Infinite Lattice II

Discussions ranging from space technology, near-earth and solar system missions, to efforts to understand the large-scale structure of the cosmos.

Infinite Lattice II

I have written a post before on 'The Infinite Cosmic Lattice' visualization of the observable universe. It was based on MC Escher's "infinite lattice' drawing of the 1950s.

Since then I have used a color variant of that "infinite" lattice as my avatar on this forum, because it can be used to give insight in the principles of a spatially flat, possibly infinite, but expanding cosmos.

After what was learned from the interaction with readers, I decided to give it another try, but with a slightly different visualization. The main problem raised was the blue bars that hold the latticework together caused confusion as to "what is between the bars"? In the real cosmos the 'holding together' is done by invisible gravitational forces permeating all of space.

I have thought to try a two-step transition from the lattice to objects held together by gravity.The problem is that just taking away the bars result in a rather incomprehensible set of cubes with difficulty to imagine the structure. In the first transformation below, I have used the effects of perspective and color coding of the spheres to indicate depth and distance from the camera. Bluer, more prominent for nearer, going towards the red end for more distant spheres, culminating in white for the cosmic microwave background (CMB) radiation. Not a realistic structure or colors, but the idea is to simply understand what we are representing.

Once one can get your head around this structure, I think it is a simple matter to understand the scrambled structure, which has a more realistic random pattern:

One should view the colored spheres as clusters of gravitationally bound galaxies, not single galaxies or stars. This is because we want to show cosmic (Hubble) expansion and gravitationally bound stuff do not follow Hubble's law - they just orbit the gravitational center of the cluster.

Before we get to the physics of expansion and how to visualize that, how do you find this static visualization? And how could it possibly be improved?

BurtJordaan
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Re: Infinite Lattice II

I like your new visualization better than the old. It looks more realistic and it is easier to compare to something related to the natural world like galaxies receding into the distance or it could be a Gram stain from a purulent wound. Anyhow, it looks good and I have no suggestions for improvement.

https://images.search.yahoo.com/search/ ... ightropetb
bangstrom
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Re: Infinite Lattice II

Thanks Bang, will try to keep the germs out of it ;)

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Infinite Lattice II (continued)

Back to the isotropic 3D matrix view of our observable universe.

What we have here is a simulated 'ultra deep field' view along one of the columns of galaxies and its nearer neighbors, with the farther-out neighboring columns coming into view due to perspective.

This view takes us all the way to the end of the early 'cosmic dark ages' (the black stuff at the center). The 'black stuff' starts from some 30 billion light years distant, when the cosmos was about 500 million years old (redshift about 10).[a] The reason for the blackness is that no observable galaxies have formed yet.

Now one must not be fooled into thinking that we see the black area so small simply because the observable universe was small then. It is just perspective - we are looking from the "inside out" and it will look the same in all directions along any column of simulated galaxies. Remember that we are always roughly at the center of the observable universe. This is precisely why I prefer the lattice analogy over the balloon analogy, where it is portrayed from a "God's eye view", from the 'outside', so to speak.

Yes, the observable universe was much smaller at age 500 million years, about 10% of its present size. It says nothing about the size of the overall universe, which was surely much, much larger then, if not infinite. In this simulation, it is precisely flat and then there is no reason to think about an 'edge'. It makes no logical sense!

I will stop this post here, because the details are quite taxing to the mind, especially for an 'old mind' like mine.:-)

Notes:
[a] The data is from my Lightcone7 cosmological calculator, modeling the LCDM cosmic model accurately.

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Re: Infinite Lattice II

I have erroneously posted the Continuation of the Infinite Lattice as a separate topic. They are now merged.

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Re: Infinite Lattice II (continued)

BurtJordaan » 12 Dec 2019, 19:25 wrote:Notes:
[a] The data is from my Lightcone7 cosmological calculator, modeling the LCDM cosmic model accurately.

Redshift and present distance of observed emissions over time.

The red curve is essentially the radius of the observable universe as it evolves over time and the blue curve is the redshift for the corresponding time, from our perspective of course.

Edit: Sorry I goofed in the last sentence - the red curve Dnow is how the radius of observable universe evolved over "look-back" time, which is Tnow-T, where Tnow is the present cosmic time and T the cosmic time.
Last edited by BurtJordaan on December 13th, 2019, 8:37 am, edited 1 time in total.
Reason: Correction in description

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Re: Infinite Lattice II (continued)

BurtJordaan » December 12th, 2019, 12:25 pm wrote:
Now one must not be fooled into thinking that we see the black area so small simply because the observable universe was small then. It is just perspective - we are looking from the "inside out" and it will look the same in all directions along any column of simulated galaxies. Remember that we are always roughly at the center of the observable universe. This is precisely why I prefer the lattice analogy over the balloon analogy, where it is portrayed from a "God's eye view", from the 'outside', so to speak.

The last image appears to be drawn from the wrong perspective. It looks too much like the view of a 3D universe from the outside looking in. The black area should appear visible in all directions as an outer shell rather than as a small square in the center. The galaxies should radiate away from us as observers in the “center” of the universe with more distant galaxies filling the gaps between nearby galaxies the way they did in the first random scatter image.
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Re: Infinite Lattice II

Tx Bang, I take your point. It becomes a bit clearer when I adjust the sphere sizes in the simulation, so that not so many distant rays are blocked by foreground rows of spheres.

Infinite Matrix View

That said, remember that this is an Ultra Deep Field simulation where only a limited patch of sky is observed with a long exposure. So we see a small patch of the observable universe's particle horizon from its center outwards. The telescope has been placed inside a row of clusters, but not inside a cluster, with it's viewing axis aiming along the row of clusters (if this word mincing makes any sense).

The distinctive straight black areas are al artifacts of the precision of the (unrealistic) matrix structure. This structure is a 'crutch' to help understanding what is observed when we look at such a patch of sky. Once sorted out here, we will see what the equivalent random scattering picture looks like.

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Re: Infinite Lattice II

Here is what the Randomized and Matrix views will look like, side-by-side, same parameters.

Random and Matrix views compared

Each has its own pro's and con's from a observable universe visualization p.o.v.

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Re: Infinite Lattice II (Spacetime)

Here is an 'external view' of a spacetime diagram of the observable universe - an expanding lattice model. Since we have only three dimensions available and one needs to be taken up by time, there is only a 2-D "flatland" available for space. So we cannot readily portray it 'from the inside', like in the case of a 3-D spatial lattice.

The dots represent galactic clusters and the space between them are the cosmic voids, where the spatial expansion takes place, meaning that the average proper distance between the clusters increases with time. The grey background outside of the observable universe is the "rest of space", which we cannot observe, but can infer that it must be there from the dynamics that we can observe.

The simulation assumes (incorrectly) that the same number of clusters existed from the "beginning", just occupying a much smaller volume and hence was much more densely packed than today. Since the scale is so large (the flat blue top is 92 billion light years across) one cannot portray the very early observable universe in this picture.[a] But it correctly indicates that the expansion rate (the inverse slope of the inverted 'cone') was very high in the beginning, 'slowing down' considerably for about the first half of our cosmic history. From then on the expansion rate gradually increased again to the slope that we observe today, due to accelerated expansion.

So where are we in this picture? In the very central top blue dot, representing the Virgo Cluster, in which we reside. What would we see from there, looking along the flat blue top disk to any side? Since light takes time to reach us and the top flat disk was moving 'upwards' all the time, we essentially look towards the inside of the expanding cone and can 'see' the 'red zone', i.e. the very distant galaxies right at the bottom.

In a 2-D spacetime diagram, the path that light would have followed takes the form of the "Cosmic Teardrop" that I have depicted before (I haven't converted it to the colorful 3-D depiction yet, but I have a 3-D view from the top blue plane, looking back in time).[b]

The 'cosmic teardrop'

The observer up top is in the center of the flat present space and the BB is at the origin (0,0). The hyperbola roughly depicts the inverted cone of the observable universe and the teardrop the past light light cone that encloses all the events that we can possibly observe at present.

Just after inflation, the expansion rate was unimaginably large and any photon or other massless particle that could have been emitted then, would be have been dragged away from our eventual (central) location. Only after some 3 billion years, the expansion rate slowed down enough for the particles to make headway towards our location.

There is a lot more to say about this way of looking at cosmic spacetime, but it will have to stand over for some later post.

Notes
[a] One needs some form of logarithmic scale that expands the early times and compresses the late times. More about that later in a later post.

[b] The 3-D cosmic spacetime diagram viewed from the 'flatlander plane', looking back down the time axis.
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Re: Infinite Lattice II (Spacetime)

BurtJordaan » 17 Dec 2019, 14:22 wrote:In a 2-D spacetime diagram, the path that light would have followed takes the form of the "Cosmic Teardrop" that I have depicted before (I haven't converted it to the colorful 3-D depiction yet, but I have a 3-D view from the top blue plane, looking back in time).

Here is the 'Technicolor' Cosmic Teardrop' from the side. It is also called the past cosmic light cone from our perspective.

Past Cosmic Light Cone

Remember that the vertical dimension is time (scaled to one Hubble time) and all that we can observe in 2-D space lies on the surface of the teardrop - all the light that reaches us from near and far crawled upwards on the surface. The red region represents the most distant and earliest galaxies/clusters and the blue the nearby ones.

Remember that we have said before that the photons emitted in our direction were originally receding from us and only started to make headway when the expansion rate dropped low enough. The light cone sits at the same origin as the inverted cone of the observable universe above.

Now one might ask: why then was the observable universe portrayed as an inverted cone on the spacetime diagram before. That answer is that the cone indicates where the things that we now observe are located today, long after the photons that we observe have been emitted. The teardrop indicates where they were when they emitted the photons that we observe today.

There is more, but this stuff is quite challenging, so I'll leave it here for now. Questions are welcome.

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Re: Infinite Lattice II - Spacetime

Here is an attempt to put the expansion curve and the (teardrop) light cone on one scaled technicolor spacetime diagram so that one can see how they relate. The z-axis represents time and the distinct rings of the 'bowl' are time-slices of the edge of observable space. The scale is Hubble time and Hubble radius (the latter is how far light can travel in one Hubble time in flat spacetime). One Hubble time is about 14.4 billion years.

Lightcone inside Observable Universe

The galaxies have been removed from the observable universe so that only the rim of first galaxies after the dark ages remained (i.e. I emptied the bowl and also cut it slightly open for clarity). This made it possible to see the light cone and the ratio of the sizes of observable universe and the light cone in the center. The light cone rests precisely on the bottom of the bowl.

So what is the difference between the two? As we have said before, the light cone is the limit of events what we can actually observe today in terms of spacetime. Similar to the light cone of Minkowski spacetime, the finite speed of light prevents us from observing any event outside of the light cone. In this case an event is when the light that hits our eyes or our telescopes today has left the galaxy, or has been released by the cosmic microwave background (CMB) radiation, for that matter.

When we observe the CMB today, we see it as if it is about 46 billion light years away - at the rim of the 'bowl' all around us. This is how far the positions from which these photons have been transmitted have been driven away from our location by the cosmic expansion. As has been said, the emitted photons 'crawled' up the teardrop light cone to reach us some 13.8 billion years later (at about 0.96 in Hubble time).

How do cosmologists know that? They use a simplified solution to Einstein's general relativity equations, valid for a homogeneous and isotropic 'perfect' gas, plus a myriad of observations to find the best possible parameter fit for the particular solution. Then the values of those mentioned values are the most likely that we have. Not perfectly certain, but within reasonable tolerances in terms of observational accuracy and the assumed model.

But all of the above is old hat. What is not so obvious from the depiction of the solution above is the fact that there is a possibly infinite number of bowls and cones, one for every possibly observer in the entirety of the universe. They are potentially stacked together densely, some overlapping, but with different spatial origins. We are always at the center of our observable universe, but never an the center of the universe - the latter does not exist.

Finally, I want to warn against viewing the open 'bowl' as a gravitational potential well, despite the apparent resemblance. The bowl is actually filled with galaxies and as far as we know, it goes on forever in all directions. At any given cosmic time slice, the entire universe is at the same gravitational potential, apart from minuscule local dips. The average is flat and there is no cosmic time dilation, which is a strictly local phenomenon.

With this goes the important fact that the cosmological redshift of the distant galaxies are caused by the expansion, the stretching out the wavelength of light in transit. It is not that they emit the light already redshifted. This is in contrast with local phenomena of gravitational redshift, where the photons are emitted redshifted.

-=0=-

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Re: Infinite Lattice II - Animations in Spacetime

Happy new year to all!

I have done a little more work on cosmological model visualization and this post is really just a kick-start for 2020.

The previous image of the spacetime of the observable universe's boundary and its cosmic light cone:

can be animated. Click on this link and then manipulate the controls below the animation as desired. It will 'Play' at around 300 million years per animation frame, so each frame produces two new 'rings': the outer one, where the first galaxies were at that cosmic time and the inner one where the photons coming from those sources were at the same time. Notice how the photons were first receding from our location at the center and then, as the expansion rate dropped, started to make headway towards our telescopes.

A rotated (side-on) snapshot.

You will notice that the scale of the image has been restored to the regular units of Gyr for time and Glyr for distances (Giga is a billion). The present time is 13.8 Gyr (we are at the blue tip of the completed light cone) and the observable universe has a radius of some 46 Glyr. The red dot at the bottom is the cosmic background (CMB) radiation at 400,000 years, not the BB. Then followed the cosmic dark ages lasting for at least 300 million years before the first galaxies started to assemble (the first red ring to form in this picture).

More later...

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Re: Infinite Lattice II - Animations in Spacetime

BurtJordaan » 01 Jan 2020, 12:40 wrote: The red dot at the bottom is the cosmic background (CMB) radiation at 400,000 years, not the BB. Then followed the cosmic dark ages lasting for at least 300 million years before the first galaxies started to assemble (the first red ring to form in this picture).

Those first galaxy clusters have not been observed yet - they are now too far and feint and also too well redshifted, way into the infra-red band and hence beyond Hubble (which is essentially limited to the visible band). They will have to wait for the James Webb Space Telescope (JWsT), which will hopefully be in operation by 2022. The JWST will cover the whole infra-red band with superior resolving power (due to its sensors and huge compound mirror).

The present Cosmic Light-Cone drawn to scale - note the 45 degree angle at the top.

We have discussed the first red ring at the bottom, but what about the first blue ring below the tip of the light-cone? The blue dot at the top represents Earth's position in this scheme if things, but since the dots are really clusters of galaxies, that top dot encompasses the whole Virgo Supercluster. It is a mass concentration of galaxies containing the Virgo Cluster and Local Group, which in turn contains the Milky Way and Andromeda galaxies.

Neither the components of the Virgo Supercluster, nor the cluster itself follow the Hubble expansion precisely, because gravity is still strong enough to keep the groups loosely bound to each other. It was later discovered that it is really part of the much larger supercluster, which will be discussed below.

The first blue ring below the top dot represents the distance scale to the center of the Laniakea Supercluster, our resident supercluster. It is large enough for the components to move away from each other, with the outlying clusters following the Hubble expansion quite closely.[a]

Now back to the cosmic light-cone. In our local area, right near the top, the light cone has a 45 degree slope, just like in the case of Minkowski spacetime - as is to be expected if we plot time in years and distances in light-years on the same scale. The 45 degrees only holds for as long as the space through which the light travels has not undergone expansion during the travel time of the light.

As said above, when we go beyond the edges of the Virgo Supercluster, distance increase over time and there is a 'bending' in the spacetime path of the photons, subtle over short distances, but getting very large as distances from us get large. But, do we observe this 'bending'? The answer is no - we never actually observe time as a dimension - we can only observe it by counting periodic events in space, like the reading on a clock face.

So what then is the purpose of such light cones and spacetime diagrams? It gives us a tool to handle what we observe mathematically, and with it some comprehension of why it looks like it does.

More on that later.

-=0=-

Notes [a] The "Great Attractor" apparently lies at the center of Laniakea and it causes some deviation from the Hubble flow, but that is easily removed from the data when studying the large scale universe.

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Re: Infinite Lattice: Evolution of the View

Imagine that there was a fictitious telescope with a Hubble-like capability somewhere in the one billion year old cosmos. As the cosmos evolved over time, this telescope has taken a series of 'ultra deep field' snaps at defined time intervals. Again using the principle that bluer dots simply mean closer to the telescope and redder dots mean farther from the telescope, a grossly oversimplified chronological selection of snaps would have looked something like this:[a]

The changing view over the lifetime of a 13 billion year old telescope

The top-left frame only shows galaxies/clusters whose light could have reached the sensor by one billion years post-BB. In a spatially flat universe, there are an unlimited number of clusters farther out (i.e. along the line of sight), but they can only gradually come into view on the camera sensor. There are also clusters coming into view from all sides due to the distance, but to some extent they are balanced by the expansion causing some clusters to shift sideways, out of the view. These complex effects were suppressed so as not to detract from the main effect under discussion here, i.e. that the depth of the frames gets larger over time, as light from more and more distant galaxies is reaching our telescope.

The top left picture was 'taken' at t=1 billion years after the BB and it has a depth of about 1.5 billion light years, the Hubble radius at that time.[b] It also depends on how one defines "depth" in this case. When the photons left the farthest observable galaxies at that time, they were less than 0.5 billion light years from the camera and when their light arrived, they were already 1.5 billion light years from the camera.

The bottom right picture represents our present time, t=13.8 billion years, with a depth of about 27 billion light years, with light leaving those first galaxies when they were only 4 billion light years from the camera. The expansion prevented light from farther "first galaxies" to have reached us, but some more will appear in the future. More about that in a future post...

-=0=-

[a] The perspective effect has been suppressed, so near and far clusters are portrayed as of equal angular size.

[b] The Hubble radius is the distance at which the recession rate away from the camera equals the speed of light. Recession rate is the change in proper distance per unit cosmic time.

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Re: Infinite Lattice II

BurtJordaan » December 14th, 2019, 2:19 am wrote:Here is what the Randomized and Matrix views will look like, side-by-side, same parameters.

Matrix-Random-30GlyDarkAgesSmall.png

Each has its own pro's and con's from a observable universe visualization p.o.v.

Nice visuals!
What is the geometry you considered for the “Matrix” view? Riemann or Euclidean? The difference between the two geometries may not matter when depicting a small patch of the sky but I am just curious as to what you consider to be the geometry of your model.

Also, why are the lines connecting the galaxies all straight? I would think that lines representing light paths moving back in time should form intersecting cones of concentric circles rather than having angular edges. The lines would curve more with a Riemann geometry than Euclidean but they should also curve with a Euclidean geometry.

Except for the lack of true circles, your “Matrix” view resembles some of the artwork done by the “Oakes Twins.”
https://www.artsy.net/artwork/the-oakes ... et-terrace

This discussion of 4D spacetime in artwork by the Oakes twins is too conventional for me but I find it interesting.
https://getpocket.com/explore/item/what ... ket-newtab
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Re: Infinite Lattice II

bangstrom » 19 Jan 2020, 11:39 wrote:What is the geometry you considered for the “Matrix” view? Riemann or Euclidean? The difference between the two geometries may not matter when depicting a small patch of the sky but I am just curious as to what you consider to be the geometry of your model.

The pure spatial geometry of the lattice analogy is Euclidean for a spatially flat model. When time is added as a visible dimension, it becomes Riemann if there is expansion. Because of all the caveats, I guess one can say that in general it is Riemann.

Also, why are the lines connecting the galaxies all straight? I would think that lines representing light paths moving back in time should form intersecting cones of concentric circles rather than having angular edges. The lines would curve more with a Riemann geometry than Euclidean but they should also curve with a Euclidean geometry.

The lines are only there to provide distance perspective and then they need to be straight for flat space. The real deep-field views are obviously more random and no lines or circles should show up. As can be seen in this Hubble Ultra Deep Field Flythrough with presumably real data, it sport fairly random structures and distance perspective, not concentric rings or such things. Remember, we look from the center of the observable universe outwards towards the observable horizon.

I guess that you will find my views also a tad too conventional... ;-)

I simply strive to make the conventional view more tractable to the quasi-novice.

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Re: Infinite Lattice II - The Hubble Sphere and Event Horizo

So far I have concentrated on the views from deep field telescopes plus the expansion curve and lightcone for the early observable universe (the flaring 'bowl' and the 'teardrop' shapes shown again below).

Fig. A - Teardrop in Expansion 'bowl'

Now I want to introduce a very important new curve - our Hubble sphere, which is here shown in 2-D space and one time dimension - as a 'cup' inside the 'bowl' and containing the teardrop - well, not quite containing it, as we shall soon.

Fig. B - Teardrop, Hubble 'cup' and Expansion 'bowl'

Just to recap, the expansion 'bowl' represents the spacetime paths of the most distant sources that we can observe, today some 46 billion light years away. The 'teardrop represents the spacetime paths of photons from those distant sources to our telescopes. Now we have introduced the Hubble 'cup', which represents the radius of the sphere where the apparent recession rate of objects equals the speed of light.[a]

Below I have taken away the wide expansion bowl and zoomed in a bit. One can see that the teardrop does not fit into the bottom part of the Hubble cup - the teardrop has fat/flattish bottom and the Hubble cup a pointy bottom. The dot at the bottom (see Fig. A above) essentially represents the observable universe at the time of the CMB radiation release, when the recession rate of that region was about 66 times the speed of light.

Fig. C - Teardrop and Hubble 'cup' compared

The Hubble radius (where the recession rate was c) was about 600,000 light years, while the photons emitted towards us were actually speeding away from us (the center) at 66-1=65 times the speed of light. Hence the flattish bottom of the lightcone. Fortunately for us, the gravitational 'pull' (due to the immense energy density) was very strong and the recession rate gradually dropped, while the Hubble cup has grown to a point where those photons found themselves inside the Hubble cup and could start coming our way.

Without these fortuitous circumstances, we would never have been able to observe the CMB, nor perhaps the very distant galaxies. The late accelerating expansion from dark energy will eventually again reverse the circumstances and we will be able to observe less, but that's for a future post.

One more important 'bowl' is the cosmic event horizon, which is presently just slightly larger than the Hubble 'cup' (17.3 vs. 14.4 billion lyr). The big difference is that it fully contains the lightcone teardrop, because it contains everything that we could have observed in the past and will ever be able to observe in the future.

Fig. D - Teardrop, Hubble 'cup' and Horizon 'bowl' compared

The cosmic event horizon is really where our observable universe 'stops'. Any signal that is or was emitted outside of it will/(could never) reach/(have reached) us. I will go deeper into this next time and also talk a bit about the future of the observable universe.

-=0=-

Note [a] The Hubble radius is essentially the inverse of the expansion rate (H) when appropriate units are used. With a present Hubble constant of 67.7 km/s/Mpc, the Hubble radius is now 14.4 billion lyr, but as the Hubble constant was larger in the past, the Hubble radius was smaller, as per Fig. C .
Last edited by BurtJordaan on January 31st, 2020, 10:41 am, edited 2 times in total.
Reason: Added the cosmic event horizon

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Re: Infinite Lattice II

As promised, we will now move into future predictions of the shapes of expansion.

In the diagrams below, you will recognize the shapes, with the exception of perhaps the particle horizon, which we have not discussed this far. The small heart was the past lightcone at about half of the present time. The large heart is the present past lightcone (13.8 Gyr).

Fig. A - The Hearts of the Past and the Present Compared

The brown dotted curves fanning out from the tips of the hearts are the future light cones of observers then and now respectively. The fainter dotted curves fanning out differently represent the world-lines of potentially other comoving observers, who can possibly communicate with us and vice-versa.

Remember that as with all spacetime diagrams, one can choose any of those observers as the reference and such an observer would have the same symmetrical light-cones and other observer spacetime paths (a.k.a. wordlines) around it.

Moving on to a projection of the future curves, we will see the heart enlarging to fill more of the available 'real estate' of our observable universe. It is pictured when cosmic time is about double what it is now, around 27 Gyr.

Fig. B - The Hearts of the Present and the Future Compared

One can envision that the heart will eventually fill virtually the whole of the Cosmic Horizon bowl, but that is far, very far into the future, according to present understanding of the scheme of thing.

Next time a bit more about the 'events within' and the rest (of the events)...

Notes
[a] I grabbed this screen from an excellent simulation by: Simon Tyran, Vienna, definitely worth a peak. Don't worry about the right-hand panel - that x-axis is scaled to co-moving distances, in which astronomers often work for convenience.

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Re: Infinite Lattice II - Observable or Not?

Coping with what the Cosmic Heart and the Cosmic Horizon mean i.t.o. observables is quite brain-bending stuff. I have annotated one of the screenshots of Simon Tyran's simulation in an attempt to explain it somewhat.

Annotated Cosmic Heart and Cosmic Event Horizon

Let's start at the top-left. "Galaxies crossing the event horizon is or was the oldest that we can ever observe them"

As stated before, the faint dotted curves are the world-lines of galaxies at a specific redshift. We see them today as they were when they have crossed the surface of the heart, mostly long ago, but there are obviously nearby ones as well.

As the cosmic heart enlarges in the future, astronomers will keep on seeing them, but obviously older and more redshifted. If they don't blink out completely, astronomers with sufficiently advanced (future) technology can keep on observing them forever - despite the fact that they have crossed the observable horizon aeons ago. Brain-bending - don't say that I did not warn you! Once one has tortured your brain around the above, the right-hand comments are somewhat simpler. Or are they?

Yes, I am fishing for some more comments/questions, otherwise this thread may die a premature death. It is in the interest of this forum to keep the science chat side alive, because it is not in a very healthy state at present - maybe because of a "shrinking head/heart", or whatever...

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