- #1
Apashanka
- 429
- 15
While studying the proper distance in cosmology I came across the thing as
The FRW metric
ds2=c2dt2-a(t)2[dr2+Sk(r)2dω2]
And Sk(r)=Rsin(r/R)
Where a(t) is the scale factor and dω2= dθ2+sin2θdΦ2,
While calculating the proper distance at the time of emmission of light the term ds and dω are taken zero and thus cdt=a(t)dr
And proper distance is taken to be ∫dr=c∫dt/a(t). The limit being from temmt. to tobserv
The explanation given is along spatial geodesic dω=0
Could someone please help me in sort out why dω and ds are taken 0 and proper distance being ∫dr.
Thanks
The FRW metric
ds2=c2dt2-a(t)2[dr2+Sk(r)2dω2]
And Sk(r)=Rsin(r/R)
Where a(t) is the scale factor and dω2= dθ2+sin2θdΦ2,
While calculating the proper distance at the time of emmission of light the term ds and dω are taken zero and thus cdt=a(t)dr
And proper distance is taken to be ∫dr=c∫dt/a(t). The limit being from temmt. to tobserv
The explanation given is along spatial geodesic dω=0
Could someone please help me in sort out why dω and ds are taken 0 and proper distance being ∫dr.
Thanks