View Full Version : Did Cosmological Constant vary since Big-Bang?

dapifo

2015-Dec-09, 03:44 PM

Cosmological constant Λ = 10 e-116 J . It is the energy that produces the current expansion of the universe.

But as the expansion of universe speed (acceleration) has been different since BB, may we say that it has been changing sinc BB ?

ShinAce

2015-Dec-09, 04:26 PM

As the universe expands, the matter in it gets thinned out. The light in the universe also thins out. So basically, the energy in the universe thins out as it expands.

Except dark energy. If the energy associated with the cosmological constant does NOT thin out during expansion, then that explains the accelerated expansion. It's called the lambda cold dark matter model and is the main model we use today: https://en.wikipedia.org/wiki/Lambda-CDM_model

Then there's inflation, which is a different beast onto itself.

So the answer is, it doesn't need to vary. It might, but it doesn't have to.

John Mendenhall

2015-Dec-09, 05:40 PM

Wiki says the cosmological constant is invariant in space and time.

Amber Robot

2015-Dec-09, 07:30 PM

Wiki says the cosmological constant is invariant in space and time.

That may theoretically be true, but we may not have the data to test that.

Grey

2015-Dec-09, 08:00 PM

So the answer is, it doesn't need to vary. It might, but it doesn't have to.Right. The simplest possibility is a cosmological constant that doesn't change with time, and that's consistent with our observations at this point. But there's enough margin of error in those observations that a different model, with a time-varying cosmological constant (maybe better to call it a cosmological parameter in that case), could also fit our observations. With better observations, we may be able to decide between those two possibilities at some point.

dapifo

2015-Dec-10, 10:09 AM

If Cosmological Constant has been always constant (same value) then the velocity of expansion of the Universe would be always the same.

But attached image tell us that the velocity has been different for different ages ... and now it is accelerating !!

Ken G

2015-Dec-10, 10:55 AM

If Cosmological Constant has been always constant (same value) then the velocity of expansion of the Universe would be always the same.No. Imagine a rocket ship, with an engine that is blasting out exhaust at a constant rate. We could call that a "rocket constant", and it would be a tiny bit like the cosmological constant-- but does it imply that the velocity of the rocket is always the same? It just doesn't follow.

We certainly need the cosmological constant to be a constant, or there is no chance we will ever be able to have a theory of the dynamics of the universe. If the cosmological parameter is allowed to change with time, so it is a parameter we can adjust to fit the dynamics of the universe, then the cosmological parameter will never be saying anything different from the dynamics of the universe-- it will never be any kind of actual theory. The problem is, the expansion of the universe is just one thing, and it only shows up on one scale-- the scale of the expansion of the universe. Science theories have to be unifying-- they have to apply to multiple things. So it's bad enough if the cosmological constant is constant, because we still have no other phenomena to unify with it, other than the expansion of the universe. But at least if it is constant, we can unify that expansion at different ages with each other, so it's still a science theory.

Cougar

2015-Dec-10, 01:35 PM

Cosmological constant.... It is the energy that produces the current expansion of the universe.

As I understand it, it is the energy that produces the current acceleration of the expansion of the universe. As to "what produces the expansion," maybe someone else knows. I don't.

Ken G

2015-Dec-10, 02:30 PM

All models of the expansion that I know of always require there to be expansion already, so I don't think there is anything in these models that "produces" expansion, it's just an initial condition.

Grey

2015-Dec-10, 03:24 PM

We certainly need the cosmological constant to be a constant, or there is no chance we will ever be able to have a theory of the dynamics of the universe. If the cosmological parameter is allowed to change with time, so it is a parameter we can adjust to fit the dynamics of the universe, then the cosmological parameter will never be saying anything different from the dynamics of the universe-- it will never be any kind of actual theory.Well, that's not really true. It would be true if you just meant that the cosmological parameter varied essentially randomly, with no pattern, and we assigned a value to it for each epoch without having any model of how or why it changes.

But on the other hand, you could have a model where the cosmological parameter changes according to some equation of state. The various "quintessence (https://en.wikipedia.org/wiki/Quintessence_%28physics%29)" models are exactly that, with a dark energy density that varies over time rather than being fixed. Those are certainly just as reasonable in principle (though slightly more complicated) than a model where the value remains constant, and certainly still science. We don't have the observations right now to distinguish between those models, so we tend to favor the simplest, with an actually constant cosmological constant. But future observations could certainly favor one of the quintessence models instead. With as little as we know about dark energy today, it's not reasonable to claim that we know all the details about it.

Ken G

2015-Dec-10, 05:40 PM

But on the other hand, you could have a model where the cosmological parameter changes according to some equation of state. The various "quintessence (https://en.wikipedia.org/wiki/Quintessence_%28physics%29)" models are exactly that, with a dark energy density that varies over time rather than being fixed. I should have been more clear by not focusing entirely on the time dependence issue. What I meant is that if the cosmological constant is allowed to be a function of time that is fit to the observed universal dynamics, then it would never be anything more than the universal dynamics. It would be like saying "we observe the scale parameter a(t) evolves like this, so our explanation of this is that the dynamics of the scale parameter is to evolve like that." That seemed to be what was being suggested in the OP.

What you are talking about would indeed be of value-- if we had some theory of how the cosmological parameter could evolve based on some other principle that was not the observed a(t), and that it in turn did fit the a(t) function with significantly fewer independent parameters than were present in the data. So I should not have said that any time-dependent function would be useless, I really just meant it would be useless to fit the "cosmological parameter" to a(t), and call that a theory of cosmology. We don't want to work backwards from a(t), and then fit some arbitrary cosmological parameter form, and as a(t) gets more accurate, we introduce more degrees of freedom into the cosmological parameter! If we start seeing that happening, that's what wouldn't be a dynamical theory any more.

At least a constant parameter is not arbitrary, so what we'd like to see is that once the data supports two or three independent fit parameters in how a(t) deviates from standard GR, we'd like to see that data still fits a single-parameter cosmological constant. What you are saying is, perhaps we will have to abandon a constant parameter, but if we have some other theory that we anticipate in advance, and it has only one free parameter even though time dependent, and it fits data that can support two or three independent fit parameters, then we still have something. I agree-- it's not so much the time dependence I was worried about, it is the arbitrariness of opening up the function to just any time dependence we need. But I don't know how long it will be before the data is accurate and reliable enough for this problem to appear, I expect it will be quite a while. I'm not sure I'll ever see the data be good enough to even distinguish a cosmological constant from a one-parameter form of quintessence, but if it's ever good enough to say "neither," we'll be in pickle.

dapifo

2015-Dec-10, 10:57 PM

But if universe has evolved to different velocity-acceleration during the different age from Big-bang....then it means that cosmological constant has been varing also during these ages.

Cosmological constant could be only a picture at the current time...

Ken G

2015-Dec-10, 11:56 PM

But if universe has evolved to different velocity-acceleration during the different age from Big-bang....then it means that cosmological constant has been varing also during these ages.First of all, velocity and acceleration are not the same thing, and there's no such thing as velocity-acceleration. Second of all.. oh never mind.

Reality Check

2015-Dec-11, 12:01 AM

dapifo, there is a big clue in the name of the cosmological constant - constant means constant :D.

The Friedmann–Lemaître–Robertson–Walker metric (https://en.wikipedia.org/wiki/Friedmann%E2%80%93Lema%C3%AEtre%E2%80%93Robertson% E2%80%93Walker_metric) describes how the universe expands.

The second equation states that both the energy density and the pressure cause the expansion rate of the universe {\dot a} to decrease, i.e., both cause a deceleration in the expansion of the universe. This is a consequence of gravitation, with pressure playing a similar role to that of energy (or mass) density, according to the principles of general relativity. The cosmological constant, on the other hand, causes an acceleration in the expansion of the universe.

A "different velocity-acceleration" does not need a varying cosmological constant.

Grey

2015-Dec-11, 02:38 AM

But I don't know how long it will be before the data is accurate and reliable enough for this problem to appear, I expect it will be quite a while. I'm not sure I'll ever see the data be good enough to even distinguish a cosmological constant from a one-parameter form of quintessence...Indeed. As I was writing that first post, I was thinking, well, presumably in the extremely long term, we'll be able to figure it out. For example, in a billion years, if we're still around, we'll have a long enough baseline of observations that we'll have actually seen any changes, and have a pretty good idea of how to characterize them. But it's true that in the shorter term, it's really hard to distinguish these cases, and we might not be able to distinguish them without that long period of observation.

but if it's ever good enough to say "neither," we'll be in pickle.Absolutely! :)

Ken G

2015-Dec-11, 03:09 AM

Yeah, I think the basic problem with dark energy is that it is only starting to dominate the universal dynamics rather recently, so it is more about what will happen than what did happen. Unfortunately, the "what will" is on a timescale rather longer than we can normally call a prediction! The larger problem is, what makes cosmology interesting and important is what it says about the past-- how the universe came to have the properties it has, nucleosynthesis of baryons, the cosmic microwave background, and so on. Dark energy had very little to say about any of that! So although it's a really amazing question how empty space can affect the expansion of the universe when there's a lot of it, it's really just plain not that important of an issue to what we care about. Maybe there's some "zero point energy" there that we could learn to harness somehow, but it's so little on scales we have access to, I am really left to wonder if dark energy is really all that important at all, or if we will ever be able to constrain its properties in any useful way. My guess is, the "cosmological constant" will remain as long as I'm around, simply because it will always be the easiest placekeeper for something that humanity just doesn't know about-- and isn't going to get to. I may be wrong, but that's how it looks.

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