No need for dark energy , gravity will suffice.

[Peter Watkins]

No need for "dark energy", gravity will suffice.

In 1929 it was observed that, with rare exception, galaxies in all directions are exhibiting degrees of red-shift that increase with distance. This information alone is sufficient to, (a), describe the structure of the universe, (b), state that collapse is inevitable, and, (c), predict that the rate at which galaxies separate will increase. This being the case, why was the "dark energy" theory ever put forward? It is totally unnecessary.

Addendum.
What the "faster with distance" view shows is that the rate of expansion is slowing. As this continues, galaxies will move apart at an increasing rate. This is what I mean by unnecessary. It is the restraint of gravity that is causing the rate of galaxy separation to increase. This is why it can be stated that collapse is inevitable

 

[ThalorB]

I recall reading something not too long ago stating that Einstein was never satisfied with his general theory of relativity because it included a "fudge" factor: I believe it was a cosmological constant. Some have found that calculations considering dark energy can produce that value almost exactly. So, it's not "necessary," unless you are looking for complete understanding of the universe. For example, is it always constant?

 

[Nabeshin]

In 1929 it was observed that, with rare exception, galaxies in all directions are exhibiting degrees of red-shift that increase with distance. This information alone is sufficient to, (a), describe the structure of the universe, (b), state that collapse is inevitable, and, (c), predict that the rate at which galaxies separate will increase. This being the case, why was the "dark energy" theory ever put forward? It is totally unnecessary.

It is not unnecessary. Hubble's expanding universe model predicts that the recession velocity of galaxies is strictly tied to its distance. However, we observe the expansion to actually be increasing in rate (not predicted in the older models).

(Correct me if I'm wrong but I believe that we see deviations in the recession velocity for very far away galaxies, indicating that in the past they were moving slower than they are today, indicating an accelerated motion?)

 

[Janus]

In 1929 it was observed that, with rare exception, galaxies in all directions are exhibiting degrees of red-shift that increase with distance. This information alone is sufficient to, (a), describe the structure of the universe, (b), state that collapse is inevitable, and, (c), predict that the rate at which galaxies separate will increase. This being the case, why was the "dark energy" theory ever put forward? It is totally unnecessary.

Simply this: The receding galaxies all gravitationally attract with each other. This acts against the expansion. IOW, the mutual gravitational attraction of the Universe tends to want to pullit together. Of course, as the galaxies get further apart, this gravitational attraction gets weaker.

So, the question became, Is the universe expanding fat enough that the distance between the galaxies grows at a great enough rate that the gravitational attraction weakens faster than it can slow down the expansion, or will gravity eventually stop the expansion and cause the universe to collapse?

In both cases you would expect the expansion to slow with time, but with the first, it never slows to zero.

In the 1990's observations were made to test which of these possible futures the universe had. As one looks out at the universe, the further away you look, the further back in time you look. If you plot a number of galaxies distances against how fast they are receding, you can get a graph that shows how the universe has expanded over time. This graph would show the rate at which the expansion was slowing and tell us if it could be expected to continue doing so.

The surprise came when it was found that the graph didn't show the universe's expansion slowing at all, but speeding up instead. It was the same as throwing a ball in the air and expecting to to slow down as it climbed higher, but instead seeing the ball climb at ever increasing speeds. And just like there would have to be something actively pushing the ball upwards for it to behave this way, the universe would need something actively pushing it apart for it to behave as the observations showed. This "something" was labeled Dark Energy.

 

[Chronos]

As a footnote to Janus, supernova studies by Perlmutter pushed the dark energy hypothesis into the mainstream - e.g., http://arxiv.org/abs/astro-ph/0303428

 

[Chalnoth]

In 1929 it was observed that, with rare exception, galaxies in all directions are exhibiting degrees of red-shift that increase with distance. This information alone is sufficient to, (a), describe the structure of the universe, (b), state that collapse is inevitable, and, (c), predict that the rate at which galaxies separate will increase. This being the case, why was the "dark energy" theory ever put forward? It is totally unnecessary.

The point is that gravity, when combined with a model for the contents of the universe, provides a very specific prediction for the relationship between redshift and distance (among a great many other things which I won't go into here...). If we assume that normal matter plus dark matter are the only contents in the universe, we get the wrong answer. Clearly this means one of two things:
1. Our model of gravity is incorrect a very large distances (potential solution: modified gravity).
2. Our understanding of the contents of the universe is incorrect (potential solution: dark energy).

Both are being investigated.

 

[Peter Watkins]

My whole point is that the increase in the rate of recession, or separation from us, is not due to an increase in the rate of universal expansion but rather, a decrease in the rate of expansion due to gravitational drag. That is why "dark energy" is not necessary.

 

[Chalnoth]

My whole point is that the increase in the rate of recession, or separation from us, is not due to an increase in the rate of universal expansion but rather, a decrease in the rate of expansion due to gravitational drag. That is why "dark energy" is not necessary.

Nobody's going to take you seriously without a well-motivated mathematical model that describes this expansion and also fits with current experiment. And even then, the fact remains that the experiments to date simply aren't good enough to distinguish between different potential explanations for the accelerated expansion, so unless your idea here has significantly fewer hypothetical entities than the cosmological constant (which only has one additional degree of freedom), there's no way anybody is going to think it likely to be true.

 

[mysearch]

Simply this: The receding galaxies all gravitationally attract with each other. This acts against the expansion. IOW, the mutual gravitational attraction of the Universe tends to want to pull it together.

Nobody's going to take you seriously without a well-motivated mathematical model that describes this expansion and also fits with current experiment.

Purely for my own education, I am trying to understand which accepted model is said to explain the expansion of the universe. As I understand it, so far, the following equation is used by many cosmology calculators to derive the expansion of the universe with time as a function of the energy density make-up:

$$\Delta t = \frac {\Delta a}{aH_0 \sqrt{ (\Omega_M /a^3) + (\Omega_R /a^4) +(\Omega_\Lambda) } }$$

1. This energy-density model appears to only include of baryons matter, cold dark matter, radiation and dark energy, but does not seem to explain how any expansion took place during the 1st 7 billion years.

$$H^2 = \left( \frac {\dot a}{a} \right)^2 = \frac{8}{3} \pi G( \rho_m + \rho_{cdm} + \rho_\lambda + \rho_\Lambda )$$

2. Based on the equation above, why is Friedmann’s equation thought to define an expansive velocity as implicit within the Hubble constant (H), when the energy density of each component would seem to be describing gravitation collapse?

$$\left( \frac {\ddot a}{a} \right)^2 = -\frac{4}{3} \pi G( \rho_m + \rho_{cdm} + 2 \rho_\lambda - 2 \rho_\Lambda )$$

3. In addition, is the acceleration equation above, derived from the Friedmann equation, not implying that the accelerated expansion of the universe would be negative, i.e. collapsing, until the negative pressure of dark energy exceeded the normal gravitational effects, i.e. post + 7 billion years?

4. If the universe is homogeneous, at the very large scale, and for most of its existence has had a very low energy density per unit volume of space, wouldn’t the universe, as a whole, approximate to a weak gravitational field model without some overall gravitational centre?

5. Can this large-scale homogeneous model be said to have any other centre of gravity, which would explain the overall gravitational slow-down of expansion as implied by Janus’ statement?

6. What is meant by the expansion of space that results in distance between galaxies increasing, i.e. if gravity is no longer described as a force, what geodesic curvature is causing the galaxies to `roll away` from each other?​

I am not trying to suggest an alternative model, simply trying to understand the details of the current accepted model. Thanks

 

[Chalnoth]

Purely for my own education, I am trying to understand which accepted model is said to explain the expansion of the universe. As I understand it, so far, the following equation is used by many cosmology calculators to derive the expansion of the universe with time as a function of the energy density make-up:

$$\Delta t = \frac {\Delta a}{aH_0 \sqrt{ (\Omega_M /a^3) + (\Omega_R /a^4) +(\Omega_\Lambda) } }$$

1. This energy-density model appears to only include of baryons matter, cold dark matter, radiation and dark energy, but does not seem to explain how any expansion took place during the 1st 7 billion years.

How does it not explain the expansion? The expansion is explicitly given by the density of these components through Friedmann's equations.

$$H^2 = \left( \frac {\dot a}{a} \right)^2 = \frac{8}{3} \pi G( \rho_m + \rho_{cdm} + \rho_\lambda + \rho_\Lambda )$$

2. Based on the equation above, why is Friedmann’s equation thought to define an expansive velocity as implicit within the Hubble constant (H), when the energy density of each component would seem to be describing gravitation collapse?

As the matter dilutes, the Hubble parameter H approaches a constant value. H is defined as:
$$H \equiv \frac{1}{a}\frac{da}{dt}$$

So if H = constant, we have:
$$\frac{da}{dt} = H_0 a$$

...which is the equation for exponential growth, meaning:

$$a(t) = a(0) e^{H_0 t}$$

$$\left( \frac {\ddot a}{a} \right)^2 = -\frac{4}{3} \pi G( \rho_m + \rho_{cdm} + 2 \rho_\lambda - 2 \rho_\Lambda )$$

3. In addition, is the acceleration equation above, derived from the Friedmann equation, not implying that the accelerated expansion of the universe would be negative, i.e. collapsing, until the negative pressure of dark energy exceeded the normal gravitational effects, i.e. post + 7 billion years?

Right, after inflation ended, the expansion of the universe decelerated until relatively recently.

4. If the universe is homogeneous, at the very large scale, and for most of its existence has had a very low energy density per unit volume of space, wouldn’t the universe, as a whole, approximate to a weak gravitational field model without some overall gravitational centre?

There is no gravitational center in the big bang theory.

5. Can this large-scale homogeneous model be said to have any other centre of gravity, which would explain the overall gravitational slow-down of expansion as implied by Janus’ statement?

I don't get what you're asking.

6. What is meant by the expansion of space that results in distance between galaxies increasing, i.e. if gravity is no longer described as a force, what geodesic curvature is causing the galaxies to `roll away` from each other?

Well, if you write down the FRW metric, there exist timelike geodesics where objects are stationary with respect to the coordinate system. It's really that simple.

 

[mysearch]

Hi Chalnoth,
Thanks for the response. Let me try to clarify some of the issues raised:

How does it not explain the expansion? The expansion is explicitly given by the density of these components through Friedmann's equations.

$$\Delta t = \frac {\Delta a}{aH_0 \sqrt{ (\Omega_M /a^3) + (\Omega_R /a^4) +(\Omega_\Lambda) } }$$

When I look at this equation, the Omega components appear to relate to energy density, which in the case of matter and radiation have no expansive properties, at least, within the general assumptions of the model after matter-radiation decoupling at +380,000 years. Dark energy is virtually a negligible issue until +5 billion years. As such, the equation seems more applicable to describing the rate of expansion in reverse, i.e. gravitational collapse, rather than expansion, especially as all components are added with the same sign.

As the matter dilutes, the Hubble parameter H approaches a constant value. H is defined as:
$$H \equiv \frac{1}{a}\frac{da}{dt}$$

So if H = constant, we have:
$$\frac{da}{dt} = H_0 a$$

...which is the equation for exponential growth, meaning:

$$a(t) = a(0) e^{H_0 t}$$

I don’t disagree that there is an exponential rate involved, but what puzzles me is what physical process describes this as exponential rate as expansive, when all the active components, in the 1st 7 billion years, seem to be associated with gravitational attraction, i.e. collapse.

Right, after inflation ended, the expansion of the universe decelerated until relatively recently.

My issue here is slightly tangential. As I have understood the expansion model, matter in the form of galaxies do not expand apart by traveling through space, but rather by the initial space that separates them continuing to uniformly expand per unit volume. This seem to suggest that ‘something’ had to actively continue to expand each unit volume throughout the 1st 7 billion years, as I don’t see that expansive momentum attributed to initial inflation is applicable to this model.

There is no gravitational center in the big bang theory.

I accept that this is the conclusion of the standard model. However, I would like to better understand how gravitational slowdown of the universe, as a whole, works without any notion of a centre of gravity.

Well, if you write down the FRW metric, there exist timelike geodesics where objects are stationary with respect to the coordinate system. It's really that simple.

If I assume a spatially flat model, i.e. k=0, the only geodesic seems to be associated with spacetime. For example, 2 photons initially traveling in parallel to each will eventually diverge in an expanding universe as a function of time. This seems to be the main conclusion of the FRW metric, especially if k=0. However, this appears to be very different to the curvature of spacetime due to an extreme gravitational centre of mass like a black hole. Again, this is why I was raising issues that suggested that a large-scale homogeneous model would appear to approximate a weak gravitational field model without any overall gravitational centre.

Again, I would like to stress that I have no pet theory of my own and the only reason for raising these issues is to get a better handle on the accepted model. Thanks

 

[Chalnoth]

I don’t disagree that there is an exponential rate involved, but what puzzles me is what physical process describes this as exponential rate as expansive, when all the active components, in the 1st 7 billion years, seem to be associated with gravitational attraction, i.e. collapse.

I really don't see why you find this disturbing. Those component dilute away, and when the cosmological constant remains, it takes over and drives an accelerated expansion.

My issue here is slightly tangential. As I have understood the expansion model, matter in the form of galaxies do not expand apart by traveling through space, but rather by the initial space that separates them continuing to uniformly expand per unit volume. This seem to suggest that ‘something’ had to actively continue to expand each unit volume throughout the 1st 7 billion years, as I don’t see that expansive momentum attributed to initial inflation is applicable to this model.

I think what you're looking for are the initial conditions of the system. Those were set by cosmic inflation, which is still poorly-understood, but appears to have been a period of very rapidly accelerated expansion (with a vastly greater Hubble factor than we have now) that occurred right at the limit of the earliest portion of our universe we can see.

I accept that this is the conclusion of the standard model. However, I would like to better understand how gravitational slowdown of the universe, as a whole, works without any notion of a centre of gravity.

I guess I don't really know what to say, except that when you construct a stress-energy tensor for a homogeneous, isotropic universe (which becomes diagonal with only two different components: energy density and pressure), and plug in the properties of the various types of matter, for normal matter, dark matter, and radiation domination, you get a decelerated expansion. The math just works. I don't really see a way to explain this other than mentioning that fact, though perhaps you might gain some satisfaction from working through it yourself.

If I assume a spatially flat model, i.e. k=0, the only geodesic seems to be associated with spacetime. For example, 2 photons initially traveling in parallel to each will eventually diverge in an expanding universe as a function of time. This seems to be the main conclusion of the FRW metric, especially if k=0. However, this appears to be very different to the curvature of spacetime due to an extreme gravitational centre of mass like a black hole. Again, this is why I was raising issues that suggested that a large-scale homogeneous model would appear to approximate a weak gravitational field model without any overall gravitational centre.

Well, while the spatial curvature of a k=0 FRW universe is indeed zero, it has space-time curvature, which is just another way of describing the expansion.

 

[PeopleSmoks]

Greetings,

I'm new to this forum, and don't claim to be a physicist or cosmologist, however I am fascinated by these subjects and hope my questions and comments aren't seen as silly.

A friend and I have often discussed the theory of chaos. Chaos simply being 'that without structure' and nothing more. When you speak of dark energy, I assume you refer to the energy of dark matter which was recently introduced as a means to account for a lack of mass in the comos. The origins of dark matter are, to my knowledge, yet unknown. My thoughts are that dark matter is a form of matter that is within chaos, but is neutral to both chaos and the cosmos which is what allows our universe to move through it.

I also buy into the theory that expansion will eventually slow, stop and the universe will collapse in on itself. I see three factors as contributing to this eventual collapse.

First, I believe that there is a black hole at the center of the cosmos which is the remnants of the singularity of the big bang acting in a manner similar to any star gone super nova. Having released it's energy to form the cosmos, it itself collapsed to form a gravity well. As it increases in mass by 'swallowing' matter, it's mass will increase, and with an increase in mass, an increase in gravity.

Second, I believe that there is little if any new energy created beyond that of the original big bang and that everything we see today is occurring as a result of that initial release of energy.

Third, I see the expansion into chaos as being resistive. Anything within chaos that is not dark matter is being pushed against and the rule of equal but opposite reaction fits my thinking. Eventually, enough pressure will build to were there is a push inward, with equal force to that which is currently pushing out.

In conclusion, I also believe that as chaos pushes, the central black hole's pull will increase exponentially to reach the speed of light to reform the singularity, and that the pressure of chaos on this sigularity will start the whole process again.

I strongly hope for comments and constructive criticism of my thoughts.

 

[Chalnoth]

Greetings,

I'm new to this forum, and don't claim to be a physicist or cosmologist, however I am fascinated by these subjects and hope my questions and comments aren't seen as silly.

A friend and I have often discussed the theory of chaos. Chaos simply being 'that without structure' and nothing more. When you speak of dark energy, I assume you refer to the energy of dark matter which was recently introduced as a means to account for a lack of mass in the comos. The origins of dark matter are, to my knowledge, yet unknown. My thoughts are that dark matter is a form of matter that is within chaos, but is neutral to both chaos and the cosmos which is what allows our universe to move through it.

The difficulty with this is that it's just not well-defined enough to actually determine what you mean by it. Any answer for what dark matter actually is must necessarily be mathematical. Mathematics is the only language that is specific enough to accurately describe the nature of dark matter.

I also buy into the theory that expansion will eventually slow, stop and the universe will collapse in on itself. I see three factors as contributing to this eventual collapse.

The evidence does not support this view.

First, I believe that there is a black hole at the center of the cosmos which is the remnants of the singularity of the big bang acting in a manner similar to any star gone super nova. Having released it's energy to form the cosmos, it itself collapsed to form a gravity well. As it increases in mass by 'swallowing' matter, it's mass will increase, and with an increase in mass, an increase in gravity.

There is no center of the universe. Far away from a black hole, its gravitational field is nothing special. If, for example, our Sun was suddenly replaced by an equal-mass black hole, the Earth would continue on its orbit precisely as before.

Finally, the big bang didn't act anything like a star going supernova. They aren't even comparable.

Second, I believe that there is little if any new energy created beyond that of the original big bang and that everything we see today is occurring as a result of that initial release of energy.

Based upon what?

Third, I see the expansion into chaos as being resistive. Anything within chaos that is not dark matter is being pushed against and the rule of equal but opposite reaction fits my thinking. Eventually, enough pressure will build to were there is a push inward, with equal force to that which is currently pushing out.

Except if the cause of the accelerated expansion is actually dark energy, then the nature of the pressure is what's driving the expansion in the first place.

 

[PeopleSmoks]

Chalnoth, I honestly appreciate your response. What I mean by chaos in my example is what the universe is expanding into. Now, from what I have read on the subject of dark matter, this is nothing more than another assumption needed to explain a lack of mass in the cosmos and it's true nature can't be measured aside from gravitational effects, the same way dark energy is used to fill gaps in so many theories. Really, I am only trying to propose a possibility as to it's origin and another alternative to how it fits in. You're more than right that mathematics is necessary to find the nature of dark matter. It seems no one has done it yet?

Einstein's adjustment to general relatiivity attempted to eliminate the possibility of acceleration and collapse, by establishing what was called the cosmological constant. This still is dependent on the density parameter, Omega and the effects of dark energy being assumed to be a positive constant. Basically, as I have read, dark energy has been theorized to be positive in order to explain constant and or accelerated expansion. I am currently trying to find something related to it possibly being neutral. String theory appears to be the only thing that seems to completely exclude the possibility of cosmic collapse or the cyclic model.

As is the case with everything related to black holes, there is some debate as to a difference between the gravitational effects of a black hole compared to a collapsed star when matter enters the event horizon. I've read that matter entering a dwarf star, polsar, super nova etc is converted to energy and expelled where as a black hole retains matter, light, etc and thus it's mass, adding it that of the black hole. This done, the mass of the black hole increases and so does it's gravitational effect. Yes, if the sun were to be replaced by a black hole of equal mass, all would remain constant according to Newton's laws. Reality is that planetary orbital decay has been measured. To use our solar syatem as a model, once Mercury enters the black hole, it's mass is added to the black hole making it's pull on Venus that much greater and so on. This is the basis for my thinking.

The whole debate about the center of the universe, whether there is a center and what's there, is exactly that, a debate. But, of what we can see within our universe most things seems to have a center. Many see no reason the universe should be any different.

Some debate also exists regarding accelerated expansion, since much of the evidence is based on red shift. Some problems with the affect of gravity on the infra red, the curvature of time/space and an unknown rate of decay of information have made red shift less accurate the further out we look. Using dark energy to fuel the rate of expansion is useless since we simply don't know it's nature. Where as if the energy produced by the big bang, which can't be measured either, is what is still fueling expansion, we at least have an event that pretty much everyone agrees happened.

The need for more energy from dark energy is only because of limitless expasion theories.

 

[Chalnoth]

Chalnoth, I honestly appreciate your response. What I mean by chaos in my example is what the universe is expanding into. Now, from what I have read on the subject of dark matter, this is nothing more than another assumption needed to explain a lack of mass in the cosmos and it's true nature can't be measured aside from gravitational effects, the same way dark energy is used to fill gaps in so many theories. Really, I am only trying to propose a possibility as to it's origin and another alternative to how it fits in. You're more than right that mathematics is necessary to find the nature of dark matter. It seems no one has done it yet?

You would be wrong. This is how it started, of course. But the evidence has mounted since then. The Bullet Cluster is particularly striking evidence, though even before that our observations of the cosmic microwave background dramatically solidified the case for dark matter.

Einstein's adjustment to general relatiivity attempted to eliminate the possibility of acceleration and collapse, by establishing what was called the cosmological constant. This still is dependent on the density parameter, Omega and the effects of dark energy being assumed to be a positive constant. Basically, as I have read, dark energy has been theorized to be positive in order to explain constant and or accelerated expansion. I am currently trying to find something related to it possibly being neutral. String theory appears to be the only thing that seems to completely exclude the possibility of cosmic collapse or the cyclic model.

Well, the thing is, the cosmological constant is a feature of General Relativity. It would be in the theory whether Einstein wrote it in or not. Theorists have supposed for a long time that there was some symmetry that set it to zero, but nobody has yet found a symmetry that could do that. The real problem, then, isn't that the cosmological constant exists, but instead why its value is so absurdly small. Granted, that is, that it's a cosmological constant at all, but then nobody has yet come up with a well-motivated alternative.

As is the case with everything related to black holes, there is some debate as to a difference between the gravitational effects of a black hole compared to a collapsed star when matter enters the event horizon. I've read that matter entering a dwarf star, polsar, super nova etc is converted to energy and expelled where as a black hole retains matter, light, etc and thus it's mass, adding it that of the black hole. This done, the mass of the black hole increases and so does it's gravitational effect. Yes, if the sun were to be replaced by a black hole of equal mass, all would remain constant according to Newton's laws. Reality is that planetary orbital decay has been measured. To use our solar syatem as a model, once Mercury enters the black hole, it's mass is added to the black hole making it's pull on Venus that much greater and so on. This is the basis for my thinking.

This is incorrect. What goes on inside the event horizon is irrelevant to what occurs outside it. Mercury's orbit would, for instance, be every bit as stable with a black hole as it currently is with the Sun. And if Mercury were to fall into the Sun, then Venus would see exactly as much mass inside its orbit as before, and so would have almost the exact same orbit (there would be a slight difference due to the minuscule difference in the distribution of that mass, but it wouldn't be significant).

Naturally, the orbits of the planets would decay on extremely long time scales. I'd have to look the exact numbers up, but we're talking a number of orders of magnitude beyond billions of years here.

The whole debate about the center of the universe, whether there is a center and what's there, is exactly that, a debate. But, of what we can see within our universe most things seems to have a center. Many see no reason the universe should be any different.

There is no debate. There simply is no center.

Some debate also exists regarding accelerated expansion, since much of the evidence is based on red shift. Some problems with the affect of gravity on the infra red, the curvature of time/space and an unknown rate of decay of information have made red shift less accurate the further out we look. Using dark energy to fuel the rate of expansion is useless since we simply don't know it's nature. Where as if the energy produced by the big bang, which can't be measured either, is what is still fueling expansion, we at least have an event that pretty much everyone agrees happened.

Well, there was no singularity in the finite past of our universe. As we look back in time, we see no starting point. What we do see is that our universe has changed with time in such a way as to hide the nature of what happened before. A number of experiments are currently underway to tease out the precise properties of the earliest epoch of our universe that we can observe.

And one thing that we do know, by the way, that the energy that currently exists in the universe was generated during inflation, which was a period of accelerated expansion early-on, the earliest period we can detect. It isn't clear what the precise properties of inflation were, but its behavior was much like a cosmological constant (with a very large value).

 

[PeopleSmoks]

Greetings Chalnoth. Thanks again for taking your time to reply to my post. When I say that dark matter and dark energy are only used to fill in gaps, I don't dispute their existense, rather the values given to them. Aside from a way to "prove" accelerated expasion, what reason is their for these to be given positive charge values? I read an article which inferred that dark matter would contain an equal number of positive and negative particles, thus making it neutral.

Once again, regarding the cosmological constant, my understanding is that Einstein made it part of his theory of general relativity for the purpose of avoiding the possibility of cosmic collapse, by giving it a value of zero? Yet, it seems that modern physicists have inferred a positive value to Omega, disregarding Einstein's original model? Also, what I meant by it being 'added' is that while working on his theory, he himself saw a variable that he didn't like and formulated the cosmological constant to correct this variable prior to general relativity being published.

And one thing that we do know, by the way, that the energy that currently exists in the universe was generated during inflation, which was a period of accelerated expansion early-on, the earliest period we can detect. It isn't clear what the precise properties of inflation were, but its behavior was much like a cosmological constant (with a very large value).

Here I again ask, if all energy was created during this period, why has a positive value been give to Omega and dark energy when Einstein's model gives Omega a value of zero? Also, I ask, if dark matter already exists within the cosmos, and is not being 'added' from an external source, wouldn't that mean that there is too much mass in the universe today, since we will need more tomorrow and it MUST be there tomorrow?

I'm currently searching articles and papers pertaining to things you've said in your comments.

 

[Janus]

Greetings Chalnoth. Thanks again for taking your time to reply to my post. When I say that dark matter and dark energy are only used to fill in gaps, I don't dispute their existense, rather the values given to them. Aside from a way to "prove" accelerated expasion, what reason is their for these to be given positive charge values? I read an article which inferred that dark matter would contain an equal number of positive and negative particles, thus making it neutral.

Once again, regarding the cosmological constant, my understanding is that Einstein made it part of his theory of general relativity for the purpose of avoiding the possibility of cosmic collapse, by giving it a value of zero? Yet, it seems that modern physicists have inferred a positive value to Omega, disregarding Einstein's original model? Also, what I meant by it being 'added' is that while working on his theory, he himself saw a variable that he didn't like and formulated the cosmological constant to correct this variable prior to general relativity being published.



Here I again ask, if all energy was created during this period, why has a positive value been give to Omega and dark energy when Einstein's model gives Omega a value of zero? Also, I ask, if dark matter already exists within the cosmos, and is not being 'added' from an external source, wouldn't that mean that there is too much mass in the universe today, since we will need more tomorrow and it MUST be there tomorrow?

I'm currently searching articles and papers pertaining to things you've said in your comments.

You are confusing Omega, which is the critical density of the universe, how it will , with Lambda which is Einstein's cosmological constant. Lambda was added by Einstein to provide an influence that would counter a static universe's (one that isn't expanding or contracting) tendency to collapse under its own mutual gravitational attraction. In order to work as needed, Lambda had to given a precise value to exactly counter gravity on the cosmological scale. If it varied by the least amount, the universe would undergo either runaway expansion or collapse.

When Hubble determined that the universe was expanding, the need for the Lambda term was dropped, as it was felt that the inertia of the galaxies' recession explained why the universe hadn't collapsed on itself.

When it was discovered that this expansion was speeding up with time, Lambda was given a new look as this was like the runaway expansion predicted by the "slightly off" Lambda mentioned above.

 

[ZapperZ]

I'm currently searching articles and papers pertaining to things you've said in your comments.

Try this on a cluster collision:

http://www.journals.uchicago.edu/doi/pdf/10.1086/508162

There's also an unbelievable amount of material already out there on DM/DE in case you are still looking.

http://arxiv.org/abs/0706.2986
http://arxiv.org/abs/0901.4090
http://arxiv.org/abs/0901.0632

Zz.

 

[Chalnoth]

When Hubble determined that the universe was expanding, the need for the Lambda term was dropped, as it was felt that the inertia of the galaxies' recession explained why the universe hadn't collapsed on itself.

When it was discovered that this expansion was speeding up with time, Lambda was given a new look as this was like the runaway expansion predicted by the "slightly off" Lambda mentioned above.

Well, not quite. Theorists never forgot about the cosmological constant. Very simple arguments demonstrated that the cosmological constant, if it were nonzero, had to be absurdly small, around 10^-120 in natural units. So most just figured that there must be some unknown symmetry that sets it to zero. No such symmetry has been found, but there are many theorists that still think it's more likely.

 

[PeopleSmoks]

Thaks to everyone for your replies to this amateur cosmologist's questions! Focusing on the way we measure cosmic expansion... this is the red shift? My question to this is how accurate is this if it is affected by gravitation? If the light is slowed by passing the mass of an object, doesn't this throw off the equations? And wouldn't multiple objects mulitpy the variable? ie. Light deflection and gravitational time delay.

It's probable that I am mistaken about Omega and Lambda, but isn't Lambda part of the Omega equation? Or is this the density equation?

From an article in Wikipedia:

When Einstein formulated general relativity, he and his contemporaries believed in a static universe. When Einstein found that his equations could easily be solved in such a way as to allow the universe to be expanding now, and to contract in the far future, he added to those equations what he called a cosmological constant, essentially a constant energy density unaffected by any expansion or contraction, whose role was to offset the effect of gravity on the universe as a whole in such a way that the universe would remain static. After Hubble announced his conclusion that the universe was expanding, Einstein wrote that his cosmological constant was his "greatest blunder".

To me, this seems to mean that Einstein was attempting to elimate both expansion and contraction of the universe? Did he himself ever recaculate his "greatest blunder" or endorse the work of anyone else? Possibly Hubble?

Well, not quite. Theorists never forgot about the cosmological constant. Very simple arguments demonstrated that the cosmological constant, if it were nonzero, had to be absurdly small, around 10^-120 in natural units. So most just figured that there must be some unknown symmetry that sets it to zero. No such symmetry has been found, but there are many theorists that still think it's more likely.

Guess my biggest question here isn't the size of the value, but why positive?

 

[Chalnoth]

To me, this seems to mean that Einstein was attempting to elimate both expansion and contraction of the universe? Did he himself ever recaculate his "greatest blunder" or endorse the work of anyone else? Possibly Hubble?

It wasn't so much about recalculation, but it's just that his static universe idea was unstable: sure, you can have a universe that has some amount of matter that happens to be balanced by a cosmological constant. But the balance has to be perfect, and if some of that matter moves just a little bit, the balance will be destroyed and the universe will either collapse in on itself or expand forever (or, more likely, some parts will collapse while others expand). This instability meant that it wasn't a workable idea in the first place, even before examining the evidence, and I suspect this was the reason why he called it his "greatest blunder".

Guess my biggest question here isn't the size of the value, but why positive?

Well, a negative cosmological constant would just cause the universe to collapse back in on itself, so we couldn't observe a universe like that anyway. As a result, we can't really say just from observation whether a negative cosmological constant is possible or even likely: intelligent beings can never observe such a thing in the first place.

 

[PeopleSmoks]

Chalnoth, what about the way in which red shift is being used? Does gravitation cause inaccuracies in the measurements?

 

[Peter Watkins]

Thank you for your various replies. With regard to the question of whether or not gravity will over-come expansion, the answer is a positive yes. And the reason is simple. If gravity was able to influence matter, (and clearly, it was), when the expansion rate was at it's highest, then this influence will remain no matter how large the universe becomes. Galaxies move apart but they also slow so the gravity/kinetic energy ratio remains the same. Doubtless there is a way to describe this matematically, but not by me! This, of course is the point where you say that the rate of expansion is increasing because galaxies are moving apart at an increasing rate. But things are not always as they seem. Look at the sun. Is it not obvious that the sun is orbiting around us, as are the stars. The only problem with the Ptolmeic universe was the "Wandering Stars". This problem was resolved by taking a mental leap to outside the universe. Of course, religeous bigotry and protection of privileged position meant that it took some 200 years before the Copernican universe was accepted. Todays problem is this apparent increase of expansion rate. Come back Copernicus.
Incidentally, if gravity was not sufficient to halt expansion, then it would have had no effect whatsoever, anywhen. The universe would have remained in sub-atomic particle form and expanded into oblivion for all eternity. Clearly this did not happen. Collapse, therefore, is inevitable.

 

[PeopleSmoks]

Peter, you're thoughts are interesting. As I have started getting deeper into the gravity well of information here, I find myself with more and more questions.

Currently, my conundrum is no longer whether the different theories are right or wrong, but why certain numbers are being used in various equations? There are times when it seems as though it is more an issue of finding a mathematical formula to support a belief rather than using known factors... but then again, I guess that's what "theory" is?

Still, as I read, I begin to question the accuracy of using red shift to measure distance in light of gravitation being a possible variant. Since red shift measurements appear to be the standard used to also measure the rate of cosmic expansion, if it is off by even a seemingly infinitesimal amount, what would that do to the equations and therefore the conclusions that have been reached?

 

[Chalnoth]

Thank you for your various replies. With regard to the question of whether or not gravity will over-come expansion, the answer is a positive yes. And the reason is simple. If gravity was able to influence matter, (and clearly, it was), when the expansion rate was at it's highest, then this influence will remain no matter how large the universe becomes. Galaxies move apart but they also slow so the gravity/kinetic energy ratio remains the same.

There are a few problems with this analysis.

First, gravity's effect may remain, but it still diminishes with distance. So if two objects are moving fast enough away from one another, their relative gravity can never bring them back together.

For instance, if we take the example of the Earth and a rock thrown up, then usual experience tells us that it will always come down. But this is only because we can't throw things very fast. If we throw a rock up fast enough, it won't. This can be understood easily in terms of energy: a rock sitting on the Earth has a potential energy of:

$$U = \frac{-GMm}{r}$$.

In this situation, U is the potential energy, G is the gravitational constant, M is the mass of the Earth, m is the mass of the object, and r is the radius of the Earth.

So, if I want to throw something up so that it never comes back down, all I have to do is give it a kinetic energy that is larger in magnitude than this potential energy. That is to say, if:

$$\frac{1}{2}mv^2 > \frac{GMm}{r}$$,

then the object is traveling fast enough that it will never lose enough energy to stop and turn back around: it'll keep going forever. So yes, you can have gravity and still have things that keep going forever away from one another. They just have to be going fast enough.

Then there's the problem that the expansion of the universe has been observed to be accelerating. This means one of two things:
1. There is more stuff that makes up our universe than just normal matter and dark matter: there is some stuff that interacts with gravity very differently, which causes gravity to actually push things apart at large distances.
2. We don't understand how gravity works at very long distances.

As of right now, it's looking like the expansion will continue forever, though this is highly tentative.

 

[PeopleSmoks]

Would this be "escape velocity"?

And what of red shift?

 

[Chalnoth]

Would this be "escape velocity"?

Yes.

And what of red shift?

Well, there is some slight uncertainty in redshift due to the peculiar velocity of the source object (an example of a "peculiar velocity" would be a galaxy falling into a massive cluster). But that's about it. Gravity doesn't affect the redshift of astronomical objects by any significant amount.

 

[matt.o]

Yes.


Well, there is some slight uncertainty in redshift due to the particular velocity of the source object (an example of a "particular velocity" would be a galaxy falling into a massive cluster). But that's about it. Gravity doesn't affect the redshift of astronomical objects by any significant amount.

You mean "peculiar" velocity.

 

[Chalnoth]

You mean "peculiar" velocity.

Yes, sorry...

 

[PeopleSmoks]

Yes.


Well, there is some slight uncertainty in redshift due to the peculiar velocity of the source object (an example of a "peculiar velocity" would be a galaxy falling into a massive cluster). But that's about it. Gravity doesn't affect the redshift of astronomical objects by any significant amount.

How does gravitational lensing affect redshift? And not to make too many assumptions, but when looking over great distances, I personally, would assume that this effect might occur several times before the light of a very distant objects reach our viewpoint. If Lambda is a very small number, and gravitational affects on redshift are very small, wouldn't there be an accumulative effect over great distances?

If we are to say that bodies in the cosmos aren't affected by gravitation because they reach terminal velocity, how are we measuring the velocity of an object moving away from us if as you say there is some slight uncertainty?

Every answer seems to bring more questions. I guess that's called learning and maybe thinking? Thanks for answering.

 

[Chalnoth]

How does gravitational lensing affect redshift?

Gravitational lensing has no effect upon redshift. It does have an effect upon brightness, however, and this does need to be taken into account when there is a massive object almost directly along the line of sight, which does happen. Most of the time it's not a significant effect.

If Lambda is a very small number, and gravitational affects on redshift are very small, wouldn't there be an accumulative effect over great distances?

Well, right, but the effect of the cosmological constant is to make distant objects dimmer than we would expect if there were no such thing, while the effect of gravitational lensing, if not accounted for, is to make distant objects brighter than we would expect (and in a very erratic way, depending upon what lies along the line of sight).

If we are to say that bodies in the cosmos aren't affected by gravitation because they reach terminal velocity, how are we measuring the velocity of an object moving away from us if as you say there is some slight uncertainty?

Er, I don't know what you mean by terminal velocity, but what we do measure is the redshift, which is a measure of how much the universe has expanded since the light was emitted, and the distance (through a variety of different methods). Measuring the redshift and distance of many different objects in the universe gives us a measure of the history of the expansion of the universe. It's not actually accurate to say that we're measuring the velocity of far-away objects, because in strict terms, the velocity of a distant object is meaningless. Relative velocity between two objects can, in General Relativity, only be determined for two objects at the same location.

Every answer seems to bring more questions. I guess that's called learning and maybe thinking? Thanks for answering.

Indeed.

 

[PeopleSmoks]

Er, I don't know what you mean by terminal velocity, but what we do measure is the redshift, which is a measure of how much the universe has expanded since the light was emitted, and the distance (through a variety of different methods). Measuring the redshift and distance of many different objects in the universe gives us a measure of the history of the expansion of the universe. It's not actually accurate to say that we're measuring the velocity of far-away objects, because in strict terms, the velocity of a distant object is meaningless. Relative velocity between two objects can, in General Relativity, only be determined for two objects at the same location.

I meant escape velocity. Terminal velocity is something completely different. Does that change anything you wrote? What I'm trying to grasp is just how is it concluded that cosmic expansion is accelerating? What is used to measure the rate of expansion?

 

[Chalnoth]

I meant escape velocity. Terminal velocity is something completely different. Does that change anything you wrote? What I'm trying to grasp is just how is it concluded that cosmic expansion is accelerating? What is used to measure the rate of expansion?

The original evidence came in from observations of distant supernovae, back in 1999:
http://adsabs.harvard.edu/abs/1999ApJ...517..565P

The basic idea is that they measured the relationship between redshift and brightness of many supernovae. General Relativity predicts a very specific relationship between the two. From the redshift of the supernova, we compute the luminosity distance:

$$D_L = c(1+z)\int_0^z \frac{dz}{H(z)}$$

Here $$D_L$$ is the luminosity distance, $$z$$ is the redshift of the object, $$c$$ is the speed of light, and $$H(z)$$ is the Hubble parameter as a function of redshift, as given by the Friedmann equation.

The luminosity distance is constructed in such a way that the observed brightness of an object falls off as $$1/D_L^2$$, so that it matches up to the brightness falloff we see for local objects. The equation can be derived directly from the FRW metric.

Once we have the luminosity distance, we have to determine how it effects the brightness of the object as observed. Objects in astronomy have their brightness measured in terms of their magnitude. The magnitude of an object $$m$$ is defined as follows:

$$m = M + 5\left(\log_{10}D_L - 1\right)$$

Here $$m$$ is the magnitude we observe from Earth, and $$M$$ is the intrinsic magnitude of the objects.

Since these supernovae are all nearly the same brightness, we can use these as "standard candles": with some uncertainty, $$M$$ is the same for all of this particular type of supernova. So we can use a large number of supernovae to get an estimate of the luminosity distance $$D_L$$ for each of them. Since we also have a redshift for each of these supernovae, we get an estimate of the function $$H(z)$$, which is the expansion history. From this measure, we find that the way $$H(z)$$ has changed through time indicates that in recent times, the second derivative of the scale factor with respect to time, $$\ddot{a}$$, has become positive.

Did that help?

 

[PeopleSmoks]

Thanks, and also thanks for the Harvard link. I'll be taking some time to better absorb the information as well as look up more articles etc. I'm sure it will only lead to a few more questions, but hopefully I will pose them based on fewer misconceptions.