be receding at more like 140 km/sec in 2 billion years for an expansion rate of 60 km/sec/mpc, lower than 70 (so that rate is going down, not up), but still faster than 35 for linear.
Post by: Eternal Student on 11/01/2022 11:45:25
I needed a distraction so I had started writing something for this thread a few days ago but it has grown a bit too large. Rather than just throwing it all away, I might as well just post what I've done. It's long, so feel free to just ignore it. I've not checked the spelling or grammar or tidied it up much, sorry
I have a bit of time to look through this and add some comments, I hope you won't mind.
Let's race through what we use as the basis for this sort of cosmology and see where "dark energy" and the expansion of space apppears and begs for some explanation. This is General Relativity and especially the Friedmann equations as far as I'm concerned.
Space is too complicated to construct the actual stress-energy-momentum tensor that should be used in the Einstein Field Equations. There are too many planets, bits of gas and assorted stuff all over the place. We find new meteors in or near our solar system all the time and looking ouside of our solar system we find new stars with our telescopes every week. The recent Hubble "deep field" photographs demonstrate that what may appear to be fairly empty space at first glance is likely to be full of stars and indeed whole galaxies.
So let's assert that there is no hope of constructing the actual stress-energy tensor we would really want. Some sources will mention that we couldn't realistically solve the Einstein Field Equations with such a complicated stress-energy tensor anyway - this is true but almost irrelevant. It's not a question of how much computing power could be brought to bear on the problem. We just DO NOT HAVE the information we need - we would need to know the location of everything in the universe.
So, what we do is simplify the situation. There is an assumption that the universe is isotropic and homogeneous. The commonly used models treat space as if it is filled by something that is referred to as a "cosmological fluid". What is a cosmological fluid? See textbooks for a full answer. I've got to rush over things here: A cosmological fluid is directly comparable to an ideal fluid in other areas of physics. Our comsological fluid has many components, each component would behave like a fluid in it's own right. The cosmological fluid is the fluid you get when you mix all those components up perfectly ("stir well") to create a homogenised fluid. The use of the term "fluid" isn't suggesting that there is some liquid thing in space, just that the stress-energy tensor we need for GR is equivalent to the stress-energy tensor produced by an ideal fluid.
- - - - - -
First stop, or pause for thought
What if modeling the contents of space as if it is a cosmological fluid is NOT reasonable. Specifically, we know that space is not isotropic and homogeneous at small scales. What if this makes an important difference to the final results you extract from General Relativity and the Einstein Field Equations (EFE)? Let's phrase this another way: We cannot use the correct stress-energy tensor in the EFE, so instead we use something that is like an idealised average and assumed to remain quite unform across the universe. We simply hope that the results we obtain will apply to the universe in some average sense, or over large enough scales.
This might sound like a small issue, if you input an average value n times then you get an output which should be much the same as if you had really inputted n different individual values. This works well where the function performed on the input is "linear", but it falls apart if the function is non-linear. The sort of calculations and manipulations perfomed in GR are sometimes non-linear.
- - - - -
Anyway, what do we get from the Einstein Field Equations with this assumption? We get the Friedmann equations.
Here's the first Friedmann equation:
= 
[This form of the Friedmann equation is from page 338, An introduction to Spacetime and Geometry, Sean Carroll]
where H = The Hubble "constant" (but it's important to note that H= H(t) will vary with time).
G = usual Gravitational constant.
ρi = energy density of the i th component of the cosmological fluid. There is just one value of the index i which represents a "fictitious" energy density contribution from the curvature of space. To say that another way, there is a term ρc which is NOT the energy density of a component of the cosmological fluid, it is just here to replace the need to add a term dependant on k into the equation. (Just for the sake of completion, ρc =
where k = curvature. So that, ρc, the energy density due to curvature is positive if k is negative and vice versa).What do we see from this equation?
H is real valued, so H2 is certainly non-negative.
Therefore, it is not possible for all of the energy densitiy components ρi to be negative.
We can apply the model for arbitrary cosmological fluids, for example, where there is JUST matter and no other fluid components. There could always be a fictitious energy density for the curvature of space, which is a shame - but we can at least reduce the right hand side of the equation to a sum of just two components. At least one of these must be non-negative by the earlier reasoning.
So if the energy density contribution from curvature is negative then the energy density of any (proper) component in the cosmological fluid must be positive. Editing: This post is too long, I can't go through all the arguments that suggest energy densities should be positive (they are only suggestions anyway).
We could just make the reasonable assumption that the energy density contribution of any real component of the contents of space must be positive. I mean, this is quite reasonable, if there is something there then it should have some mass (which is equivalent to energy density) or else be something with a positive energy like a photon. However, the full situation is potentially more complicated and I would refer anyone to chapter 4, section 6 of the aforementioned book (Spacetime and Geom, Carroll) where the various Energy conditions that might constrain the stress-energy tensor are discussed. Without further discussion, we will be assuming the Weak Energy Condition (WEC), so that all energy densities of any component of our cosmological fluid will be non-negative.
OK, We need to take the idea that ρi ≥ 0 for every real component of the cosmological fluid and go forward to look at the second Friedmann equation:
= 
Where ρi = energy density of i th component (as before) ;
Pi = Pressure of the i th component.
and a = a(t) is the scale factor.
In this equation we don't have to include the index, i, that represented a component from the curvature of space. We can if you want but the (fictitious) pressure from the curvature component would be precisely negative one-third of it's fictitous energy density, so the whole term ρ + 3P becomes 0 and including another 0 in the sum is just needless work.
Now we are assuming that every ρi ≥ 0. So if the pressure, Pi , from each component of the cosmological fluid was also positive, then the entire right hand side of the equation is negative. Since the scale factor, a, is always non-negative, we see that
would always be negative.This quantity
is one parameter that can be used to describe the acceleration of expansion of space. There is another parameter 
which can also be used to examine and describe the acceleration of expansion. They are not the same and there can be situations where > 0 but <0 (for example consider a(t) = t2). This, I think, is where most of the discrepency between Halc and Origin has come from in one of the earlier posts.I'm going to follow the convention from the textbook previously mentioned:
In practice, "accelerating" usually refers to a situation where
>0, even if < 0. [page 339, Spacetime and Geometry, Sean Carroll]
Anyway, what we conclude is that if every component of the cosmological fluid had the properties you would imagine for a fluid - specifically that they have positive energy density and positive pressure - then it is inescapable that the acceleration of the expansion of space would be negative (
<0). To paraphrase this, the expansion would NOT be accelerating it would be slowing down.This is not what we have actually observed. In our real universe it seems that
> 0 at the current time ("the expansion of space is accelerating"). Let's do exactly what some physicist(s) had to do: Look at the Friedmann equations again and recognise that what we need is a component of the cosmological fluid that is most unusual. It would have properties that are unlike any real fluid you might find in your house. We need a component with negative energy density OR ELSE a negative pressure (or both would be just fine). This really strange component of the contents of space is what you might like to call "dark energy".1. Could it be something with a negative energy density? Well, maybe. This would violate the Weak Energy Condition (WEC) but maybe that was just too restrictive and far too optimistic anyway. We could replace this with another condition like the Null Energy Condition (NEC) which effectively allows a cosmological fluid component to have negative energy density provded the pressure of the fluid is positive and compensates sufficiently. What does this mean? Let's be honest, it's not worth discussing here. See page 175 of Spacetime and Geometry, Sean Carroll if you're intersted. It's not the choice that most physicists have made and seems less promising as an explanation of what dark energy is.
2. Could it be something with a negative pressure? Again maybe. This is the choice more physicists will make. It is possible to imagine that there is a component of the contents of space that we will call "vacuum energy". Vacuum energy can be modeled with the stress energy tensor of a fluid with parameter ω = -1. All this means is that it's a fluid (as far as the stress energy tensor is concerned) and its pressure is precisely the negative of its energy density.
3. Just for the sake of completion we could mention that if we were to assume the Strong Energy Condition (SEC) must apply to components of the cosmological fluid, then it is inescapable that ρ + 3P ≥ 0 for every component and then
is always negative. Hence, the acceleration of expansion is quite bad news for the SEC: At least one component of the cosmological fluid must have properties that violate the Strong Energy Condition.Are we all done? Almost, we need to just take a quick glance at the Einstein Field Equation (EFE). Here it is:
Gμν = k . Tμν (where k = a constant)
The left hand side involves the geometry, especially the curvature, of space. The right hand side involves the contents of space. In particular, the right hand side involves the energy and momentum of the contents of space. It's an equation, so if you change one side then the other side must change and vice versa - change the other side and the first side has to change. There is a well known saying that I will paraphrase here: The left hand side tells matter how it should move. The right hand side tells space how it should curve.
At the moment, with the EFE in the form shown above, vacuum energy is included in the over-all stress-energy tensor of the universe Tμν but we can break this tensor apart into two pieces, one part from the vacuum energy and the other part being... well everything else that isn't vacuum energy (so that will be the other cosomological fluid components we had in our cosmological model).
We get this:
Gμν = k . T'μν - Λ. gμν (where k and Λ = some constants). Note that T'μν does have a dash ' in it but it's not printing clearly - it's not quite the same as Tμν we have subtracted the vacuum energy component out of it.
Anyway, being an equation, we can take the last term over to the other side as usual. We get this:
Gμν + Λ gμν = k . T'μν (where k and Λ = some constants)
Now that form of the EFE shown just above is known as the EFE with a cosmological constant, Λ. It describes how space curves in response to some stress-energy given by the tensor T' under the assumption that there should be a cosmological constant Λ. Equally the equation tells us how the contents described by the tensor T' must move in response to spatial curvature given by the left hand side (under the assumption that there is a cosmological constant Λ).
There is very subtle shift here but it all happens just because something was put on one side of the equation and not the other side. I'm going to phrase it another way: With a cosmological constant, there is a change in the rules of movement for the contents of space. However, the contents of space is given by the tensor T' which does not need to include any component so strange as vacuum energy (we subtracted that bit out).
Without a cosmological constant the rules of movement are different (arguably simpler) BUT there must be a strange component in the contents space that behaves like vacuum energy.
Finally we're ready to answer a question from Aeris directly:
Has anyone ever considered the possibility that Dark Energy may not exist at all and that the space can just expand without anyYes, very much so. With a cosmological constant in the Einstein Field Equations, the rules of movement for the contents of space are just different and space can expand and indeed accelerate even if all it has in it is just the more conventional contents (not dark energy) that we're all happy with.outside forcedark energy acting on it?
Is that all there is to it then? There isn't any dark energy, it's just that we should have a cosmological constant in the EFE, i.e. just accept that General Relativity needed a slight adjustment?
Most of what we attribute to dark energy can be explained by a non-zero cosmological constant but not necessarily all of it. The terms "vacuum energy" and "dark energy" are sometimes used interchangeably but there should really be a fine distinction between the two. Vacuum energy is presumed to be a constant and uniform characteristic (or component) of any volume of space, so it's energy density never changes. No matter where or when you sample 1 cubic metre of space there should be the same amount of vacuum energy in it. Dark energy may be something that does have a little variation through space (and possibly time).
Here's one example: Refer to page 360 of Spacetime and Geometry, Sean Carroll - where it is suggested that the comsological constant may not quite as "constant" as we might have hoped. This means it would be more like a parameter or quantity associated with something specific to that piece of space (let's call it the "dark energy" in that bit of space). So dark energy mimics the behaviour of vacuum energy as far as General Relativity is concerned but the amount of dark energy might vary slightly across the universe and through time.
The spatial variation in dark energy should be small (according to Carroll) otherwise the effects of a high concentration in one area of space would have been noticed similar to the way dark matter was detected.
--- This is too long, I'm stopping now. Bye and best wishes ----
Post by: Aeris on 15/01/2022 10:36:11
Post by: Petrochemicals on 16/01/2022 08:48:34
Post by: Eternal Student on 16/01/2022 17:56:56
There is a lot that could be discussed here. However, before we do this, I've got to ask if it is possible that you might have accidentally merged several ideas?
We know it makes galaxy's edges rotate faster than they are calculated to do.That's interesting but more usually considered to be something caused by dark matter rather than dark energy.
This seems remenisant of the orbit of Mercury precessing faster than calculated.Could that be the discovery of Neptune due to its effect on the orbit of Uranus? Mercury was quite well away from all of this.
Mercury and the precession of its orbit is usually explained another way (by using GR instead of Newtonian Gravity etc.)
Best Wishes.
Post by: Petrochemicals on 17/01/2022 08:16:22
Hi @Petrochemicals ,quite right, I am thinking of dark matter. I will have to pay a bit more attention.
There is a lot that could be discussed here. However, before we do this, I've got to ask if it is possible that you might have accidentally merged several ideas?
Yes, relativity and Mercury's procession. It all seems fairly similar to me.We know it makes galaxy's edges rotate faster than they are calculated to do.That's interesting but more usually considered to be something caused by dark matter rather than dark energy.This seems remenisant of the orbit of Mercury precessing faster than calculated.Could that be the discovery of Neptune due to its effect on the orbit of Uranus? Mercury was quite well away from all of this.
Mercury and the precession of its orbit is usually explained another way (by using GR instead of Newtonian Gravity etc.)
Best Wishes.
Post by: Iannguyen on 10/02/2022 09:06:39
Dark Energy alternatives have been offered. According to some scientists, our Galaxy is located within a low-density area induced by the passage of a density wave. This large-scale wave in space-time might have been caused by the Big Bang. As this primordial wave traveled across the cosmos, it left a low-density ripple tens of millions of light-years across, which is now home to the Galaxy. While this discrepancy in space-time features is theoretically feasible, it would violate the Copernican principle, which claims that the cosmos is homogeneous on enormous scales.
Post by: Colin2B on 14/02/2022 08:59:49
Dark Energy is a theorized kind of energy that has a negative, repulsive force and behaves similarly to gravity. .........lThe material you are quoting is copyrighted and should be acknowledged as such eg “All material is © Swinburne University of Technology except where indicated”
Please don’t quote large sections without acknowledging the source.
Post by: evan_au on 15/02/2022 09:18:53
- It is widely known that some of the candidates for Dark Matter are hypothetical Weakly-Interacting Massive Particles (WIMPs) predicted by Supersymmetry.
- What was new to me today is that Supersymmetry can have something to say about Dark Energy too (Dark Energy is more commonly identified with Einstein's Cosmological Constant)
- Apparently, in some Quantum field theories, the "Cosmological Constant" could take on different values
- And it could suddenly jump from one value to another (with dire consequences for the universe we know)
- But if some Supersymmetry conjectures hold true, you can constrain the values of the Cosmological Constant (so it is more constant)...
Listen from 1 hour 7 minutes (for about 2 minutes)
https://www.preposterousuniverse.com/podcast/2022/02/07/183-michael-dine-on-supersymmetry-anthropics-and-the-future-of-particle-physics/
...if you listen for 2 minutes before & after this, he also talks about some Dark Matter candidates
Post by: Eternal Student on 16/02/2022 01:24:51
I've listened to the time between about 1:03 and 1:12.
I couldn't find any mention of WIMPS but you might have just included that in your own general discussion.
- Apparently, in some Quantum field theories, the "Cosmological Constant" could take on different valuesI did find that. This seemed to be in the context that other universes entirely could have different values of the cosmological constant.
And it could suddenly jump from one value to another (with dire consequences for the universe we know)I more or less found something like that.
- But if some Supersymmetry conjectures hold true, you can constrain the values of the Cosmological Constant (so it is more constant)...
I might listen to the whole of the podcast later.
Thanks again and best wishes to you.