Recent content by hedgehug

Bad habit from programming. Me and everyone I worked with have been calling a variable divided by its maximum value normalized.

##a(t_{emit})/a(t_{rec})=1/(z+1)\le 1## for ##t_{emit}\le t_0## and ##t_{rec}>t_0## in the expanding universe.

I think you just need to have a last word. When I said that there has never been and there never will be other time for anyone, I meant the time when you are alive.

Physical, proper distances are equal after substituting Ly/1101 for NLy.

True. It's just a matter of the words used in the definition. Formula remains valid. Your explanations are correct. Just note that there was a Blushift in the title of the thread since the beginning.

##z## is no longer redshift if ##z+1<1##.

If the radiation was emitted at the time of the expansion reversal and observed during the collapse, then ##a_{rec}/a_{emit}<1##. How about ##1+z##?

@Ibix Note that I only really need ##a(t)/a(t_0)=1/(z+1)##, because ##t_0=t_{rec}## and ##t=t_{emit}##.

https://en.wikipedia.org/wiki/Scale_factor_(cosmology)#Detail Radiation emitted at the time of the expansion reversal and observed later during the collapse would be blueshifted, but this formula definition accounts only for the redshift. Does it mean that the FLRW metric is valid only for the...

There has never been and there will never be other time for anyone, assuming atheism :) And whenever you live, you simply must have ##a(t)/a(t_0)=1/(z+1)\le 1## for your ##t_0>t##. If I define ##A(t)=a(t)/a(t_0)## and use it instead of ##a(t)## and ##a(t_0)##, then it will be just like...

No. I regard the ratio ##a(t)/a(t_0)\le 1## as normalized. That's what must be normalized and that answers my question. Thank you @PeterDonis and @Ibix.

Correct. Thank you. Again, for the third time, this cancellation looks exactly like normalization to me. Again it's dividing and multiplying 1 by the same factor, in my case 1101.

Right. Proper distance is ##d(t)=a(t)\chi## where the comoving distance is ##\chi=\int_{0}^{t_0}cdt/a(t)##, so the proper distance equal to the observable universe radius should be ##d(t_0)=a(t_0)\int_{0}^{t_0}cdt/a(t)##, and in my case ##a(t_0)=1100+1##. Is ##d(t_0)=47\text{ GLy}##? If not...

Equal.

That's also my case with ##a_0=a(t_0)=1100+1## and ##a(t)/a_0=1/(z+1)\le 1##. The ratio ##a(t)/a_0## is normalized, because ##1/(z+1)\le 1##. Again in my opinion it's practically like normalizing the scale factor itself. This time even literally and explicitly.