# What is the No-Boundary Wave Function of the Universe?

## TL;DR

This paper defines a semiclassical no-boundary wave function of the universe without functional integrals, using saddle points satisfying regularity conditions, enabling probabilistic predictions consistent with observations.

## Contribution

It introduces a novel semiclassical framework for quantum cosmology that does not rely on functional integrals and incorporates saddle points satisfying regularity conditions.

## Key findings

- Provides a predictive semiclassical quantum cosmology framework
- Achieves agreement with observational data in simple models
- Discusses holographic approaches beyond semiclassical approximation

## Abstract

We specify the semiclassical no-boundary wave function of the universe without relying on a functional integral of any kind. The wave function is given as a sum of specific saddle points of the dynamical theory that satisfy conditions of regularity on geometry and field and which together yield a time neutral state that is normalizable in an appropriate inner product. This specifies a predictive framework of semiclassical quantum cosmology that is adequate to make probabilistic predictions, which are in agreement with observations in simple models. The use of holography to go beyond the semiclassical approximation is briefly discussed.