How to avoid singularities in AS Gravity? Find non perturbative inflation

[MTd2]

http://arxiv.org/abs/1008.2768

"To pursue our analysis further, we must determine more carefully the relationship between the renormalization scale µ and the density ρ. One appealing choice, advocated by Weinberg in his analysis of inflation in asymptotically safe gravity [3], is to take the renormalization group mass scale µ to be

µ ∼ [G(µ) ρ]^1/2 (3.8)

which has the appearance of the inverse of a “gravitational length” related to the energy density ρ andis equivalent to taking µ to be the inverse of the timescale over which the scale factor a(τ) changes."

One should treat G in a non perturbative way to avoid singularity.

So, it is like inflation counters a singularity, when gravitational collapse is treated non perturbatively

 

[Finbar]

Think your confused here a little. Inflation and gravitational collapse are two different physical phenomena. Here what they want to do is relate the RG scale $$\mu$$ to the density $$\rho$$ so they use the same relation Weinberg does in his paper(and has been used in other papers).

They then find that this doesn't remove the singularity and conclude that they need a different equation $$G(\mu)$$ in eq 3.5.
They don't however ask whether 3.8 is right or wrong (though it may be a logical choice)

Anyway by their own definition they don't have a non-perturbative formulation that removes the singularity.

 

[MTd2]

Yes, sure, they are different phenomena. And yes, I was a bit confused... Hmm, I guess this is because I read the paper on a smartphone with a very small screen...

 

[atyy]

Smartphones are not asymptotically safe.

 

[MTd2]

I wonder why didn't they put the mass renormalization scale depending on the cosmological constant.

 

[MTd2]

Anyway by their own definition they don't have a non-perturbative formulation that removes the singularity.

The whole FRGE method yields a parameter space which depends on 2 parameters, G and /\, with a UV point to where infinite coupling constants of gravity flow to. u is related to /\, and p to G. Notice that eq. 3.8, unless for constant G, is a non linear equation, whose approximate solutions should just work around the vicinity of parameters, yet the authors try to find a relation that should relate u and p through out the whole space.

They shouldn`t conclude that they do not have a non-perturbative formulation, because 3.9 is an example of one. The problem it is that they try to find one for the whole parameter space, which it will never work.