Should a radiation-filled Universe be scale invariant?
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Imagine a spatially flat Universe, without cosmological constant, filled only with EM radiation.
As Maxwell's equations without charges or currents are scale invariant then should this Universe be scale invariant as a whole? i.e. should there be no length scale associated with such a Universe?
Friedmann's equation for such a Universe is conventionally given by:
(a˙a)2∝1a4(a˙a)2∝1a4
The solution is:
a(t)=t1/2t1/20a(t)=t1/2t01/2
where t0t0 is the current age of the Universe.
Now let us calculate the particle horizon distance DD given by:
D=∫t00dta(t)D=∫0t0dta(t)
We find that:
D=2t0D=2t0
Therefore conventional theory says there is a length scale associated with this Universe.
But is that reasonable?
PS If for some reason we had ρ∝1/a2ρ∝1/a2 so that a(t)=t/t0a(t)=t/t0 then we could have a truly scale invariant cosmology where both the particle horizon and the cosmological event horizon diverge leaving no length scale.
As Maxwell's equations without charges or currents are scale invariant then should this Universe be scale invariant as a whole? i.e. should there be no length scale associated with such a Universe?
Friedmann's equation for such a Universe is conventionally given by:
(a˙a)2∝1a4(a˙a)2∝1a4
The solution is:
a(t)=t1/2t1/20a(t)=t1/2t01/2
where t0t0 is the current age of the Universe.
Now let us calculate the particle horizon distance DD given by:
D=∫t00dta(t)D=∫0t0dta(t)
We find that:
D=2t0D=2t0
Therefore conventional theory says there is a length scale associated with this Universe.
But is that reasonable?
PS If for some reason we had ρ∝1/a2ρ∝1/a2 so that a(t)=t/t0a(t)=t/t0 then we could have a truly scale invariant cosmology where both the particle horizon and the cosmological event horizon diverge leaving no length scale.
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There should be an almost scale-invariant spectrum of fluctuations. If quantum physics is real, then the Universe should have experienced quantum
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