How long until the universe can write a googolplex?

[Max7291]

Hi everyone, sorry to bother you with a really random question, and I hope I'm posting this in the right board, but here goes anyway...

The universe is currently too small in size to write out an entire googolplex. The visible universe is 4 x 10⁸⁰ m³ (according to the ever reliable Wikipedia, you may have some more accurate figures). The amount of books it'd take to write an entire googolplex would require 8.1 x 10⁹⁰ m³ of space, again according to Wiki
Assuming this data to be true and assuming that the universe is expanding at approximately 70 km s^-1 Mpc^-1, how long would it take before the universe is big enough to theoretically be able to write a googolplex?

You'll have to forgive me if any of that info's wrong and for the stupid question in the first place, but this is the kind of thing I think about at 2 in the morning

 

[Simon Bridge]

Welcome to PF;
You want to do things like define what you mean by the "volume of the Universe".
Once you know that you can make sense of figures about the expansion - you need the volume expansion of the Universe.

You still have an issue because all those books have to be made out of matter at some level and the volume of matter in the universe is much smaller than the volume of universe.

But it's basically a math problem.

 

[marcus]

The visible universe is 4 x 10⁸⁰ m³ (according to the ever reliable Wikipedia, ...would require 8.1 x 10⁹⁰ m³ ...

Setting aside the talk about filling the visible universe with books which are in turn filled with zeros, you are asking a simple question about volume increasing by a factor of about 2 x 10¹⁰.

that is, you are asking how long will it take for current volume of visible to become 20 billion times larger than it is today.

I'll tell you how long it will take (according to standard cosmic model that most cosmologists use) for volume to increase a MILLION fold. You can take it from there or some other folks will help. This will give you an idea.

Go here:
http://www.einsteins-theory-of-relativity-4engineers.com/LightCone7/LightCone.html

It says that now is year 13.8 billion and it says by year 92 billion distances will have increased 100-fold. That means VOLUMES will have increased 100 x 100 x 100 fold. A million-fold.
So that is a bit less than 80 billion years.

Now at that time, distance expansion will be locked into a steady percentage growth rate of 1/173 % per million years. So if you can calculate exponential growth at some fixed percent rate you can figure out how long going the rest of the way will take.

My guess is that another 60 billion years would do it, at that rate. So overall you are talking 80+60
or 140 billion years of expansion to increase current volumes by the factor you indicated namely multiply volumes by a factor of 20 billion.