Understanding Cosmology (Post 7)

[Meow Mix]

Continuing with dark energy for this post. In Post 6, we covered the equation of state (which can be thought of like this: we have two independent equations with two unknowns, so we can make an equation that relates the them. In this particular case, we want to relate energy density and pressure using a parameter that has a unique value for every type of thing in the universe, w.)

We covered in Post 6 that anything that exists in the universe with an equation of state parameter that's more negative than -1/3 could, given prevalence in the universe, cause the universe to accelerate its expansion. You can simplify thinking about this by imagining this as being like having a significant negative pressure.

We left off the end of Post 6 by noting that scientists were aware since Einstein that it was possible to have this "negative pressure" term appear in the Friedmann equations, but until the late 90's, had the expectation that this term would be zero. However, when plotting the magnitude to redshift of a special type of supernova, it quickly became apparent that the data wasn't falling in line with that term (which is called lambda) equaling zero.

So, we have a couple of mysteries up to this point in the series on our hands:

1. Observations reveal that we can no longer ignore lambda (which can be thought of in a simplified way as a "negative pressure"). However, what is the density parameter of lambda: how much of the universe's energy density comprises this "pressure?" (Covered in this post)
2. What is lambda's equation of state parameter: what is the relation between its energy density and its pressure? (Covered in the addendum to this post, at the bottom)

From all of the dark matter posts, we might recall that we have a very good idea of the density parameter of matter in the universe (it's about 0.31. Recall that this is out of 1 because we mathematically set it up that way, so this is the same as saying matter of all types makes up 31% of the energy density of the universe).

Recall also from earlier posts that the density parameter for radiation (including neutrinos) is negligible, and on the order of 10^(-5).

This would imply that in order to get a universe that appears flat, we would expect everything else in the universe that isn't matter or radiation to have a density parameter of about 0.69. But how can we be sure that lambda comprises all of that: after all, what if there are multiple different kinds of things that we don't know about making it up?

Well, fortunately, we have some ways to measure lambda and its equation of state parameter: the history of the universe's size. If lambda affects the rate of the expansion of the universe, then the scale factor of the universe would actually be different over time than we would expect it to be if we didn't consider lambda! So, what are some possible universes we could have if we had different values of lambda?

[GALLERY=media, 9521]Lambdaplot by Meow Mix posted Jul 7, 2021 at 8:17 PM[/GALLERY]

What we have here are multiple possible universes, each with the known value of the density parameter of matter (at about 0.31), but with different values for lambda. The y-axis is the scale factor of the universe at different points of time. Each different universe produces the universe that we see today (so it is not a coincidence that they all coincide with the red dot that says "now," these values were picked specifically to produce the universe that we see -- at least in terms of the scale factor).

Note that one of these universes didn't have a Big Bang, but instead went through a crunch and a re-expansion (the solid line, with the density parameter of lambda = 1.8, and curvature k = +1)! We can rule this one out by other observations. The alternating dash-dot line with lambda = 1.7289 was far too big for too long (this one is called a "loitering universe"), so it also flies against observations. The regular dashed lines with the green text represents a universe that will eventually experience a Big Crunch, but it is also younger than some of the oldest objects that have been observed.

It seems like the only value of lambda that gives us a universe like the one that we observe and measure, both in the past and the present, is the one where lambda makes up the entire "missing" 0.69 density parameter of the universe.

Let's make a phase space of every possible universe with every possible value for the density parameters of matter and lambda:

[GALLERY=media, 9522]Lambdavsmatter by Meow Mix posted Jul 7, 2021 at 8:43 PM[/GALLERY]

Here, our y-axis is possible values of lambda's density parameter. The x-axis is possible values of matter's density parameter. Since radiation's density parameter is negligible, this phase space represents every possible universe, with some details written in.

For instance, for any universe where lambda is zero (a horizontal line across from the 0 on the y-axis), such a universe is doomed to a Big Crunch as matter's gravity inevitably slows the expansion of the universe and eventually reverses it.

Everything above the dotted line is a positively curved universe, and everything below the dotted line is a negatively curved universe.

If you recall, observationally, we know that the universe is flat: even with the very basic information given in this series, the reader should be able to know that the universe we inhabit falls somewhere on that dotted line (which is where k = 0, curvature is zero).

Understand that prior to the late 90's, the expansion of the universe wasn't thought to be accelerating: it was thought to be constant at most (so, where the dotted line meets the red line) or, more likely, decelerating because gravity would constantly be fighting the expansion (so, anywhere on the dotted line beneath the red line could have represented the universe we live in as far as they knew at the time).

So, let's bring a few things we've talked about over the entirety of this post together on this same plot:

1. We get a very accurate measurement of matter's density parameter using galactic clusters, as discussed in the dark matter sections of this series. If it very accurately constrains matter, then we would expect this data, when plotted, to be very vertical with as little thickness as possible (meaning it is saying, "matter's density parameter is between here and here.")
2. Baryon acoustic oscillations (also covered in the dark matter section) constrain both lambda and matter density parameters, so we would expect this data, when plotted on this graph, to constrain along the line of curvature since it is very sensitive to the components that go into this.
3. We use type 1a supernovae over large ranges of redshifts to give us an understanding of the actual relationship between scale factor vs redshift over time: only certain combinations of density parameters would allow for these observations, so we'd expect this data (when plotted) to cover a range of values of lambda and matter, manifesting diagonally on the plot.

What happens when we plot all of these constraints together? What would we expect to see? If any one of the constraints doesn't touch the dotted line, then we know we've made some kind of terrible mistake, for one thing. If the constraints covered different portions of the graph (if they didn't overlap anywhere), we'd also know that we've made some kind of mistake. But when we plot them together, we find, as expected, that they do touch the line where k = 0, and they do overlap in places. Furthermore, they happen to overlap where k = 0:

[GALLERY=media, 9523]Concordantcosmology by Meow Mix posted Jul 7, 2021 at 9:40 PM[/GALLERY]

When we plot constraints together, they look like we'd imagined them to, they converge in the same location at their highest confidence levels (the lighter the color, the lower the confidence level); and, most importantly, they happen to converge somewhere that makes sense based on everything else that we've covered in these posts.

What you should get out of this is that this is like finding three clocks running on independent mechanisms agreeing on the same time: it's not a coincidence. It tells us we're on the right track. (This particular mode of constraints is currently called "convergent cosmology.")

So, where do the constraints put us? It looks like our universe is most likely on the k = 0 line as we expected, where the density parameter for matter is around .3 as expected, and where the density parameter for lambda is about .7 as expected.

There is a lot more to this, but as I promised, I have tried to keep this series from becoming too dense or technical for most readers to digest. Thus I will conclude the series with the hope that now you know a little bit more about why cosmologists are able to make a reasonable consensus about the existence of dark matter and dark energy.

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Addendum: the equation of state of dark energy

We can use similar convergent cosmology constraints to help lock down what dark energy's equation of state might be. Remember, we expected it to be more negative than -1/3 to account for the observation that the universe is accelerating its expansion (as shown by supernovae in the post before this one):

[GALLERY=media, 9524]Eosparamconstraint by Meow Mix posted Jul 7, 2021 at 9:42 PM[/GALLERY]

[GALLERY=media, 9525]Eosparamconstraint2 by Meow Mix posted Jul 7, 2021 at 9:42 PM[/GALLERY]

Not all of the constraints are pretty, but again we at least find constraints that make sense.

Keep in mind that at any time, if the data tells us something that doesn't make sense, then we have a good indicator that something is wrong somewhere with the models and understanding. While we may not have perfect knowledge about the nature of dark matter or dark energy, we have at least correctly inferred their existence and impact on the universe at large.

 

[JoshuaTree]

So what do you think causes the accelerated expansion of space, quantum fluctuations?

 

[Meow Mix]

So what do you think causes the accelerated expansion of space, quantum fluctuations?

There are a couple modes of thought: either it comes from relativity (and we would expect the equation of state to be exactly -1 if so), or it comes from quantum effects, like Quintessence (where we would expect to see some negative fraction equation of state, like around -1/3).

 

[Meow Mix]

Supernovae unfortunately don't strongly constrain the equation of state parameter for dark energy, but current observations favor a value of -1.

They don't favor it enough for us to call it settled, though.

 

[JoshuaTree]

I'm sure I'm persistently annoying ha ha, but if a particle poofs into existence in empty space and poofs back out again, doesn't that leave more empty space behind resulting in expansion? The more empty the space the greater the expansion, the more the expansion the more empty space, and so on? What's the fallacy here? Thanks!

 

[Meow Mix]

I'm sure I'm persistently annoying ha ha, but if a particle poofs into existence in empty space and poofs back out again, doesn't that leave more empty space behind resulting in expansion? The more empty the space the greater the expansion, the more the expansion the more empty space, and so on? What's the fallacy here? Thanks!

You're not annoying!

The short answer is that pair creation doesn't "fill" space in the sense that something existing in space pushes space out to make room for itself. It's not like dropping a ball in water, and the more dense ball takes up space the water would otherwise fill, so the water rises. Things existing in space are just taking up a coordinate in space, in relation to other things. It's not that the area the particle is taking up isn't still space: it's definitely still space, just not empty space now (see how this is different from a ball in water, where the area the ball is filling is NOT water?)

I would need to double check for any weird QFT consequences but I'm pretty sure if those exist they would just be on the cosmological horizon and not the actual observer-external expansion of space.

 

[JoshuaTree]

You're not annoying!

The short answer is that pair creation doesn't "fill" space in the sense that something existing in space pushes space out to make room for itself. It's not like dropping a ball in water, and the more dense ball takes up space the water would otherwise fill, so the water rises. Things existing in space are just taking up a coordinate in space, in relation to other things. It's not that the area the particle is taking up isn't still space: it's definitely still space, just not empty space now (see how this is different from a ball in water, where the area the ball is filling is NOT water?)

I would need to double check for any weird QFT consequences but I'm pretty sure if those exist they would just be on the cosmological horizon and not the actual observer-external expansion of space.

I think I understand what you are saying, and you are most certainly probably correct.

Suppose I have a sealed container filled with water, if I magically insert a ball into the water wouldn't the container expand, and wouldn't the container remain expanded when the ball is magically removed from the water? Of course in the case of the sealed container of water a void would be left behind, but in the case of empty space that void is just more empty space, so space expands?

 

[Meow Mix]

I think I understand what you are saying, and you are most certainly probably correct.

Suppose I have a sealed container filled with water, if I magically insert a ball into the water wouldn't the container expand, and wouldn't the container remain expanded when the ball is magically removed from the water? Of course in the case of the sealed container of water a void would be left behind, but in the case of empty space that void is just more empty space, so space expands?

In a sealed container it depends on the tensile strength of the container: magically adding the ball (ostensibly in a way that displaces the water) would increase the pressure of the water. (Adding particles in space does not increase pressure of space: this is because of conservation of energy. Omega_0, the density parameter of the universe, would remain unchanged).

 

[ChristineM]

@Meow Mix

Thanks so much for this series of well written posts. I am into cosmology as a hobby and you have not only confirmed and clarified much of my thought but educated me to some extent also. Suchva shame the series must end...

Thanks again.

 

[Native]

Keep in mind that at any time, if the data tells us something that doesn't make sense, then we have a good indicator that something is wrong somewhere with the models and understanding. While we may not have perfect knowledge about the nature of dark matter or dark energy, we have at least correctly inferred their existence and impact on the universe at large.

Well this is certainly not something I forget to have in mind

Are you 100 % aware of what you´re saying here? How can it be correct to assume something (dark matter) which doesn´t show up in the picture when former data (galactic rotation) is contradicted by observation?

Personally I would not have titled your excellent theoretical description of the standing theories as "Understanding Cosmology", as it more precisely should be called "Hypothesizing Theoretical Cosmology".

As for many of the other theoretically issues in this post, I really admire the human skills of imagination - even when these have no natural fundations.

"Big Bang, a flat Universe which expands like a balloon (sometimes exceeding the speed of light), multiverses, black holes, dark matter, dark energy" etc. etc. - all mostly based on a one-way-force which no one have explained at all.

"Understanding Cosmology"? NOPE! It is just "understanding the theories" in a cosmos of which astrophysical and cosmological science only understand about 4 % of it all.

 

[Meow Mix]

@Meow Mix

Thanks so much for this series of well written posts. I am into cosmology as a hobby and you have not only confirmed and clarified much of my thought but educated me to some extent also. Suchva shame the series must end...

Thanks again.

I will likely add a Post 8+ to cover little things I couldn't/shouldn't have in the prior series; things that weren't necessary to understand a thing, but could help add understanding.

I didn't want to overwhelm people with tangents and such, especially since I was already asking people to remember some terms between posts.

 

[JoshuaTree]

In a sealed container it depends on the tensile strength of the container: magically adding the ball (ostensibly in a way that displaces the water) would increase the pressure of the water. (Adding particles in space does not increase pressure of space: this is because of conservation of energy. Omega_0, the density parameter of the universe, would remain unchanged).

But we observe a particle horizon that seems to violate the conservation of energy, the particle popping in and then out cancels, so the net effect of the fluctuation must somehow be expansion of empty space to balance the expansion of empty space, right?

 

[Meow Mix]

But we observe a particle horizon that seems to violate the conservation of energy, the particle popping in and then out cancels, so the net effect of the fluctuation must somehow be expansion of empty space to balance the expansion of empty space, right?

Conservation of energy isn't violated, it's more that it's "borrowed against," and there are some ideas (like inflation) that spend the deficit anyway. As Paul Davies put it, pair creation is a free lunch: 1 + -1 = 0. Virtual particles do not affect the density parameter of the universe.

However, there are some effects by which the reverse is the case (where the expansion of the universe causes virtual particles to become real). I don't know the consensus on this, I don't know the formalisms on this, this is something I'd have to read some papers on with more specificity and come back to speak more about. In any case, I know it does not cause an effect like you're speaking of though. (But it is interesting. And technical. A lot of QFT stuff is technical, which makes it dense to read through.)

I have the highest level grad quantum stuff this semester and the following semester, so I'll be able to field these QFT questions better off the top of my head in like a year.

 

[wellwisher]

One of the problems with cosmology is the analysis does not begin before time=0. The singularity of the BB becomes the starting point for cosmology. This analysis does not include what came before, to create that starting spot. The most important variable, with the power to create a universe is not included, because this is unknown.

Say for the sake of argument the variable that created the BB singularity and universe, is still in affect and did not disappear after the BB. You cannot leave it out and expect the analysis to be right. Rather one needs to explain how that one big dog variable to do both things.

Special Relativity; SR gave me a hint. If we plug in the speed of light into the three equations of SR, we get discontinuities in time, distance and mass. This means space-time become discontinuous at the speed of light. One way to interpret this is space-time become discontinuous and separates into distance and time that can act independent of each other. One can move in time without the constraint of distance and move in distance without the constraint of time. The former has been historically called omniscience; knows what is happening everyone simultaneously in time, and the second was called omnipresence; everywhere at the same time.

If this source of creation was still in affect, then space-time should see an overlap of time that is not dependent on distance, and distance that is not dependent on time. For example, all forces create acceleration, with has the units of d/t/t or one part distance and two parts time. This is space-time plus time potential.

This extra time vector is most evident in gravity. Gravity causes space-time to contract. However, in the center of stars, where reference time is most contracted, we get the fastest frequencies due to fusion. Time is going in two directions; slower and faster. The faster time is coming from the same place that formed the BB.

 

[ChristineM]

New One of the problems with cosmology is the analysis does not begin before time=0. The singularity of the BB becomes the starting point for cosmology. This analysis does not include what came before, to create that starting spot. The most important variable, with the power to create a universe is not included, because this is unknown.

In the last 10 or 15 years cosmologists have dared to pose the question, 'what came before the bb' and have produced several hypothesis (i know of about 30) based on observation of current observation and or mathematics.

A hypothesis must actually make logical sense to be accepted as a possibility with no guesswork allowed.

 

[JoshuaTree]

One of the problems with cosmology is the analysis does not begin before time=0. The singularity of the BB becomes the starting point for cosmology. This analysis does not include what came before, to create that starting spot. The most important variable, with the power to create a universe is not included, because this is unknown.

Say for the sake of argument the variable that created the BB singularity and universe, is still in affect and did not disappear after the BB. You cannot leave it out and expect the analysis to be right. Rather one needs to explain how that one big dog variable to do both things.

Special Relativity; SR gave me a hint. If we plug in the speed of light into the three equations of SR, we get discontinuities in time, distance and mass. This means space-time become discontinuous at the speed of light. One way to interpret this is space-time become discontinuous and separates into distance and time that can act independent of each other. One can move in time without the constraint of distance and move in distance without the constraint of time. The former has been historically called omniscience; knows what is happening everyone simultaneously in time, and the second was called omnipresence; everywhere at the same time.

If this source of creation was still in affect, then space-time should see an overlap of time that is not dependent on distance, and distance that is not dependent on time. For example, all forces create acceleration, with has the units of d/t/t or one part distance and two parts time. This is space-time plus time potential.

This extra time vector is most evident in gravity. Gravity causes space-time to contract. However, in the center of stars, where reference time is most contracted, we get the fastest frequencies due to fusion. Time is going in two directions; slower and faster. The faster time is coming from the same place that formed the BB.

Fascinating! So if space time becomes discontinuous at the speed of light would gravity be the underlying frabric of space-time?

 

[wellwisher]

In the last 10 or 15 years cosmologists have dared to pose the question, 'what came before the bb' and have produced several hypothesis (i know of about 30) based on observation of current observation and or mathematics.

A hypothesis must actually make logical sense to be accepted as a possibility with no guesswork allowed.

The main point I was trying to make was what came before the BB, may exist both before and after the BB, and it may still be responsible for many observations that we attribute to the singularity and BB. For example, why do we have a quantum universe? Is this unique to the BB or did this come and continue to come from the original source?

The analogy is like buying a new computer. We control what the computer does and stores in terms of information and activities. However, no computer comes to us as a complete blank, but rather it has its own internal data from the factory, that is responsible for many operations behind the scenes that allow the user to make it function to their own tastes.

My approach was to go back to the factory blue print before the model was produced and sold. If we assume time and space was separated before the BB, and the BB uses connected and integrated space-time, one should be able to see separated time and separated space in our space-time reality. A quantum universe saves time since it limits the options, so even random processes occurs faster. In a sense, a quantum universe forms six sided dice instead with dice with infinite sides. If we need to roll a 3 for step one to become step two, the 6 sided dice will save time.

Fascinating! So if space time becomes discontinuous at the speed of light would gravity be the underlying frabric of space-time?

.

The answer is yes and no. Mass cannot travel at the speed of light and mass occupies space. Mass is what induces the union of space and time into what we call space-time. Since mass occupies space; exclusion principle, the formation of mass will also cause space to expand. If we take away mass, space becomes zero and space-time becomes separated space and time.

Gravity in this model comes from the speed of light place, where time and space separate. What we call gravity is the original reference trying to recycle the mass. Notice how gravity causes mass and space-time reference to compress. If there is enough mass space-time contracts toward the speed of light reference. The black hole is very close at the limit of space-time. A little more and space-time will break down. Now distance and act part from time; white hole appears.

If we were in a reference where time and space could act independently, we would have infinite entropy, since there are no practical limits on combinations of time and space. This would set a potential with inertial reference and space-time, that we call the second law. The second law leads space-time back to its origins. Increase entropy need heat to increase this comes from mass burn among other things.

I liked the idea of space and time separating at the discontinuity of the speed of light; Special Relativity, since time without space and space without time defines the classic attribute of God; omniscience and omnipresence. It is consistent with ancient wisdom, which was often ahead of its time. Heaven and Earth were two places with different laws of nature, with heaven eternal and earth temporal. The ancient saw angels; potentials, interacting with the earth; time interacting with space-time. I found this integrating seam using classic science from Albert Einstein. It also connects to consciousness. That will be another time and space.

 

[ChristineM]

The main point I was trying to make was what came before the BB, may exist both before and after the BB, and it may still be responsible for many observations that we attribute to the singularity and BB...

Yes it may still exist, new universes may be spawned all the time. Andrai Linde estimates 10^10^16 universes that can be comprehended as universe's by humans and many more beyond our comprehension.

Its yet another hypothesis

 

[JoshuaTree]

I liked the idea of space and time separating at the discontinuity of the speed of light; Special Relativity, since time without space and space without time defines the classic attribute of God; omniscience and omnipresence. It is consistent with ancient wisdom, which was often ahead of its time. Heaven and Earth were two places with different laws of nature, with heaven eternal and earth temporal. The ancient saw angels; potentials, interacting with the earth; time interacting with space-time. I found this integrating seam using classic science from Albert Einstein. It also connects to consciousness. That will be another time and space.

Absolutely fascinating. Are you referring to the Akashic records?

 

[wellwisher]

Yes it may still exist, new universes may be spawned all the time. Andrai Linde estimates 10^10^16 universes that can be comprehended as universe's by humans and many more beyond our comprehension.

Its yet another hypothesis

There is a consideration that most theories overlook. In this universe, entropy has to increase according to the 2nd law. Entropy will absorb energy usually in the form of heat. The implication of the second law is that the universe is net bleeding energy into its ever increasing entropy. Therefore, the amount of useable energy, in the universe, is decreasing with time due to the second law. The material universe has a self life. It cannot go on forever nor can it return to whence it came, since it bleeds off irretrievable energy with time. Most cosmology theories violate the second law.

Conservation of energy says that energy cannot be created or destroyed but can only be transformed into other forms of energy. In the case of entropy absorbing and transforming energy, a check valve of sorts will appear that makes the material universe unable to further transform this bled off energy. The pool of lost energy grows as the universe loses useable energy to entropy; aging universe. Old man universe cannot become a baby again or live forever due to the second law.

Based on the conservation of energy, the constant energy loss, due to entropy will be conserved even though it is not net reusable by the material universe. There should be a pool of energy associated with entropy that is not net re-useable by the material universe. However, due to energy conservation, it is still part of the universe; dark energy?The ancients called this segregated pool of entropic energy the spiritual realms. There is a one check valve of sorts, created by the second law, that segregates the two realms. The universe has been adding to this pool since it was born.

What is interesting is that life; living, and the brain; thinking, generate a lot of entropy. Life and consciousness constantly add to the pool of conserved but unusable energy. In a sense our essence and memory; soul, is conserved by the universe through the increase in entropy we generate and our unique addition to the pool. This is called the eternal soul; information based. Separated time and distance can address this.

Absolutely fascinating. Are you referring to the Akashic records?

I am not sure what the Akashic records are. I developed this theory independently. It is may be version number 20 and I finally reached steady state.

If you consider our imagination, one can use the imagination to think things that can defy the laws of physics. In my imagination, I can build a bridge made of rice noodles across the ocean. I can use my imagination and fly to sun in a second. These things are not possible in our material realty. The imagination can go outside the physical limits of space-time, and it can think scenarios that would require separated space and time to be possible. Consciousness has a connection to the speed of light reference via the imagination.

The reference at the speed of light, where mass cannot exist and space-time breaks down, has infinite entropy since all possible scenarios can exist, like within the imagination. There is no practical limits created by space-time and matter This reference implies infinite entropy and therefore an infinite pool of entropic based energy.

To create the inertial universe; primordial atom from nothing but imagination, the speed of light reference would need to lower its infinite entropy. This could occur by placing limits on the universal imagination; omniscience and omnipresence; brooding over the deep. For example, Instead of being omnipresent, it comes to a focus at a junction of separated space and time. This instant of lowering entropy will be highly exothermic; boom! Shortly there after the energy/matter of the universe appears, the second law then begins to return this borrowed energy, back to the speed to light reference. Our universe's entropic energy pool starts to collect and the big bang baby starts to age.