Let us consider five dimensional Kaluza-Klein metric which is given below
ds2 = -dt2 + R2(t)[{dr2/(1-kr2)}+ r2 d(theta)2+ r2sin2(theta)] + A2(t)d2(phi)
Here k, R(t) and A(t) are curvature constant, four dimensional scale factor and fifth dimensional scale factor respectively. $phi$ is fifth dimension. R(t) and A(t) have been obtained by solving Einstein field equations. Einstein field equations are derived from the following equation
Gij = Rij - 1/2 Rgij = -8(pi)GTij + (lambda)gij
where Rij is the Ricci tensor and R - Ricci scalar.
We also assumed 8(pi)G = c= 1 as per cosmic principle and A(t) = Rn(t).
R(t) is obtained as R(t) = [{2k/(n-1)}t2+C1t +C2]1/2
A(t) = [{2k/(n-1)}t2+C1t +C2]n/2
for compactification it is necessary to have negative value of n.
From above explanation is it possible to comment the variation of effective gravitational constant. I want to clear this point. As per my opinion compactification does not affect effective gravitational constant.
you are right .Compactification has nothing to do with gravitational constant
Sir, Thanks a lot for your answer.
Is it possible to have references which can provide an answer to my question? It will be quite helpful to clear my doubt.
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