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

1. Aug 18, 2010

### 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

2. Aug 18, 2010

### 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.

3. Aug 18, 2010

### 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....

4. Aug 18, 2010

### atyy

Smartphones are not asymptotically safe.

5. Aug 18, 2010

### MTd2

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

6. Aug 18, 2010

### MTd2

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.

Last edited: Aug 18, 2010