Understanding Cosmology (Post 1)

[Meow Mix]

There are a lot of posts going on where people have questions about cosmology, particularly the more interesting parts like the Big Bang, dark matter, dark energy, and so on. So, I thought I'd type up a series on cosmology for interested parties. Plus, it's a good way for me to keep refreshed on the basics.

So where do we start with something as ambitious as studying the entire universe?

First, we have to get assumptions out of the way, but I think we can be convinced that they're reasonable ones.

1. We assume that the laws of physics behave the same way here as they do over there; that they do not depend on their location in space and time (Lorentz invariance).
2. The universe is homogeneous and isotropic: it contains the same sorts of things, and it contains the same sorts of things in the same way in every direction.

"Now hold on," we might object. "Surely there are different things in the universe. If I draw an imaginary cube with the Sun as the center, that box will contain completely different kinds of things than if I drew an imaginary cube of the same size somewhere in the middle of a nebula."

And that's true: when we say the universe is homogeneous and isotropic, we mean at certain scales it is. Your room isn't homogeneous and isotropic, nor is planet Earth, nor the solar system, nor the Milky Way Galaxy or even the local cluster.

[GALLERY=media, 9486]Isohomo by Meow Mix posted Jun 23, 2021 at 8:31 PM[/GALLERY]

It's not until we "zoom out" to about 100 Mpc (that's Megaparsecs, or about 3.26 million light years) that we get a picture of the universe that's homogeneous and isotropic.

It would make things considerably easier if the universe were also time-invariant, but we know that isn't the case: the size of the universe itself changes with time, and the stuff within it behaves differently based on when we're talking about.

[GALLERY=media, 9487]Sfrd by Meow Mix posted Jun 23, 2021 at 8:35 PM[/GALLERY]

Here, we see that the star formation rate differs with redshift, and we will discuss how looking at different redshifts is looking at the universe at different points in time.

So, most of us here are probably at least colloquially familiar with the concept of redshift: the universe is expanding, so light that reaches us from distant sources will have their spectra redshifted compared to the spectrum of a similar object (say, a similar star) at rest with respect to the observer.

[GALLERY=media, 9488]Redshift by Meow Mix posted Jun 23, 2021 at 8:48 PM[/GALLERY]

(We use "z" for redshift)

This often gets misattributed to the Doppler effect, but it's actually not. The Doppler effect is related to the actual motion of a source relative to an observer's location in space. In cosmology we call galaxies' actual motion peculiar motion, because they do move with respect to one another, especially within the contexts of their local clusters. So, the redshift and blueshift of nearby galaxies may be due to a true Doppler effect, but when you zoom out enough (get to high enough redshifts), the redshifting is not technically a Doppler effect: it's due to space itself stretching the wavelength of the light as it expands.

Perhaps I can convince you that this is different from a true Doppler effect with an analogy:

[GALLERY=media, 9490]Paperclips by Meow Mix posted Jun 23, 2021 at 8:56 PM[/GALLERY]

Here, a couple of ants (observers) are sitting on a couple of paperclips which do not move from their fixed positions on a rubber band. In a true redshift situation, whether the light is redshifted or blueshifted would depend on if a paperclip is moving towards you or away from you. But since the space itself (the rubber band) is expanding, all paperclips will receive redshifted light from all other paperclips. If the light had to travel across the rubber band (to be true to the space analogy), the distance between the peaks and troughs of the wavelength of the light would get stretched as it travelled.

[GALLERY=media, 9489]Expansion by Meow Mix posted Jun 23, 2021 at 8:56 PM[/GALLERY]

The above is a visualization of the expansion of space. Galaxies retain their positions with respect to one another, but the space between them expands.

Why does it matter that we make this distinction between true galactic motion (true redshift via peculiar motion) and redshift via spacetime expansion?

[GALLERY=media, 9491]Peculiar by Meow Mix posted Jun 23, 2021 at 9:05 PM[/GALLERY]

Because the redshift caused by the expansion is mostly linear (not perfectly, thanks to some relativistic effects, but consider it close enough for right now in this series). In the above image, the blue oval shows a large number of outliers in the data. Why?

Because the blue oval contains data from the Virgo cluster: galactic clusters tend (for gravitational reasons) to have galaxies that are moving with respect to one another (high peculiar motion), so it "fuzzies" up measurements of their redshift due to universal expansion. Imagine if the paperclips in the example above had multiple paperclips in a cluster around point E (in that image), all moving forward and backward, left and right, etc. An observer from paperclip A would see some of the paperclips moving away slower or faster simply because of their motions relative to each other being added to the apparent motion of the rubber band stretching.

Fortunately, there appears to be a physical "speed limit" to peculiar motion (around 1,000 km/s). Since, due to the expansion of the universe, objects that are further apart will appear to one another that they are receding away faster than closer objects (think of this like there is more space between them that's expanding, so each unit of space there is to expand means more expansion), we can look out far enough (to great enough redshifts) that the noise caused by peculiar velocity is negligible. This would be good if we wanted to, for instance, measure the Hubble parameter.

All this talk of expansion brings us to a good stopping point (and a good setting up point for all the stuff people really care about, like the Big Bang, dark matter, dark energy, etc. that people keep asking questions about on the forum) from here: the scale factor of the universe.

We define a scale factor a(t) of the universe such that when t = 0 (so, now in time), a = 1. If at any point the universe is half the size of the universe today, a would equal 1/2, and so on. This is where we get the Hubble parameter with a simple differential: H = (da/dt) / a. The Hubble parameter relates the apparent recession velocity with the size of the universe at any given time relative to the size of the universe now (hence why people often mischaracterize the Hubble parameter as a constant; which it clearly is not: the value of H changes as the value of a changes!)

Many things are related to the scale factor (remember, this is a, the size factor), and I'll have to decide if I want to spend time proving them or asking folks to take my word for it; but among things that are related are temperature (T is proportional to a^-1), redshift, and the age of the universe itself.

These are all the ingredients we need to make a real cosmology post next time, which will be about the Friedmann equations and how we will use them to answer a lot of these people have; and why we have good reason to do so.

*Mod edit: Links to the follow-up threads:*

Understanding Cosmology (Post 2)

Understanding Cosmology (Post 3)

Understanding Cosmology (Post 4)

Understanding Cosmology (Post 5)

Understanding Cosmology (Post 6)

Understanding Cosmology (Post 7)

 

[JoshuaTree]

So what about the particle horizon?

 

[Meow Mix]

I debated on whether to get into why we know space is expanding, but at a certain point I'd be explaining the basics forever. So, I will answer questions under each different post about the subjects they contain.

 

[Shadow Wolf]

I'll sum it up for you:
It's a bunch of wibbly-wobbly, timey-whimey stuff.

 

[JoshuaTree]

I debated on whether to get into why we know space is expanding, but at a certain point I'd be explaining the basics forever. So, I will answer questions under each different post about the subjects they contain.

Why do you think space is expanding? Quatumn fluctuations?

 

[rational experiences]

A human applies by their choice the measure they infer to the study of the propose.

Yet your human measure is not natural presence. As it does not measure itself or own measure.

If you pretend you don't exist being the theory the perusal of the space condition. Then nor does the measure.

The biggest and only mistake any human ever made.

It is determined lying for self purpose only.

 

[Meow Mix]

So what about the particle horizon?

I was waiting to get into GR before talking about this, but I can give a brief blurb about it.

The particle horizon or cosmological horizon is a distance from any observer at which objects recede away so fast that light emitted from them will never reach the observer (they are no longer in the observer's causal universe).

The fact that light takes time to reach an observer is in fact one of the best empirical observations that can be made about the expansion. For a while, there was a paradox called Olber's paradox: why is the sky dark?

If you imagine a homogeneous and isotropic universe that stretches infinitely (or at least "enough to appear infinite") in all directions, why would the sky be dark at night? There would be no patches of sky where there wouldn't be some bright object like a star. The night sky should uniformly look as bright as the surface of the sun, so why isn't it?

The answer is, of course, because despite there being enough stars and galaxies to do this, it takes time for their light to reach us; and there hasn't been enough time for most of the stuff in the universe to reach us observers. (On top of that, there was a period of time before stars began to shine; but that's a separate topic).

If light hasn't had enough time to reach us, that implies that there's a finite amount of time in the past where the universe looked the way it does now. This leads into how scientists started thinking about the Big Bang when combining this fact with the fact that the universe is expanding with time.

 

[JoshuaTree]

A human applies by their choice the measure they infer to the study of the propose.

Yet your human measure is not natural presence. As it does not measure itself or own measure.

If you pretend you don't exist being the theory the perusal of the space condition. Then nor does the measure.

The biggest and only mistake any human ever made.

It is determined lying for self purpose only.

So if a tree falls in the forest?

 

[Meow Mix]

Why do you think space is expanding? Quatumn fluctuations?

Yes, it's a consequence of QFT (quantum field theory). The short answer is "inflation decay." I don't have a lot of first hand experience in QFT yet, but I actually will by the end of the year. So I can tell you yes, but not with as many specifics as I'll be able to later.

 

[rational experiences]

I was waiting to get into GR before talking about this, but I can give a brief blurb about it.

The particle horizon or cosmological horizon is a distance from any observer at which objects recede away so fast that light emitted from them will never reach the observer (they are no longer in the observer's causal universe).

The fact that light takes time to reach an observer is in fact one of the best empirical observations that can be made about the expansion. For a while, there was a paradox called Olber's paradox: why is the sky dark?

If you imagine a homogeneous and isotropic universe that stretches infinitely (or at least "enough to appear infinite") in all directions, why would the sky be dark at night? There would be no patches of sky where there wouldn't be some bright object like a star. The night sky should uniformly look as bright as the surface of the sun, so why isn't it?

The answer is, of course, because despite there being enough stars and galaxies to do this, it takes time for their light to reach us; and there hasn't been enough time for most of the stuff in the universe to reach us observers. (On top of that, there was a period of time before stars began to shine; but that's a separate topic).

If light hasn't had enough time to reach us, that implies that there's a finite amount of time in the past where the universe looked the way it does now. This leads into how scientists started thinking about the Big Bang when combining this fact with the fact that the universe is expanding with time.

Teachings for consciousness in human life no longer present. Being expressed.

Effect metal AI radio wave radiation interference.

Light is a fixed state heavenly constant. Gases of our heavens burning in a void.

We experience as we live change by earths rotation movement of mass in change.

Balances stated the experience 12 hours light 12 hours clear dark.

Yet the light constant for earth is constant as light in heavens and does not move. The planet rotating does.

The bible theism to preach stated that the conscious experience gets fooled by earths movement as light never travelled. The human experiences consciously the travel as the experience.

What you were warned about theorising about Satan in the deep pit of space. Burning objects. Not relevant to life experiencing life.

Feelings do not own a theory.

 

[JoshuaTree]

Yes, it's a consequence of QFT (quantum field theory). The short answer is "inflation decay." I don't have a lot of first hand experience in QFT yet, but I actually will by the end of the year. So I can tell you yes, but not with as many specifics as I'll be able to later.

Seems to me if a particle "poofs" into existence empty space and then "poofs" out of existence again then the net effect is empty space expands by the volume of the particle, the more empty the space the more unstable the more fluctuations, do you think this could explain observed expansion?

 

[rational experiences]

So if a tree falls in the forest?

Are you the tree falling.

No.

 

[JoshuaTree]

Teachings for consciousness in human life no longer present. Being expressed.

Effect metal AI radio wave radiation interference.

Light is a fixed state heavenly constant. Gases of our heavens burning in a void.

We experience as we live change by earths rotation movement of mass in change.

Balances stated the experience 12 hours light 12 hours clear dark.

Yet the light constant for earth is constant as light in heavens and does not move. The planet rotating does.

The bible theism to preach stated that the conscious experience gets fooled by earths movement as light never travelled. The human experiences consciously the travel as the experience.

What you were warned about theorising about Satan in the deep pit of space. Burning objects. Not relevant to life experiencing life.

Feelings do not own a theory.

Are you equating variable speed of light with Satan fall?

 

[Meow Mix]

Seems to me if a particle "poofs" into existence empty space and then "poofs" out of existence again then the net effect is empty space expands by the volume of the particle, the more empty the space the more unstable the more fluctuations, do you think this could explain observed expansion?

In QFT there are dualities between particles and fields; and so we would have an unstable inflaton field that decays in an analogous way to how a clump of uranium might decay. GR allows for a negative pressure (which would appear to observers as an expansion, or "antigravity"), and we'll get into that with dark energy, but it's the same here.

So, to thoughtfully answer the question, we have to consider questions like background independence (does space exist, or is it a useful descriptive tool). For instance, consider a universe consisting of only three points. No matter how many dimensions you have and no matter what configuration the three points take (with the caveat that they can't cohabitate), you will end up with a two dimensional triangle from some perspective. The movements of these three points might be set upon a fixed Cartesian grid, and we might describe one of them as the origin at (0,0), another one perhaps at (-1,3), and another one perhaps at (4,5) if we look at this triangle face-on. This is the "background dependent" way to think of it: space as a thing, a grid, upon which objects dance.

The background independent way to think about it is to think of it solely in terms of relations between the three objects. We'd call that a configuration space, where space itself doesn't exist, only the objects do (but we refer to "space" as a useful tool defined by those objects).

Bernard d'Espagnat wrote a lot about this in his book On Physics and Philosophy, and Roland Omnes, Lee Smolin, many others: which is right, background dependence or background independence? The best theories are background independent, like GR. But many quantum theories are background dependent.

So the really convoluted answer to your question is we don't know whether space is fundamental or whether objects are fundamental. There may be a duality, where it doesn't matter which is true as long as you pick one and go consistently with it.

What we do know is that we can at least describe what is happening with the expansion in great detail (and again, I have worked only a little with QFT, namely for some papers I wrote on black hole thermodynamics because QFT is at the heart of the Unruh effect and therefore Hawking radiation which is critical for black hole thermo. I will be able to probably give better insight after my further quantum classes this fall and spring semester).

 

[lewisnotmiller]

I was waiting to get into GR before talking about this, but I can give a brief blurb about it.

The particle horizon or cosmological horizon is a distance from any observer at which objects recede away so fast that light emitted from them will never reach the observer (they are no longer in the observer's causal universe).

The fact that light takes time to reach an observer is in fact one of the best empirical observations that can be made about the expansion. For a while, there was a paradox called Olber's paradox: why is the sky dark?

If you imagine a homogeneous and isotropic universe that stretches infinitely (or at least "enough to appear infinite") in all directions, why would the sky be dark at night? There would be no patches of sky where there wouldn't be some bright object like a star. The night sky should uniformly look as bright as the surface of the sun, so why isn't it?

The answer is, of course, because despite there being enough stars and galaxies to do this, it takes time for their light to reach us; and there hasn't been enough time for most of the stuff in the universe to reach us observers. (On top of that, there was a period of time before stars began to shine; but that's a separate topic).

If light hasn't had enough time to reach us, that implies that there's a finite amount of time in the past where the universe looked the way it does now. This leads into how scientists started thinking about the Big Bang when combining this fact with the fact that the universe is expanding with time.

Excuse any dumb questions, this isn't an area I've read much on, less studied. But your posts are clear.
Is there an implication in this that our sky would potentially get lighter over time as distant light reaches us? Or does the decay of objects mean that the overall light that reaches us is practically similar even whilst sources may change?

I'm thinking it's entirely possible that the scales we're talking about here precludes measurement, but thought I'd ask.

 

[Meow Mix]

Excuse any dumb questions, this isn't an area I've read much on, less studied. But your posts are clear.
Is there an implication in this that our sky would potentially get lighter over time as distant light reaches us? Or does the decay of objects mean that the overall light that reaches us is practically similar even whilst sources may change?

I'm thinking it's entirely possible that the scales we're talking about here precludes measurement, but thought I'd ask.

When we get to dark energy, we will see that not only is the universe expanding, but it's accelerating as it's expanding: so more and more objects will recede behind a cosmic horizon; so the reverse will be true. The night sky will be dark outside of gravitationally bound objects.

Future astronomers will only be able to see the stars in the Milky Way and will only be able to see the galaxies in the local cluster. All other objects will be gone behind a horizon, a sad reality!

 

[JoshuaTree]

When we get to dark energy, we will see that not only is the universe expanding, but it's accelerating as it's expanding: so more and more objects will recede behind a cosmic horizon; so the reverse will be true. The night sky will be dark outside of gravitationally bound objects.

Future astronomers will only be able to see the stars in the Milky Way and will only be able to see the galaxies in the local cluster. All other objects will be gone behind a horizon, a sad reality!

Seems like empty space begats more empty space, hence the acceleration. How does dark energy figure into this accelerating expansion? Is dark energy the cause of fluctuations?

 

[Meow Mix]

Seems like empty space begats more empty space, hence the acceleration. How does dark energy figure into this accelerating expansion? Is dark energy the cause of fluctuations?

Indeed, the more space there is, the more there is to expand: objects that are further away will expand away faster, even if the rate of expansion were constant (and it's not).

Dark energy enters the picture when we say the rate of expansion is increasing. All the matter in the causal universe interacts gravitationally: they resist the expansion by wanting to get closer together. That's why despite the universe expanding, our solar system, galaxy, local cluster, etc. don't expand apart: gravity is enough to counteract the expansion. But for objects that are further away, the expansion dominates gravity.

We will see in some of my next posts that there are several possible universes that we can rule out. For instance, one possible universe would be where there is enough mass from matter to completely counteract the expansion, causing the expansion of space to decelerate and eventually reverse (called the Big Crunch). However, as I will also get into, we now know that there's not enough mass to do this.

Are you equating variable speed of light with Satan fall?

I'm not sure what you mean here, this post isn't really about Biblical stuff.[/QUOTE]

 

[JoshuaTree]

Indeed, the more space there is, the more there is to expand: objects that are further away will expand away faster, even if the rate of expansion were constant (and it's not).

Dark energy enters the picture when we say the rate of expansion is increasing. All the matter in the causal universe interacts gravitationally: they resist the expansion by wanting to get closer together. That's why despite the universe expanding, our solar system, galaxy, local cluster, etc. don't expand apart: gravity is enough to counteract the expansion. But for objects that are further away, the expansion dominates gravity.

We will see in some of my next posts that there are several possible universes that we can rule out. For instance, one possible universe would be where there is enough mass from matter to completely counteract the expansion, causing the expansion of space to decelerate and eventually reverse (called the Big Crunch). However, as I will also get into, we now know that there's not enough mass to do this.



I'm not sure what you mean here, this post isn't really about Biblical stuff.

[/QUOTE]

Biblical stuff no, apologies... But the post I replied to seemed to suggest Satan's fall was analogous to a change in the speed of light, I was trying to understand the point being made.

So if gravity propagates at the speed of light then gravitational effects beyond the particle horizon are zero, right?

 

[sayak83]

There are a lot of posts going on where people have questions about cosmology, particularly the more interesting parts like the Big Bang, dark matter, dark energy, and so on. So, I thought I'd type up a series on cosmology for interested parties. Plus, it's a good way for me to keep refreshed on the basics.

So where do we start with something as ambitious as studying the entire universe?

First, we have to get assumptions out of the way, but I think we can be convinced that they're reasonable ones.

1. We assume that the laws of physics behave the same way here as they do over there; that they do not depend on their location in space and time (Lorentz invariance).
2. The universe is homogeneous and isotropic: it contains the same sorts of things, and it contains the same sorts of things in the same way in every direction.

"Now hold on," we might object. "Surely there are different things in the universe. If I draw an imaginary cube with the Sun as the center, that box will contain completely different kinds of things than if I drew an imaginary cube of the same size somewhere in the middle of a nebula."

And that's true: when we say the universe is homogeneous and isotropic, we mean at certain scales it is. Your room isn't homogeneous and isotropic, nor is planet Earth, nor the solar system, nor the Milky Way Galaxy or even the local cluster.

[GALLERY=media, 9486]Isohomo by Meow Mix posted Jun 23, 2021 at 8:31 PM[/GALLERY]

It's not until we "zoom out" to about 100 Mpc (that's Megaparsecs, or about 3.26 million light years) that we get a picture of the universe that's homogeneous and isotropic.

It would make things considerably easier if the universe were also time-invariant, but we know that isn't the case: the size of the universe itself changes with time, and the stuff within it behaves differently based on when we're talking about.

[GALLERY=media, 9487]Sfrd by Meow Mix posted Jun 23, 2021 at 8:35 PM[/GALLERY]

Here, we see that the star formation rate differs with redshift, and we will discuss how looking at different redshifts is looking at the universe at different points in time.

So, most of us here are probably at least colloquially familiar with the concept of redshift: the universe is expanding, so light that reaches us from distant sources will have their spectra redshifted compared to the spectrum of a similar object (say, a similar star) at rest with respect to the observer.

[GALLERY=media, 9488]Redshift by Meow Mix posted Jun 23, 2021 at 8:48 PM[/GALLERY]

(We use "z" for redshift)

This often gets misattributed to the Doppler effect, but it's actually not. The Doppler effect is related to the actual motion of a source relative to an observer's location in space. In cosmology we call galaxies' actual motion peculiar motion, because they do move with respect to one another, especially within the contexts of their local clusters. So, the redshift and blueshift of nearby galaxies may be due to a true Doppler effect, but when you zoom out enough (get to high enough redshifts), the redshifting is not technically a Doppler effect: it's due to space itself stretching the wavelength of the light as it expands.

Perhaps I can convince you that this is different from a true Doppler effect with an analogy:

[GALLERY=media, 9490]Paperclips by Meow Mix posted Jun 23, 2021 at 8:56 PM[/GALLERY]

Here, a couple of ants (observers) are sitting on a couple of paperclips which do not move from their fixed positions on a rubber band. In a true redshift situation, whether the light is redshifted or blueshifted would depend on if a paperclip is moving towards you or away from you. But since the space itself (the rubber band) is expanding, all paperclips will receive redshifted light from all other paperclips. If the light had to travel across the rubber band (to be true to the space analogy), the distance between the peaks and troughs of the wavelength of the light would get stretched as it travelled.

[GALLERY=media, 9489]Expansion by Meow Mix posted Jun 23, 2021 at 8:56 PM[/GALLERY]

The above is a visualization of the expansion of space. Galaxies retain their positions with respect to one another, but the space between them expands.

Why does it matter that we make this distinction between true galactic motion (true redshift via peculiar motion) and redshift via spacetime expansion?

[GALLERY=media, 9491]Peculiar by Meow Mix posted Jun 23, 2021 at 9:05 PM[/GALLERY]

Because the redshift caused by the expansion is mostly linear (not perfectly, thanks to some relativistic effects, but consider it close enough for right now in this series). In the above image, the blue oval shows a large number of outliers in the data. Why?

Because the blue oval contains data from the Virgo cluster: galactic clusters tend (for gravitational reasons) to have galaxies that are moving with respect to one another (high peculiar motion), so it "fuzzies" up measurements of their redshift due to universal expansion. Imagine if the paperclips in the example above had multiple paperclips in a cluster around point E (in that image), all moving forward and backward, left and right, etc. An observer from paperclip A would see some of the paperclips moving away slower or faster simply because of their motions relative to each other being added to the apparent motion of the rubber band stretching.

Fortunately, there appears to be a physical "speed limit" to peculiar motion (around 1,000 km/s). Since, due to the expansion of the universe, objects that are further apart will appear to one another that they are receding away faster than closer objects (think of this like there is more space between them that's expanding, so each unit of space there is to expand means more expansion), we can look out far enough (to great enough redshifts) that the noise caused by peculiar velocity is negligible. This would be good if we wanted to, for instance, measure the Hubble parameter.

All this talk of expansion brings us to a good stopping point (and a good setting up point for all the stuff people really care about, like the Big Bang, dark matter, dark energy, etc. that people keep asking questions about on the forum) from here: the scale factor of the universe.

We define a scale factor a(t) of the universe such that when t = 0 (so, now in time), a = 1. If at any point the universe is half the size of the universe today, a would equal 1/2, and so on. This is where we get the Hubble parameter with a simple differential: H = (da/dt) / a. The Hubble parameter relates the apparent recession velocity with the size of the universe at any given time relative to the size of the universe now (hence why people often mischaracterize the Hubble parameter as a constant; which it clearly is not: the value of H changes as the value of a changes!)

Many things are related to the scale factor (remember, this is a, the size factor), and I'll have to decide if I want to spend time proving them or asking folks to take my word for it; but among things that are related are temperature (T is proportional to a^-1), redshift, and the age of the universe itself.

These are all the ingredients we need to make a real cosmology post next time, which will be about the Friedmann equations and how we will use them to answer a lot of these people have; and why we have good reason to do so.

So more of a curious question.
How do we distinguished using evidence between a situation where space is expanding and where all galaxies are in fact actually moving away from us at a speed that is proportional to the distance from us, with us being in the true centre of the universe?