Question: We live in an expanding universe - so I'm told. But how can that be possible? Everything imaginable is attracted by a bigger thing. So, why can't gravitation stop the expansion of the universe? I know the "Big Bang" theory, but is it possible that the expansion of the universe is caused by the attraction of a bigger object?

Answer: 
Something the other answers don't really delve into is this: **Space itself is what's expanding**

Let's think about a regular Newtonian Spacetime with zero expansion, borrowing Jim's example of a car on the road. You're sitting completely still, as is a friend you're following on a roadtrip, with about a hundred feet of distance between you. If I move towards them at a few feet per second, then my distance is going to decrease at the same rate. I'll also be approaching another car a few hundred feet ahead of them at the same speed, because again none of us are moving.

Now, if we were in a classical, flat, non-expanding spacetime that's more or less what we'd see. Galaxies would gravitationally attract, and eventually (Meaning over a literally infinite timeframe) everything would re-merge.

This is where things get bizzare, and well outside the scope of our daily experience. We're not on a road as we know it, **The road itself is growing. Space itself is expanding.**

Imagine that, somehow, every 10 feet of road is growing an extra foot every second. If I were standing still, I'd see my friend move away from me at about 10 ft/s for the first second. A car 500 feet away would move away at 50 ft/s, and a car a mile away would rocket off at **over 500 ft/s** If I started moving towards my friend at 20 ft/s, I'd only see him getting closer at a rate of 10 ft/s, and the car a mile away would still be speeding into the distance faster than I could catch up to it.

This is where the idea of the Observable Universe comes from. There are points in space that we can never see, because they're "expanding" away from us faster than the speed of light.
Everything is measured with atoms (upon atomic properties) 

oooooo < these are atoms in the lab now  

|\_\_\_\_\_| This space at left is $\approx 5\ $ units long . 

**OOOOOO** < the very same atoms in the past 
 radiated at longer wavelengths (redshifted).  

|\_\_\_\_\_| This space at left is $\approx 3.5\ $ units long. 

Is it clear that any space expansion is an artifact of the measuring process ? 

If you do not beleive in your eyes and intuition please present one fundamental equation (from all physics) able to discriminante between the atoms version 1 and version 2 (besides the radiated light wavelengths as said above). 

For those that want to check the validity of, or deny, my viewpoint please comment the proof in this document "[A self-similar model of the Universe unveils the nature of dark energy](http://vixra.org/pdf/1107.0016v1.pdf)". 

In physics there is no mention to any *absolute or invariant* size of the particles. This absolute notion was never questioned before and is an hidden postulate of the standard Model. 

Because the "oos/OOs" is not clear enough here is the balloon analogy: 

[![matter shrinking](https://i.stack.imgur.com/y5w0n.jpg)](https://i.stack.imgur.com/y5w0n.jpg)

Explaining "more field" in ligth blue in the 'present' balloon:  

The light cone of the fields associated with the particles grows as time goes by. Thus, the overall energetic content of particles+field is constant thru time.  

The next ideas are not part of the Model because it is speculation:  

There are infinite events of matter creation, with CMB, in a cyclic way.  

The one versioned Universe of Standard Model, with a begining and an end, is phylosophically repugnant to my mind. I'm a rationalist and I fully respect the PSR-Principle of Sufficient Reason as Spinoza, ...Poincaré, and Einstein did.