I Fulvio Melia's new argument for a linear cosmology

[jcap]

I would be interested in what people think of Fulvio Melia's new cosmological paper in which he argues that the comoving frame is locally inertial only if we have a linearly expanding Universe (or Minkowski spacetime):

https://www.researchgate.net/publication/336827324_The_lapse_function_in_Friedmann-Lemaitre-Robertson-Walker_cosmologies

 

[kimbyd]

I would be interested in what people think of Fulvio Melia's new cosmological paper in which he argues that the comoving frame is locally inertial only if we have a linearly expanding Universe (or Minkowski spacetime):

https://www.researchgate.net/publication/336827324_The_lapse_function_in_Friedmann-Lemaitre-Robertson-Walker_cosmologies

On its face, his conclusion seems absurd. He's claiming that a co-moving observer is a non-inertial observer. I'm really not sure how that's supposed to work. I would tend to think there's some subtle error in his math, but I'm not completely sure what it is.

Edit: I suspect it may have something to do with the derivation of eqn. (7). In deriving this, they perform two integrals, leading to two constants of integration (which may be functions of (r)). They then claim that they can choose g(r) to be zero, and that f(r) is irrelevant. My bet is that this isn't valid, though I haven't worked through the details to be sure.

 

[Orodruin]

Is there a more reliable reference than Research Gate?

 

[Vanadium 50]

Is there a more reliable reference than Research Gate?

Annals of Physics 411:167997 · October 2019 

 

[Dale]

Hmm, I am not following the argument. Changing the lapse function is just a coordinate transform, so it cannot possibly be inpermissible unless the resulting mapping is not smooth and invertable

 

[PAllen]

I think the whole argument is nonsense. It is easy to derive that comoving world lines are geodesics in any FLRW solution, whether using standard coordinates (the ones setting g-tt to 1, which the paper criticizes) or any other coordinates. If the comoving observers are following geodesics, they are ipso facto in free fall, as is any local frame attached to them.

 

[Dale]

It is easy to derive that comoving world lines are geodesics in any FLRW solution, whether using standard coordinates (the ones setting g-tt to 1, which the paper criticizes) or any other coordinates

Agreed.

I could see that some FLRW time coordinates might not be affine parameters for the comoving geodesics, but does that even matter? The foliation is the same.

 

[Orodruin]

Honestly, after looking at it, it is based on serious misconceptions. I would expect the better of my students taking GR for the first time to do better and to spot the errors in that "paper".

Now, it is easy to show that comoving coordinates are not going to be locally inertial (in fact, I did so in an Insight), but that in no way implies that comoving observers are not freely falling. Local normal coordinates are also generally valid only at one single event. There is no need that the frame should be parallel transported along with a free falling observer.

 

[PAllen]

Honestly, after looking at it, it is based on serious misconceptions. I would expect the better of my students taking GR for the first time to do better and to spot the errors in that "paper".

Now, it is easy to show that comoving coordinates are not going to be locally inertial (in fact, I did so in an Insight), but that in no way implies that comoving observers are not freely falling. Local normal coordinates are also generally valid only at one single event. There is no need that the frame should be parallel transported along with a free falling observer.

Though, with total generality, a local inertial frame can be Fermi-Walker transported along a geodesic - that is the basis of Fermi-Normal coordinates, which have Minkowski metric and vanishing connection all along origin world line (I leave aside more generalized Fermi-Normal coordinates for non-inertial and/or rotating observers).

 

[PeterDonis]

a local inertial frame can be Fermi-Walker transported along a geodesic - that is the basis of Fermi-Normal coordinates, which have Minkowski metric and vanishing connection all along origin world line

This is true, but Fermi normal coordinates centered on some particular comoving worldline in FRW spacetime are still not the same as standard FRW coordinates in which the spatial origin is placed at that worldline.

In fact, doing that comparison might be a good thing to ask the author of the paper to do.

 

[PAllen]

This is true, but Fermi normal coordinates centered on some particular comoving worldline in FRW spacetime are still not the same as standard FRW coordinates in which the spatial origin is placed at that worldline.

In fact, doing that comparison might be a good thing to ask the author of the paper to do.

I never implied they were. The comparison was in contrast to parallel transport, where @Orodruin made the point that the local inertial frame was not parallel transported along comoving geodesics. All I wanted to add was that it is Fermi walker transported.

 

[PeterDonis]

I never implied they were.

Yes, agreed, I was just thinking that confusing the two might be part of the author's misunderstanding.