[cowlinator (OP)]

Let's assume that the entire observable universe was moving through a larger space comprised of vacuum, and that the speed of the observable universe was 0.99 c in some direction. 

According to Galilean invariance, it should be impossible to ever determine whether or not this is true.
Even according to relativity, there would be time dilation, but uniformly throughout the universe, so the speed of the universe could not be detected that way.

But we know that light, no matter the speed of it's source, travels at a constant speed.
This would mean that if I shine a light into my eyes from one direction, it would be red-shifted, and from another direction, it would be blue shifted.  This would allow us to determine our own absolute velocity.
Since we know the velocity of other parts of the universe relative to us, we could then determine the absolute net velocity of the observable universe.

Now, couldn't we use this method to discover our own absolute velocity in real life, and thus the absolute net velocity of the observable universe, however slight it may be?

[PmbPhy]

Let's assume that the entire observable universe was moving through a larger space comprised of vacuum, and that the speed of the observable universe was 0.99 c in some direction. 

First, it's not meaningful for our universe to be moving through a larger space. Our universe is actually defined as all of space. Therefore nothing can exist outside of it nor can it be considered moving. And it's not possible for something to travel at the speed of light anyway.

But we know that light, no matter the speed of it's source, travels at a constant speed.

It's not merely constant, it's also invariant which means that it has the same value in all inertial frames of reference.

This would mean that if I shine a light into my eyes from one direction, it would be red-shifted, and from another direction, it would be blue shifted.  This would allow us to determine our own absolute velocity.

That's incorrect. While light is blue/red-shifted when observed in other frames the speed of light is still invariant.

[cowlinator (OP)]

First, it's not meaningful for our universe to be moving through a larger space. Our universe is actually defined as all of space. Therefore nothing can exist outside of it nor can it be considered moving. And it's not possible for something to travel at the speed of light anyway.

I'm not talking about the whole universe in relation to a larger space, I'm talking about the observable universe in relation to a larger space
We don't know what is beyond the observable universe, but we know that it is possible for things to travel from within the observable universe to outside of the observable universe.  There must be someplace for them to go.

And it should be theoretically possible for matter (in some form) to travel at 0.99 c, which is definitely not the same speed as 1.0 c.

It's not merely constant, it's also invariant which means that it has the same value in all inertial frames of reference.

While light is blue/red-shifted when observed in other frames the speed of light is still invariant.

Ah, I didn't realize that.  Thank you.

[cowlinator (OP)]

Just to clarify, so does this mean that an observer in our 0.99 c universe would not see a flashlight he's holding as dopler-shifted, but someone from a (relatively) stationary frame of reference would see the flashlight's color doper-shifted?

[PmbPhy]

I'm not talking about the whole universe in relation to a larger space, I'm talking about the observable universe in relation to a larger space.

Whoops. So you did. My bad.

We don't know what is beyond the observable universe, ...

We're talking about how nature is currently explained by physics, are we not? If so then general relativity holds that what is beyond the observable universe is just more space. What we don't know for certain is what's in that space.

And it should be theoretically possible for matter (in some form) to travel at 0.99 c, which is definitely not the same speed as 1.0 c.

Correct.

Ah, I didn't realize that.  Thank you.

You're most welcome.

Just to clarify, so does this mean that an observer in our 0.99 c universe would not see a flashlight he's holding as dopler-shifted, but someone from a (relatively) stationary frame of reference would see the flashlight's color doper-shifted?

Again, you're not using the term "universe" correctly so it's difficult to answer your question. You should speak of matter rather than "our .99 c universe" since that appears to be what you're referring to.

Also, the invariance of the speed of light only holds locally. Due to the expansion of the universe distant galaxies are actually moving away from ours faster than c.

[cowlinator (OP)]

Just to clarify, so does this mean that an observer in our 0.99 c universe would not see a flashlight he's holding as dopler-shifted, but someone from a (relatively) stationary frame of reference would see the flashlight's color doper-shifted?

Again, you're not using the term "universe" correctly so it's difficult to answer your question.

Whoops, so I did.  My bad.  I mean observable universe.

You should speak of matter rather than "our .99 c universe" since that appears to be what you're referring to.

Ok, so if a just a flashlight and observer were traveling at .99 c, the observer would not see the flashlight as dopler-shifted, but someone from a (relatively) stationary frame of reference would see the flashlight's color dopler-shifted?

Also, the invariance of the speed of light only holds locally. Due to the expansion of the universe distant galaxies are actually moving away from ours faster than c.

But doesn't the expansion of the universe only affect the relative velocity of distant galaxies, and not the speed of light itself?
Does expansion directly affect the speed of EM waves?  And even if it did, my meter stick would expand also, so I would measure the speed of light traveling from distant galaxies to here as still being c.