The Cosmic Heart

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The Cosmic Heart

Postby BurtJordaan on October 17th, 2019, 1:25 am 

After a very brief discussion of the "cosmic teardrop" in the closed thread, I thought might be interesting to show some different representations of the same physical model (LCDM) by just changing the projection and/or the scale of the picture. To refresh memories, here is the cosmic teardrop from that thread (actually looking rather more like a streamlined air-to-ground bomb than a teardrop, which such a weapon may surely be the cause of).

Image

Recall that the scale of the picture was arbitrarily chosen as 100a, where a=1, the traditional scale factor at the present time, because one could show the changing time scale clearly in the form of the differences in separation between the 'two-gigayear-rings'. If one would re-scale the radius to the distance that light could have traveled in the age of the universe, 13.7 Gly in Minkowski coordinates (remember that the scale of the radius is arbitrary), we get this interesting picture

Image

where only a portion if the circle is shown. I don't know how to make the text flow around this smaller picture in this forum's editor, like it was on the forum where I originally posted it a decade ago. You might agree that it resembles the title of this thread, "The Cosmic Heart" rather well.

The shape of the heart is not arbitrary once the scale has been fixed (which now is essentially just the observable universe). We can make photons move along the (shrinking) circle in both ways. For every time-step Δt, photons move an angle cΔt/R around the origin, while R reduces by dR/dt every step, following the Friedmann equations. In this way we can "wind" the photons back until they reach the origin, essentially the CMB, where photons were first released to travel freely. Adding all the Δt's will yield the 13.7 billion years, roughly the age of the universe - yes it is as simple as that. :-)

The curvature of the circumference is obviously highly exaggerated, because the actual universe is very, very close to as flat as a tabletop. If we draw it as flat it should be, we get this beautiful teardrop. It represents the same data, just drawn on a flat graph (essentially Cartesian coordinates instead of polar). Since we do not have to bother about the scale factor here, time can now be shown on a proper time axis,

Image

This is exactly the light cone of Tamara Davis's top panel in this figure that I posted before, from her "Expanding Confusion" mainstream paper, scaled slightly differently.

Image

It is important to understand that all the pictures in this post represent exactly the same cosmological model (LCDM) and for the same cosmological parameters - just presented in different coordinate systems. Coordinate system choices do not influence physics, they just make it more presentable and more understandable (well mostly...). They may also portray human emotions like fear of bombs, romantic hearts and teardrops (of joy or sadness). Someone may care to write a few poems about them...

Comments and questions are welcome, but please limit it to discussion of the mainstream cosmic model and not some private one. As I've just done, a sprinkle of philosophy or art will do no harm. ;-)
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Re: The Cosmic Heart

Postby davidm on October 17th, 2019, 2:21 pm 

Thanks for the link to the Expanding Confusion article. I had been a bit flummoxed about this myself, and then I saw the light, so to speak, and made a post at this forum, I believe more than a year ago, in which I talked about how we can observe objects that are receding superluminally. Superluminal expansion also does not violate SR. Very interesting stuff. Maybe I’ll even try to work up a poem. :-)
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Re: The Cosmic Heart

Postby BurtJordaan on October 18th, 2019, 12:04 pm 

BurtJordaan » 17 Oct 2019, 07:25 wrote: If one would re-scale the radius to the distance that light could have traveled in the age of the universe, 13.7 Gly in Minkowski coordinates (remember that the scale of the radius is arbitrary), we get this interesting picture

Image


How can it be that the scale of the radius is arbitrary? Isn't it supposed to reflect the spatial radius of curvature of the universe? The answer is "not at all". Irrespective of whether the universe is spatially flat, like we think it is, the evolution of spatial curvature cannot follow this picture. Why? Because spatial curvature, if it is not exactly zero, evolves away from zero, not towards it. The "curved space" in the picture is just a consequence of the polar coordinate system chosen.

The reason why the spatial curvature of the cosmos evolves away from zero is slightly technical, but it can be loosely explained as follows. Spatial curvature at any specific cosmic time works similarly to escape velocity from a massive body. Escape velocity requires the kinetic energy of the speeding object to precisely balance its potential energy at the distance from the body. If the speed is just slightly below that balance, the object will eventually fall back to the massive one. This means that unless the object's speed is exactly right, it evolves away from escape speed. The same happens it it is just slightly too high.

Since the expansion dynamics is a balance between energy densities, it follows the same principle.

Clear as mud? Don't worry, it took me a long time to get my head around this too. ;-)
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