1201.5720 (Stefano Viaggiu)

The fractal bubble model with a cosmological constant    [PDF]

Stefano Viaggiu

We generalize the fractal bubble model (FB), recently proposed in the
literature as an alternative to the standard $\Lambda$CDM cosmology, to include
a non-zero cosmological constant. We retain the same volume partition of voids
and walls as the original FB model, and the same matching conditions for null
geodesics, but do not include effects associated with a nonuniform time flow
arising from differences of quasilocal gravitational energy that may arise in
the coarse-graining process. The Buchert equations are written and partially
integrated and the asymptotic behaviour of the solutions is given. For a
universe with $\Lambda=0$, as it is the case in the FB model, an initial void
fraction with hyperbolic curvature evolves in such a way that it asymptotically
fills completely our particle horizon. Conversely, in presence of a non
vanishing $\Lambda$, we show that this does not happen and the voids fill a
finite fraction $f_{v_{\infty}}<1$, where the value of $(1-f_{v_{\infty}})$ is
expected to depend on $\Lambda$ and the initial fraction $f_{vi}$ and also to
be small. For its determination, a numerical integration of the equations is
necessary. Finally, an interesting prediction of our model is a formula giving
a minimum allowed value of present day dark energy as a function of the age of
the universe and of the matter and curvature density parameters at our time.

View original: http://arxiv.org/abs/1201.5720