1211.4279 (Hyeyoun Chung)

Measures for a Multidimensional Multiverse    [PDF]

Hyeyoun Chung

We explore the phenomenological consequences of generalizing the causal patch and scale factor cutoff measures to a multidimensional multiverse, where the vacua can have differing numbers of large dimensions. We consider a simple model in which the vacua are nucleated from a $D$-dimensional parent spacetime through dynamical compactification of the extra dimensions, and compute the geometric contribution to the probability distribution of observations within the multiverse for each measure. We then study how the shape of this probability distribution depends on the timescale for the existence of observers, the timescale for vacuum domination, and the timescale for curvature domination ($t_{obs}, t_{\Lambda},$ and $t_c$, respectively.) We find that in the case of the causal patch cutoff, when the bubble universes have $p+1$ large spatial dimensions with $p \geq 2$, the shape of the probability distribution is such that we obtain the coincidence of timescales $t_{obs} \sim t_{\Lambda} \sim t_c$. Moreover, the size of the cosmological constant is related to the size of the landscape. However, the exact shape of the probability distribution is different in the case $p = 2$, compared to $p \geq 3$. In the case of the fat geodesic measure, the result is even more robust: the shape of the probability distribution is the same for all $p \geq 2$, and we once again obtain the coincidence $t_{obs} \sim t_{\Lambda} \sim t_c$. These results require only very mild conditions on the prior probability of the distribution of vacua in the landscape.

View original: http://arxiv.org/abs/1211.4279