# Accelerating Expansion of Cosmos: Measured in Multiple Directions?

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• exmarine
In summary, it is possible for the acceleration of the separation between galaxies to be positive, regardless of direction.

#### exmarine

Does anyone know if the accelerating expansion of the universe was measured in more than one direction? Unlike the expansion having no obvious center, it seems like the accelerating expansion would have to point to a “center”.

Our galaxy, for example, cannot be accelerating away from a supernova in one direction as well as another in the opposite direction.

Thanks.

exmarine said:
Our galaxy, for example, cannot be accelerating away from a supernova in one direction as well as another in the opposite direction.
This conclusion is wrong. It is perfectly possible.

Consider ants moving on an elastic band that stretches such that at time ##t## it has total length ##a(t)##. The ants may describe their positions in terms of their fractional position on the band, e.g., an ant at the mid point would say it is at ##x = 0.5##. The actual distance between two ants at ##x_1## and ##x_2##, respectively, is then ##a(t) |x_1 - x_2|##. Given that the ants remain at fixed ##x_i##, their relative separation speed is ##a'(t)|x_1 - x_2|## (which is the ant-universe equivalent of Hubble's law) and the acceleration of their relative separation is ##a''(t)|x_1 - x_2|##. Note that this is positive if ##a''(t) > 0## regardless of whether ##x_1 < x_2## or ##x_2 < x_1##.

Bandersnatch and Dale
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Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?

exmarine said:
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Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?
Why not! Say the middle one is standing still, and the other two are accelerating away from it, one to the left, one to the right.

exmarine said:
??
Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?

In Newtonian physics, the two end ants would have to accelerate away from the middle ant. In General Realtivity, all three ants can all be "at rest" (relative to the cosmological frame, the Cosmological Microwave Background frame), but due to the acceleration expansion of the universe, all three ants can and do accelerate away from each other.

The "baloon" analogy is often used to illustrate how this is possible - it's only an analogy, but it may be helpful. See for instance http://www.astro.ucla.edu/~wright/balloon0.html or try google.

exmarine said:
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Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?
You are entirely missing the point. The ants are not themselves accelerating relative to the elastic band. It is the growth of the elastic band that is accelerating and therefore the growth speed of the distance between the ants is increasing.

exmarine said:
Can you line up 3 ants in a row, and maintain that the middle one can accelerate away from both #1 and #3?
"Accelerate" in the context of space inflation means that the distances are increasing at an increasing rate. That is perfectly possible for 3 ants on a rubber band.

Orodruin said:
This conclusion is wrong. It is perfectly possible.

Consider ants moving on an elastic band that stretches such that at time ##t## it has total length ##a(t)##. The ants may describe their positions in terms of their fractional position on the band, e.g., an ant at the mid point would say it is at ##x = 0.5##. The actual distance between two ants at ##x_1## and ##x_2##, respectively, is then ##a(t) |x_1 - x_2|##. Given that the ants remain at fixed ##x_i##, their relative separation speed is ##a'(t)|x_1 - x_2|## (which is the ant-universe equivalent of Hubble's law) and the acceleration of their relative separation is ##a''(t)|x_1 - x_2|##. Note that this is positive if ##a''(t) > 0## regardless of whether ##x_1 < x_2## or ##x_2 < x_1##.

Oh I see what you are saying. The a(t) is the scale factor in the Friedman metric? Got it. Thanks very much.