Question

Does a charge appear to change magnitude in a non-flat expanding universe?

Answer 1

It is most probably a very basic question, but I'm a bit stuck with it. Let us consider a spatially flat Friedmann universe with the usual metric

ds2=dt2−a2(t)(dr2+r2dϑ2+r2sin2(ϑ)dφ2)

where dl2 is just the line element of the equal time hypersurface. Let us also consider a scalar quantum field Φ(x) living in the Friedmann spacetime,

Φ(x)=∫d3k(2π)3(a^kvk(t)e−ikx+a^†kv∗k(t)eikx)

where vk are the mode functions in the given case. Then, if x=(t,r⃗ (r,ϑ,φ)) is the four vector in comoving coordinates, k is the conjugate momentum which I would understand as the comoving momentum.

Answer 2

Use Given Formulae(s)

1. E→=q4πϵ0R2sin2(χ)χ^

1. E→=q4πϵ0R2sin2(χ)χ^2. E→R(d0)=q4πϵ0R2sin2(d0R)χ^