Undergrad Cosmology: Inertial Reference Frames & Misconceptions

[Arman777]

I was reading an article about the misconceptions in cosmological horizons and I wanted to clarify an idea.

https://arxiv.org/abs/astro-ph/0310808

In cosmological perspective, is there a global inertial reference frame (maybe CMB) ? Or all inertial frames are defined locally and there is no global inertial one ?

Is this is the one of the reasons why observing superluminal objects does not violate SR ?

 

[PeterDonis]

In cosmological perspective, is there a global inertial reference frame

No.

all inertial frames are defined locally and there is no global inertial one ?

This is true of any curved spacetime, including the one that describes our actual universe.

Is this is the one of the reasons why observing superluminal objects does not violate SR ?

"Violate SR" is a misnomer, since SR does not apply to curved spacetimes. "Superluminal objects" is also a misnomer (though unfortunately a common one), since coordinate speeds have no physical meaning (that's true even in flat spacetime, where SR applies).

A better way of describing what is going on is that, if we pick some distant galaxy that is commonly referred to as having "superluminal" velocity with respect to us, and look at the local region of spacetime around that galaxy, where SR applies, nothing is moving faster than light relative to anything else, and no massive object is moving faster than light rays going in the same direction. If we set up a local inertial frame centered on that distant galaxy, coordinate speeds in that frame of objects in that local region of spacetime will all be less than or equal to $c$ (and only the coordinate speeds of light rays will be equal to $c$), just as we expect in SR. But there will be no way to extend that inertial frame to cover more than that local region.

 

[Arman777]

Thanks a lot