I have been reading about Hubble\'s constant and trying to make \'sense\' of the

ID: 1324014 • Letter: I

Question

I've tried to work the math as follows:

Using the continuously compounding interest formula

So it would take 9 billion years for the distance between any two points in space to double in length?

Since the Universe is only about 15 billion years old and started from a singularity of volume 0,

I would have to assume that the rate of expansion of space isn't constant over time?

Does the time for the distance between two points to double in length vary based on the original distance between those to points?

I have been reading about Hubble's constant and trying to make 'sense' of the theory of the expanding Universe. Is is possible that space in the universe expands uniformly? If so, absent of other forces (ie gravity), how long does it take for the distance between any to dimensionless points in the universe to double in length? I've tried to work the math as follows: 2^3 = 8 8 so the time it would take for space itself to double in size would be t=1,141,768,813 yr Since the Universe is only about 15 billion years old and started from a singularity of volume 0, I would have to assume that the rate of expansion of space isn't constant over time? Does the time for the distance between two points to double in length vary based on the original distance between those to points? T = 9,134,150,511 yr So it would take 9 billion years for the distance between any two points in space to double in length? If this is so, when two points in 3D space double in distance apart, the space itself increased by Using the continuously compounding interest formula

Explanation / Answer

The way to answer your question is to take the Friedman equation and put in the components you want to. In the Standard Model of Cosmology you'd put in radiation, matter and lamdba. You then solve the equation for the scale factor a(t). (This can be automated with a program like Mathematica.) You'll get an explicit a(t) function that you can plot and see how the Universe expands.

A very nice pedagogical introduction is in Barbara Ryden's "Introduction to Cosmology", there's a PDF version online:

http://www.astro.caltech.edu/~george/ay21/readings/Ryden_IntroCosmo.pdf

Pg. 119 Figure 6.5 is just what you're looking for.

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I have been reading about Hubble\'s constant and trying to make \'sense\' of the

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