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Read in several publications that the Universe during a very short time (inflation), increased its size by a factor of $10^{50}$. What does it mean to increase the size of $10^{50}$ if you do not specify, from what? If I go from 1 mm and the increase of $10^{50}$ I will have a final measure, for example if I go by the Planck length I'll have another ..

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In the standard model of cosmology, we say that the universe we live in is an FRW-universe. The FRW part just refers to the initials of the guys who first wrote down the description. The equation that describes such a universe is: $$ds^2=a(t)^2\left[-d\tau^2+d\vec x^2\right]$$ Note: this is for a flat, homogeneous, isotropic FRW-universe.

In the above equation, the $d\tau$ term is called the "conformal time" (it's a fancy name for basically the time coordinate) and the $d\vec x$ term is the co-moving spatial coordinates (again, fancy name for essentially distances). The factor out front is called the scale factor. We define the scale factor as $1$ today and $0$ at the time of the big bang. $a(t)$ times a co-moving distance gives you the distance that you would measure with a meter stick at that time (that's why it is $1$ today). But, you may be asking, why am I telling you all of this? When cosmologists say the universe is expanding, what we mean is that the $a(t)$ factor is increasing. When they say that during inflation the universe increased by a factor of $10^{50}$, they mean that the ratio between the initial scale factor and the final scale factor is,

$$\frac{a(t_\mathrm{end})}{a(t_\mathrm{init})}=10^{50}$$

where $t_\mathrm{end}$ is the time at the end of inflation and $t_\mathrm{init}$ is the time at the beginning of inflation. Essentially it just means that something that measured $1~\mathrm{m}$ at the beginning of inflation measured $10^{50}~\mathrm{m}$ at the end of inflation.

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  • $\begingroup$ What were the values of $a(t_{end})$ and $a(t_{init})$? What were the values of $t_{end}$ and $t_{init}$? $\endgroup$ – mmesser314 Apr 20 '14 at 1:42
  • $\begingroup$ @mmesser314 great question. I'll run some simulations in the morning and get back to you with estimates $\endgroup$ – Jim Apr 20 '14 at 2:05

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