## Authors

Alireza Parizhkar

## Abstract

The vacuum catastrophe is a fundamental puzzle, where the observed scales of the cosmological constant are many orders of magnitude smaller than the natural scales expected in the theory. This work proposes a new ``bi-world'' construction that may offer an insight into the cosmological constant problem. The model generally includes a $(3+1)$-dimensional manifold with two different geometries and matter fields residing on them. The diffeomorphism invariance and causality highly constrain the two metrics to be conformally related, $\eta_{\mu \nu} = \phi^2 g_{\mu \nu}$. This reduces the theory to a standard single-world description, but introduces a new inherently geometrical ``moir{\'e} field,'' $\phi$. Interestingly, the moir{\'e} field has the character of both a dilaton and Higgs field familiar in the conventional theory. Integrating out the moir{\'e} field naturally gives rise to the Starobinsky action and inflationary dynamics. In the framework of the Friedmann-Lemaitre–Robertson–Walker solution, we reduce an effective action for the moir{\'e} field to that of a particle moving in a Mexican hat potential. The equations of motion are then solved numerically and the moir{\'e} field is shown to approach a Mexican-hat minimum in an oscillatory fashion, which is accompanied by the decay of the Hubble parameter. Under additional reasonable assumptions, the vacuum energy asymptotically approaches zero in the end of inflationary evolution. The physics presented here shares similarities with the moir{\'e} phenomena in condensed matter and elsewhere, where two similar structures superimposed upon give rise to a superstructure with low emergent energy scales compared to the native theories.