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Here's another Lc7z picture that can help us get familiar with the way the cosmos operates.
Recall from post #49 that the Hubble radius is an abstract length that helps us keep track of the expansion rate. It varies over time in a different manner from an ordinary cosmic-scale physical distance like the separation between two galaxies. In fact the Hubble radius is converging to a constant value: one light zeon. It is not expected to increase indefinitely.
The Hubble radius is currently 0.83 light zeon. And it is increasing at a speed which is a little less than half the speed of light, 0.4575 c to be precise. It is increasing not along with physical distances but in a way the reflects the declining rate H(x).
A physical distance like the separation between two galaxies, if it currently equals the Hubble radius in size and is therefore equal to 0.83 light zeon, would be increasing at speed c. That's by definition of the Hubble radius. It's the threshold size for superluminal expansion: At any given time it's supposed to tell us the size of distances which are growing at speed c.
What we see in this figure is the speed history of a sample physical distance which happens to coincide with the Hubble radius in size at one point in its existence, it is 0.83 lightzeon at the present era. This is the curve that swoops down to a minimum around time x = 0.44 and then rises back up.
The other curve is the scalefactor a(x) which shows exactly how distance grows over time (normalized to equal one at present, so multiply the distance's current size by the scale factor and you have it whole growth history.) This applies to physical distance, say between two galaxies, neither of which is moving significantly in the space around it. Such objects are said to be "comoving" or at rest with respect to the expansion process and the background of ancient light.
With regard to the speed history, notice that all other speed histories look the same just with different vertical scales. If a distance is twice the size of our sample one, its speed is scaled up by a factor of two, or if half the size, its speed is taken down by half. the minimum point always comes at the same place in history. Around 0.44 zeon.
You can find 0..44 zeon approximately by eye, on the graph. Go halfway between the 0.4 and the 0.6 mark, that would be 0.5, and then about half way between that and 0.4. That should be where the minimum of the speed curve comes, and also it should be where the inflection point of the scalefactor a(x) curve comes---that is, where the a(x) curve changes from convex upwards to concave.
You can see where there is a time period six tenths of a zeon long during which the sample curve is growing slower than the speed of light. Its speed dips below c around x = 0.2 zeon and finally gets back up to c right at the present x = 0.8 zeon.
EDITED after Jorrie's post #52, where he pointed out that the earlier version of this post wasn't clear enough about the difference between the Hubble radius and an ordinary expanding distance that just happens to coincide it at one point in time. This version is an attempt to avoid any possible confusion about that.
Recall from post #49 that the Hubble radius is an abstract length that helps us keep track of the expansion rate. It varies over time in a different manner from an ordinary cosmic-scale physical distance like the separation between two galaxies. In fact the Hubble radius is converging to a constant value: one light zeon. It is not expected to increase indefinitely.
The Hubble radius is currently 0.83 light zeon. And it is increasing at a speed which is a little less than half the speed of light, 0.4575 c to be precise. It is increasing not along with physical distances but in a way the reflects the declining rate H(x).
A physical distance like the separation between two galaxies, if it currently equals the Hubble radius in size and is therefore equal to 0.83 light zeon, would be increasing at speed c. That's by definition of the Hubble radius. It's the threshold size for superluminal expansion: At any given time it's supposed to tell us the size of distances which are growing at speed c.
What we see in this figure is the speed history of a sample physical distance which happens to coincide with the Hubble radius in size at one point in its existence, it is 0.83 lightzeon at the present era. This is the curve that swoops down to a minimum around time x = 0.44 and then rises back up.
The other curve is the scalefactor a(x) which shows exactly how distance grows over time (normalized to equal one at present, so multiply the distance's current size by the scale factor and you have it whole growth history.) This applies to physical distance, say between two galaxies, neither of which is moving significantly in the space around it. Such objects are said to be "comoving" or at rest with respect to the expansion process and the background of ancient light.
With regard to the speed history, notice that all other speed histories look the same just with different vertical scales. If a distance is twice the size of our sample one, its speed is scaled up by a factor of two, or if half the size, its speed is taken down by half. the minimum point always comes at the same place in history. Around 0.44 zeon.
You can find 0..44 zeon approximately by eye, on the graph. Go halfway between the 0.4 and the 0.6 mark, that would be 0.5, and then about half way between that and 0.4. That should be where the minimum of the speed curve comes, and also it should be where the inflection point of the scalefactor a(x) curve comes---that is, where the a(x) curve changes from convex upwards to concave.
You can see where there is a time period six tenths of a zeon long during which the sample curve is growing slower than the speed of light. Its speed dips below c around x = 0.2 zeon and finally gets back up to c right at the present x = 0.8 zeon.
EDITED after Jorrie's post #52, where he pointed out that the earlier version of this post wasn't clear enough about the difference between the Hubble radius and an ordinary expanding distance that just happens to coincide it at one point in time. This version is an attempt to avoid any possible confusion about that.
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