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How long does it take for expanding space to double in size

According to the standard concordence model, I heard that it's likely that space is doubled after 11.4 billion years. Am I right? Then, how fast (<-acceleration) is this happening? (By speed, I mean distance/time)

Also, is space being doubled based on observation data? Thanks.

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marked as duplicate by Qmechanic, Raskolnikov, Manishearth Dec 11 '12 at 11:39

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If the doubling time is constant, and it will only be constant once the Universe is totally dominated by the cosmological constant (today the CC is just 73% of the energy density so we're close but not yet there), then it means that the distance between a pair of galaxies goes like $L=L_0 \cdot 2^{t/t_0}$ where $t_0$ is the time from the moment when the distance was $L_0$ and $t_0$ is those 11.4 billion years. The speed between them goes like $v_0\cdot 2^{ t/t_0}$, exponentially growing, too. You can't quote any "universal value of the speed" here. According to Hubble's law, the speed is proportional to the distance between the galaxies. This distance will keep on exponentially increasing with time which is why the speed will be doing the same thing. The coefficient $H$ of the Hubble law $v=Hd$ is variable but as the Universe is increasingly more dominated by the cosmological constant, $H$ will approach a constant (proportional to the cosmological constant), too.

Normal people would write the exponents as powers of $e$, not $2$, by rewriting $2^x$ as $\exp (x\cdot \ln 2)$ where $\ln 2=0.693$ would convert the factor $1/11.4$ billion years to the (inverse) $e$-folding time, $1/16.4$ billion years after which the distances jump by the factor of $e=2.718$. So the power of two would be replaced by $\exp(t/t_1)$ where $t_1$ is $16.4$ billion years.

Otherwise the claim that it's exponential may be derived from a special "simplified form" of Einstein's equations of general relativity, the FRW equations, and these equations were found to agree with the observations in the last 13.7 billion years when not only the CC but also matter density and radiation played role for the evolution of the universe's shape. So the expansion wasn't quite exponential - but its shape agreed with the predictions of the theory that also predicts that the expansion will be ever closer to the exponential one in the future.

The visible and dark matter combined represent about 27 percent of the energy density today. However, in 11.4 billion years or so from now (it may be 9 billion years because the matter perturbs things these days), the linear distances will double, the volumes will be multiplied by 8, and the percentage of the dark and visible matter will drop about 8 times well, to 3 percent. When the Universe is 25 billion years old or so, the dark energy will be 97% of the energy density. These are approximate estimates. One could give you the precise equations, too.

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