Ying-li Zhang, Misao Sasaki
We consider a model of non-local gravity with a large bare cosmological
constant, $\Lambda$, and study its cosmological solutions. The model is
characterized by a function $f(\psi)=f_0 e^{\alpha\psi}$ where
$\psi=\Box^{-1}R$ and $\alpha$ is a real dimensionless parameter. In the
absence of matter, we find an expanding universe solution $a\propto t^n$ with
$n<1$, that is, a universe with decelarated expansion without any fine-tuning
of the parameter. Thus the effect of the cosmological constant is effectively
shielded in this solution. It has been known that solutions in non-local
gravity often suffer from the existence of ghost modes. In the present case we
find the solution is ghost-free if $\alpha>\alpha_{cr}\approx0.17$. This is
quite a weak condition. We argue that the solution is stable against the
includion of matter fields. Thus our solution opens up new possibilities for
solution to the cosmological constant problem.
View original:
http://arxiv.org/abs/1108.2112
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