Quantum Gravity 154.7: Gravity Overtaken by Expansion Above a Certain Radius
- From: OsherD <mdoctorow@xxxxxxxxxxx>
- Date: Thu, 14 Jun 2007 10:36:03 -0700
From Osher Doctorow
Let's consider the equation motivated by the previous posts:
1) F_expansion = k/r^(1/2)
where r^(1/2) is of course sqrt(r) for r radius or principal radius or
similarly of the Universe (from some particular point), and where
F_expansion is the Expansion Force for inflation and/or the
Cosmological Constant, Chalyapin gas, Quintessence, etc.
Comparing this with the Newton Law of Universal Gravitation:
2) F_g = Gm1m2/r^2
we notice that:
3) F_expansion > F_g iff k/r^(1/2) > Gm1m2/r^2
and incorporating constant into k (or rewriting k ' = Gm1m2/k)) we
get:
4) 1/r^(1/2) > k ' /r^2 iff r^(3/2) > k ' iff r > (k ' )^(2/3) = k"
where k" is a constant defined as (k ' )^(2/3).
So below radius k", F_g > F_expansion, and below it F_expansion >
F_g.
We don't necessarily have to consider this equation as holding
throughout time for the Universe, and there may be extra terms or
factors for the constant or slower expansion phases preceding later
accelerations, but at least for the earliest Universe it expresses an
initial stronger phase of gravitation than of expansion followed at a
critical radius r" by the opposite. And at list piecewise or on
particular intervals, similar equations can hold for late acceleration
scenarios.
What about the usual idea that r increases at least exponentially
during Inflation? 1/r^(1/2) is closer to exponential than 1/r^2
above r = 1, so at least we're going arguably in the right direction.
Osher Doctorow
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