Natural solution to the naturalness problem -- Universe does fine-tuning

Abstract

We propose a new mechanism to solve the fine-tuning problem. We start from a multi-local action $S={\sum }_i{c}_i{S}_i+{\sum }_{i,j}{c}_{i,j}{S}_i{S}_j+{\sum }_{i,j,k}{c}_{i,j,k}{S}_i{S}_j{S}_k+\cdots$, where $S_i$'s are ordinary local actions. Then, the partition function of this system is given by \begin{equation} Z=\int d\overrightarrow{\lambda} f(\overrightarrow{\lambda})\langle f|T\exp\left(-i\int_{0}^{+\infty}dt\hat{H}(\overrightarrow{\lambda};a_{cl}(t))\right)|i\rangle,\nonumber\end{equation} where $\overrightarrow{\lambda }$ represents the parameters of the system whose Hamiltonian is given by $\hat{H}(\overrightarrow{\lambda };a_{cl}(t))$, $a_{cl}(t)$ is the radius of the universe determined by the Friedman equation, and $f(\overrightarrow{\lambda })$, which is determined by $S$, is a smooth function of $\overrightarrow{\lambda }$. If a value of $\overrightarrow{\lambda }$, ${\overrightarrow{\lambda }}_0$, dominates in the integral, we can interpret that the parameters are dynamically tuned to ${\overrightarrow{\lambda }}_0$. We show that indeed it happens in some realistic systems. In particular, we consider the strong CP problem, multiple point criticality principle and cosmological constant problem. It is interesting that these different phenomena can be explained by one mechanism.

Comments: 21 pages, 4 figures