I don't like this solution.
But it's the standard way the luminosity distance is defined.
There is nowhere the speed of light to be seen there.
Units with c = 1 are used in the formulas.
OTOH, the "curvature of space" they mention, is not very necessary in our flat space.
Space alone is flat (within measurement uncertainties), but space-time is curved, because space expands with time.
But the Lorentz factor would be needed here.
It's not the easiest way to treat objects moving with the Hubble flow...
Not only for the time dilatation factor, by which the energy output is to be reduced - but also for the relativistic mass increase by the same factor.
Yes, there are two (1+z) factors, one because fewer photons are emitted per unit time because "time was slower back then" (I know, not a very clear way to put it) and one because each photon is redshifted. The luminosity distance is defined with one (1+z) factor so that when you divide by its square you get (1+z)^-2.
And for the length contraction as well!
No, because we're talking about the total luminosity of the galaxy -- if its length is contracted and its luminosity density is increased by the same factor, nothing changes.
That's the real problem, I think.
What do you mean? It's not like this is an open question in cosmology. The implications of the FLRW metric have been well known for decades.
Me: I don't like this solution.
GBP: But it's the standard way the luminosity distance is defined.
Still don't like it.
Me: There is nowhere the speed of light to be seen there.
GBP: Units with c = 1 are used in the formulas.
c = 1, but v isn't. Therefore the gamma factor is NOT a single exponential.
Me: OTOH, the "curvature of space" they mention, is not very necessary in our flat space.
GBP: Space alone is flat (within measurement uncertainties), but space-time is curved, because space expands with time.
At any moment, space has some size, a...
If it's worth saying, but not worth its own post, then it goes here.
Notes for future OT posters:
1. Please add the 'open_thread' tag.
2. Check if there is an active Open Thread before posting a new one. (Immediately before; refresh the list-of-threads page before posting.)
3. Open Threads should start on Monday, and end on Sunday.
4. Unflag the two options "Notify me of new top level comments on this article" and "