Question

Is our locally measured time actually conformal time?

Answer 1

The FRW metric at the origin r=0r=0, with c=1c=1, is given by:

ds2=−dt2+a(t)2dr2ds2=−dt2+a(t)2dr2

Now one can change variables so that near the origin the FRW metric is approximated by the Minkowski metric describing flat spacetime:

dS2=−dT2+dR2dS2=−dT2+dR2

where:

dT=dta(t)dT=dta(t)

dS=dsa(t)dS=dsa(t)

dR=drdR=dr

All the physics experiments that we perform locally are assumed to occur in flat spacetime as described above.

Surely therefore our locally measured time is not the cosmological time tt but rather the conformal time TT 

Answer 2

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✔️✔ therefore our locally measured time is not the cosmological time tt but rather the conformal time TT

Is our locally measured time actually conformal time

dS2=−dT2+dR2dS2=−dT2+dR2

where: dT=dta(t)dT=dta(t) dS=dsa(t)dS=dsa(t) dR=drdR=dr

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