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An'shur
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17 Oct 2018 13:06

What if the universe was contracting instead of expanding ever since the big bang? Meaning, how would we see the universe if the Hubble constant was not 72.5 (km/s)/Mpc, but -72.5 (km/s)/Mpc

Would very far galaxies be approaching us faster than light? What would be the proper distance to the edge of the observable universe (the distance which in our real universe is 46 billion ly)? Would the universe be getting crowded enough for galaxy mergers to be happening significantly more often?

Speaking of far away galaxies, I imagine they would be blueshifted. Which gets me to another question. Why are the galaxies in the deep field images so red? Even if the whole visible spectrum was redshifted far into infrared, shouldn't ultraviolet or shorter wavelengths shift into the visible spectrum, making the galaxies visible?
 
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17 Oct 2018 17:54

An'shur wrote:
Source of the post Meaning, how would we see the universe if the Hubble constant was not 72.5 (km/s)/Mpc, but -72.5 (km/s)/Mpc? 

One consequence we should think about is for how we figure out what the age of the universe is.  If the universe started out as a singularity state, and has expanded at a constant rate to the present time, then it is simple to find the age by taking the inverse of the Hubble constant:

Distance = (velocity)x(time), so time = distance/velocity.  But the expansion rate (Hubble constant) has dimensions of velocity/distance, so 1/(Hubble's Constant) has dimensions of time and equals the age.  The way to think about this is to imagine a stretchy rubber cord, with a bunch of evenly-spaced dots along it.  If you stretch the cord at a constant rate, measure the speed at which two dots move away from each other, and divide by their current separation, then this is the "Hubble constant" for that cord, and the inverse of that tells you how long ago all the dots were on top of each other -- assuming that the expansion actually extrapolates back that far.

If H = 70km/s/Mpc, then 1/(70km/s/Mpc) works out to be 4.4x1017 seconds, or about 14 billion years.  (The real expansion rate actually varies with time, depending on the density of matter, radiation, and dark energy, so this turns the calculation of the age into an integral, but it is still the same idea, and in fact this is exactly how we determine the age of the real universe).  

If the universe is instead contracting, then this logic doesn't work.  What was the initial size of the universe?  Has it been contracting forever?  Instead of using the inverse of Hubble's constant, we would need to estimate by other methods, like the universe must be at least as old as the oldest objects we can find and measure ages of.  We could also use light-travel-time arguments with the most distant objects we can observe, since the universe must be at least as old as the time it takes for light from those sources to reach us.

We could make things simple by considering a contracting universe that is the same age as the real universe but contracting at ~70km/s/Mpc.  What will this look like?

  • Instead of distant objects appearing redshifted, they will look blueshifted (just as you imagined). :)  Photons will be "squeezed" by the contraction of space, shortening their wavelength and increasing their energy.
  • The distant (older) universe will be seen to have a lower density than the nearby (younger) universe.  The density increases with time.  This also means galactic collisions will become more frequent, until inevitably there is a "Big Crunch" (unless something halts the contraction).
  • Very distant galaxies may approach us faster than light.  This does not mean that they move through space faster than light (they may be moving very slowly relative to the space in their neighborhood), but rather that the space between them and us is contracting fast enough so that Hubble's Law will yield |v|>c (negative v in this case), just as there are objects in the real expanding universe that have recession velocities greater than c.

Aside:  One important, counter-intuitive, and very frequently misunderstood fact that I'd like to mention here: not only are there distant galaxies in the real universe that recede from us faster than light -- we can also see them.  There are even galaxies that we observe which are not only receding faster than light now, but have always had recession velocities faster than light.  It is difficult to visualize how this is possible, but it can be made sense of by thinking about how the photon moves through the expanding space, at the same time that the expansion rate changes.  (Before dark energy took over, the expansion rate was decreasing, so the distance at which the recession speed exceeds c was increasing).  So some photons cross over that boundary and were then able to reach us, even as the sources were never inside that region.  There is a wonderful paper "Expanding Confusion" that explains this and many other common misconceptions about the superluminal expansion in great detail (highly technical but worth looking at).


An'shur wrote:
Source of the post Which gets me to another question. Why are the galaxies in the deep field images so red? Even if the whole visible spectrum was redshifted far into infrared, shouldn't ultraviolet or shorter wavelengths shift into the visible spectrum, making the galaxies visible?


You are right that ultraviolet and shorter wavelengths can be shifted into the visible range by the expansion (in fact this sometimes caused confusion when looking at highly redshifted spectra -- we might have a difficult time identifying spectral lines in the optical, because they are actually ultraviolet lines!)  However, this doesn't necessarily keep the redshifted spectrum as bright because there is usually less light emitted overall in those wavelengths.  The majority of light from galaxies is emitted by the stars, and the majority of that is in infrared to visible (depending on the typical ages of the stars -- spirals tend to be bluer than ellipticals for example).  So there is typically less UV and higher energy light being shifted into the visible to replace what was shifted out of it.  

The other problem is that the redshift reduces the total brightness (over all wavelengths) that we receive.  Think of it like this: not only is each photon being stretched out, but the photons are also being pulled apart from one another.  So we receive fewer of them per unit time, regardless of what their wavelength was.  The same thing will happen to the image of something falling into a black hole -- it not only turns redder, but also fainter, and eventually vanishes in all wavelengths, even though we as outside observers say it never crossed the horizon.
 
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19 Oct 2018 06:58

"Behind every atom of this world hides an infinite universe". ~Rumi

Why do all electrons have the same charge and the same mass? Because, they are all the same electron! ~Wheeler

World lines traced out across spacetime by every electron is actually all part of one single line like a huge tangled knot, traced out by the one electron. Any given moment in time is represented by a slice across spacetime, and would meet the knotted line a great many times. Each such meeting point represents a real electron to us at that moment.

At those points, half the lines will be directed forward in time and half will have looped around and be directed backwards.

These backwards sections appear as the antiparticle to the electron, the positron. While there are many, many more electrons than positrons, the missing positrons might be hidden within protons.

The eventual creation and annihilation of pairs that may occur now and then is no creation or annihilation, but only a change of direction of moving particles, from past to future, or from future to past.

Could the Big Bang have arisen from a single atom?

Is the universe made of a hyperfinite number of fractal hierarchies described by isomorphic von Neumann algebra within a Hilbert space?
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20 Oct 2018 00:47

Gnargenox wrote:
Source of the post Could the Big Bang have arisen from a single atom?

Well, no, because there were no atoms during the first nanoseconds of the Big Bang. Those formed 300'000 years later mostly as hydrogen, some helium and a tiny amount of lithium during the aptly named Matter Era. Almost all of the original atoms from that era were destroyed since they existed in an environment that was not conducive to their existence.


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Oh well, looks like we're not getting our hyperloop trains from Musk anymore. His new habit caught on :lol:.
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21 Oct 2018 05:44

An'shur wrote:
Source of the post [For a shrinking universe] What would be the proper distance to the edge of the observable universe (the distance which in our real universe is 46 billion ly)?

I have been thinking about how to answer this question specifically.  The very short answer is "it depends!" (on what the contents of the hypothetical collapsing universe are, which in turn determine how it collapses, and what sort of initial state it began with).  The Hubble constant alone will not determine where the edge of the observable universe is.  

Probably the simplest scenario we could consider is to just flip the sign on the Hubble constant and keep everything else (the density of matter, radiation, and dark energy) the same.  But this would imply a universe that did not begin with a Big Bang, but rather one which has always been shrinking -- faster at earlier times -- and then shrinking faster again in the future as it approaches an ultimate end in a Big Crunch.

We can imagine a few different kinds of universes that are collapsing.  We can ask what they look like to someone inside, and how far away the edge of their observable universe is (from how far has light had time to reach them).  We will generally find different answers for these different scenarios, and I think they are all quite interesting.

So, in another post coming in the hopefully near future, I will share results from some computer simulations I have done, and explain in more detail how it all works. :)
 
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21 Oct 2018 08:58

Watsisname, I was thinking about a universe which starts with a big bang, inflates and then instead of slowly expaning as our universe does, it slowly contracts. But I'll await what the other scenarios would look like.
 
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23 Oct 2018 00:44

Watsisname wrote:
Source of the post I will share results from some computer simulations I have done, and explain in more detail how it all works.

An'shur, this is code for "I'm going to look that one up online later" :P.

I'm sorry, Watsisname, I couldn't resist :D.

Anyway, based on my meager knowledge of this, I would hedge my bet that in such a Big Crunch scenario, we might see a reverse of the universe's development at some point? Like it would go through a Matter Era, reverse reionization, then a Dark age, succession of new nucleosynthesis, etc etc until it catalyses into the Planck Epoch? I'm probably wrong, but that seems to be the general Big Crunch gist. Of course, it's unlikely that the Big Crunch will happen anyway based on the current consensus.

I'm also curious to know the answer to this question.
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23 Oct 2018 05:30

Stellarator wrote:
Source of the post this is code for "I'm going to look that one up online later"

Actually it is code for "I have been working on it", as in writing my own Python code which solves the Friedmann equations for a universe containing any abundance of matter, radiation, and dark energy that I want.  I have already showed some of that progress on the Discord server, but I can show some more here as well, which now includes tracing the path of photons as the universe evolves.

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Simulating a closed or collapsing universe is easy, simply by tweaking the cosmological parameters like the matter density.  In fact here's one which is closed (total density greater than critical density), but with an (unnatural) component of energy which behaves like radiation (photons), in that the energy density decreases with the size of the universe to the 4th power, but are gravitationally repulsive, so that they turn the Big Crunch into a bounce. :)  I also added a negative (attractive) dark energy so that the turnaround from expansion to collapse happens more quickly.

Image

The parameter 'w' is especially fun to play with, as it defines how the energy density of dark energy depends on the size of the universe (w=-1 means it does not dillute, unlike matter and radiation, while w<-1 means it gets even stronger as the universe expands and can eventually result in a Big Rip).
 
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23 Oct 2018 19:26

More questions arise with every answer, but out of all scenarios what is the soonest and latest the universe would end? And how could the Big Rip happen without the heat death of the universe happening first?

Also the other day I was politely reminded that during the first few hundred thousand years of the universe there were no atoms, but as far as I recall the most distant objects we see (quasar) are populated with supermassive black holes containing the mass of billions of stars. Is the light we see from these objects showing them as younger than they truly are now, meaning we are seeing objects that couldn't possibly exist? There simply wasn't enough matter to create these supermassive black holes, much less Stars of normal Mass at such a young age in the universe.

And lastly, during the first Planck second of the universe, microscopic primordial black holes where the rage in fashion. Could these have become the protons that make up the matter we see today? Or the BH in quasar or are those completely unrelated things?

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23 Oct 2018 20:11

Watsisname wrote:
Source of the post as in writing my own Python code which solves the Friedmann equations for a universe containing any abundance of matter, radiation

What machine did you use to implement this code? I recall that PCs are generally not the weapon of choice for lots of operations like these.
 
Anyway, very cool presentation.

Gnargenox wrote:
Source of the post Is the light we see from these objects showing them as younger than they truly are now, meaning we are seeing objects that couldn't possibly exist? There simply wasn't enough matter to create these supermassive black holes, much less Stars of normal Mass at such a young age in the universe.

These black-holes formed out of the first galaxies as a result of super-sonic solar winds in the early universe and the collapse of the so-called Dark Stars. These mysterious stars push the very edge of what we think is possible for a star to form out of, and are enigmatic in the extreme.
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23 Oct 2018 23:38

Stellarator wrote:
Source of the post What machine did you use to implement this code? I recall that PCs are generally not the weapon of choice for lots of operations like these.

My home desktop computer, which is not extraordinary in any way.  This works because what I am interested in is how the scale factor of the universe changes with time, which depends only on the average densities of the different forms of matter and energy in the universe, and not how they are distributed (because on large enough scales they are uniformly distributed).  So all I need to do is numerically iterate through the differential equations governing the expansion rate and how it changes, which is not terribly many computations per time step, and for which a home computer is perfectly well suited. :)

If I were instead interested in simulating the individual motions of a bunch of interacting particles in the universe over time (like the Millenium simulation, showing the evolution of galaxies and the cosmic web), then that would require a supercomputer, because modelling the interactions of a system of N particles requires close to N2 computations per time step.  For N in the millions or billions, that rapidly becomes impractical for a home computer.
 
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24 Oct 2018 00:17

Gnargenox wrote:
Source of the post More questions arise with every answer, but out of all scenarios what is the soonest and latest the universe would end? And how could the Big Rip happen without the heat death of the universe happening first?

Very fun questions that I will be delving deeply into soon.  So stay tuned. :)
Gnargenox wrote:
Source of the post There simply wasn't enough matter to create these supermassive black holes, much less Stars of normal Mass at such a young age in the universe.

There was plenty of matter available!  The density of matter then was even greater than it is today.  The hard question is how that matter got collapsed into supermassive black holes so quickly.  We often think of black holes being formed in the deaths of massive stars, but it is also possible for them to form directly by collapse of a sufficiently massive cloud of gas.  Or maybe the stars that formed the seed black holes just formed more quickly than we thought.  This is still an open question for research.

I think the "dark star" hypothesis for their formation is not very likely though, simply because of how dark matter behaves dynamically (it is very difficult for it to lose the necessary energy to collapse into something that small, because it does not radiate).  Some dark matter will inevitably be drawn into the black holes, of course, but it is not very much.  Dark matter is more important for understanding how the cosmic web structure formed so quickly.

Gnargenox wrote:
Source of the post Could these have become the protons that make up the matter we see today? Or the BH in quasar or are those completely unrelated things?

Black holes cannot turn into protons, and a black hole with the mass and charge of a proton would be nonphysical (too much electric charge per mass), in a similar way as a black hole with too much angular momentum per mass (spinning too fast).  Protons instead form from quarks meeting up shortly (less than millionths of a second) after the Big Bang.

It is possible that the period shortly after the Big Bang did also produce a lot of microscopic black holes (and this could also explain dark matter), but they have little to do (directly) with the supermassive black holes like those we see in quasars.
 
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24 Oct 2018 00:48

Watsisname wrote:
Source of the post I think the "dark star" hypothesis for their formation is not very likely though, simply because of how dark matter behaves

Black-holes aside, what do you think of this 'Dark Matter Star' theory? At first it seemed quite like another wild gap-filler for dark matter measurements, but the more I read about them, the more they made some sense to me, at least from a early,  pre-nucleosynthetical point of view. I do get it though - they are just a theory for now, what with their reaction-dependence on hypothetical neutralino particles.  
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24 Oct 2018 01:41

Stellarator wrote:
Source of the post Black-holes aside, what do you think of this 'Dark Matter Star' theory?

I think the physics behind it is good conceptually.  If there is enough dark matter annihilation in a virialized cloud of gas and dark matter to produce a lot of heat, then it can certainly influence the equilibrium of that cloud.  The hard questions for it lie in the details -- are enough dark matter particles really captured into such a bound system, and do they really annihilate enough to have this effect?

I think I would find it more convincing if there was a convergence of evidence to favor this model.  That could come from it being a single and natural way to explain some oddities in current observations.  Of course it's great and practically necessary to successfully predict future observations, but if that is all it does then I don't think it is as compelling.

Relativity earned its place as an established theory after many beautiful predictive successes (time dilation, lensing of light, gravitational waves, etc).  But if it had only made those predictions, and did not also naturally explain previous mysteries like the Michelson Morely experiment, or the precession of Mercury, then it would have been harder to take seriously before these other observations could be made.  The best models are those that predict things both old and new. :)
 
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25 Oct 2018 05:11

Cosmological Simulations


Introduction:

As promised, I am now ready to share some results of cosmological simulations I have run on the computer, which model the evolution of universes filled with different amounts of matter, radiation, and dark energy.  Creating such simulations is something I have wanted to do for a long time, and An'shur's question earlier provided the motivation to finally do it. :)


There is quite a bit to cover, so I'll break this up into spoilerized sections.  First, I'll review the equations and techniques for building a cosmological model.  Then I will present the standard Lambda-CDM model, which is currently the best model for observations.  We will see what the evolution of our universe looks like over time, and also encounter some surprises!


Then, to explore An'shur's question, I will flip things around and examine a model universe which started with a Big Bang, but contains much more matter -- enough to halt and reverse the expansion and eventually lead to a Big Crunch.  I will set the matter density so that after 13.8 billion years, this model universe is collapsing at negative 68km/s/Mpc -- the opposite of the expansion rate we observe in the real universe today.



Building a Cosmological Model

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Simulating the Lambda-CDM Universe

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A Collapsing Universe:
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