The Universe is expanding at a pretty significant rate to that of light speed if we look far enough. Does that mean that objects who experience such high speeds due to the Expansion relative to us come into the effects of the special theory of relativity? Or are speeds due to the Expansion excluded from Relativistic Effects?

In: 3

Yes and no, because your question is unclear to me.

The model of expansion of the universe includes general relativity, and general relativity includes special relativity, so relativistic effect are already in there.

However, special relativity is for *flat* spacetime (the Minkowski spacetime). In general relativity, you have to deal with curved spacetime and thus special relativity has a much more limited role: the usual special relativity effect only hold locally to 1st order approximation; because in a small area spacetime is approximately flat, up to 1st order. That is, if you consider object near you, special relativity almost hold, and the error is less than a constant times the square of the proper distance. The concept of the frame of reference also is different.

So when you look at the object far away, the error (if you try to apply special relativity naively) can be massive. In particular, it’s perfectly okay for object to have its distance from you increase at a speed larger than the speed of light.

In fact, it’s not impossible for objects to have speed larger than speed of light compared to some other object in general relativity. The theoretical Alcubierre drive allow a spaceship to travel faster than light by distorting spacetime (Wikipedia only talk about a version that require negative mass, but there are already other version that don’t need that).

The key thing to remember is that special relativity only hold up to 1st order locally. Or to put it in a different way, objects are only limited by speed of light when we are talking about its movement on the fabric of spacetime. Things can move faster than speed of light away from each other.

[removed]

What you are talking about is called **recessional velocity**. This is not the same thing as local velocity. Special relativity applies to objects moving THROUGH space. Universal expansion is the idea of literal distances between objects getting bigger. If two objects were at rest, that means they are not moving, however expansion declares the distance between them will grow. Again, no object is moving but literal space is simply being created between them.

There are objects whose recessional velocities are greater than 3c. Does this mean SR is wrong? No. It means SR applies to local velocity.

The principles of relativity and the fundamental laws governing motion, matter, gravity, and time are exactly the same everywhere and affect all objects and movement.