# Why there is something rather than nothing (out of everything)?

## TL;DR

This paper explores a quantum cosmology model using path integrals over geometries, proposing a microcanonical ensemble that explains the universe's initial conditions, inflation, and dark energy within a unified framework involving complex saddle points and instantons.

## Contribution

It introduces a novel quantum cosmology approach using a microcanonical ensemble and complex instantons to explain inflation and dark energy, constraining string vacua.

## Key findings

- The path integral describes a microcanonical ensemble in quantum cosmology.
- Cosmological instantons are limited to a bounded range of the cosmological constant.
- Inflationary cosmologies from these instantons can undergo late-time acceleration.

## Abstract

The path integral over Euclidean geometries for the recently suggested density matrix of the Universe is shown to describe a microcanonical ensemble in quantum cosmology. This ensemble corresponds to a uniform (weight one) distribution in phase space of true physical variables, but in terms of the observable spacetime geometry it is peaked about complex saddle-points of the {\em Lorentzian} path integral. They are represented by the recently obtained cosmological instantons limited to a bounded range of the cosmological constant. Inflationary cosmologies generated by these instantons at late stages of expansion undergo acceleration whose low-energy scale can be attained within the concept of dynamically evolving extra dimensions. Thus, together with the bounded range of the early cosmological constant, this cosmological ensemble suggests the mechanism of constraining the landscape of string vacua and, simultaneously, a possible solution to the dark energy problem in the form of the quasi-equilibrium decay of the microcanonical state of the Universe.