So you're now about 14 billion years into this.

The third law is also easily demonstrated.

But it's very useful for studies of galaxy evolution.

Water expands with heat.

And what does a warming atmosphere do?

Oxygen in your body will expand rapidly, rupturing your lungs.

Volume

Alan, look at this. ...the amount of blood distending your vessels, imperfections in the skin...

Good luck on the next test.

Our universe is expanding.

Her chewing muscles grow so vast

Hey, look, my stomach's distended!

Again, on complicated mi , mixtures of cosmological parameters.

Instead of blowing the balloon up like a party balloon, they use a giant flame to heat the air inside that envelope.

The other one is the nucleosynthesis of light elements.

You feel deep, deep guilt.

If epsilon is equal to minus 1.2, then the plus string is fixed in comoving coordinates.

The blowfish puffs up.

And we infuse that clay with an ingredient that we call leaven.

The permanent ice is marked in red.

I just showed you this picture.

Proper size is larger than the comoving size, because comoving coordinates have expanded since then and it's larger by exactly power of one z.

Let me try my best to draw this neatly.

Will the universe expand indefinitely?

Heat expands most things.

But Diemand et al shown in the following The simulation starts at the redshift of 12, a very low contrast.

We learned that it's accelerating.

Okay, he's got lines of distention... across the duodenum.

The test itself is a cheat, isn't it?

Well, they also tell us that the volume is 405.

So let's think about it.

And, if we go further say, beyond local supercluster, most of the velocities due to Hubble expansion.

So if I had a little cube here in the volume under consideration, that's a little cube you consider that dv.

So how do we figure out the volume under a surface like this?

In units, what are the dimensions of the box?

We can do it because in space there are no aerodynamics.

And this wastebasket part, that's to represent what the structure of space time itself is doing during this period.

So here we have the opposite scenario.

Gravity separated away from the other forces.

Since that power is less than one, the universe is decelerating.

And that seems pretty reasonable for our reality.

And that little cube has side length 2.

This is now known as the Hubble diagram and was immediate evidence for an expanding universe.

They are the same for photons and baryons in terms of number densities.

So dy, which is this. dy times dx, dx times dz.