Spontaneous Creation of the Universe from Nothing via Wheeler-DeWitt Equation

Jul 6, 2026

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A rigorous proof is presented for how the early universe can arise spontaneously from “nothing” using analytic solutions of the Wheeler–DeWitt equation in a minisuperspace model for a true vacuum bubble. For specific operator orderings (p = −2 or 4), a small bubble created by quantum fluctuations of a metastable false vacuum expands exponentially regardless of spatial curvature. The de Broglie–Bohm quantum trajectory framework shows that the quantum potential acts as an effective cosmological constant, driving the expansion until the bubble becomes large.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages5

Reading Time13 min

Introduction

WDWE for the Simplest Minisuperspace Model

Quantum Trajectory from WDWE

Spontaneous creation of the universe from nothing arXiv : 1404 . 1207v1 [gr-qc] 4 Apr 2014 Dongshan He, 1, 2 Dongfeng Gao, 1 and Qing-yu Cai 1, ∗ 1 State Key Laboratory of Magnetic Resonances and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, China 2 Graduate University of the Chinese Academy of Sciences, Beijing 100049, China An interesting idea is that the universe could be spontaneously created from nothing, but no rigorous proof has been given. In this paper, we present such a proof based on the analytic solutions of the Wheeler-DeWitt equation (WDWE) . Explicit solutions of the WDWE for the special operator ordering factor p = −2 (or 4) show that, once a small true vacuum bubble is created by quantum 􀀍uctuations of the metastable false vacuum, it can expand exponentially no matter whether the bubble is closed, 􀀍at or open. The exponential expansion will end when the bubble becomes large and thus the early universe appears. With the de Broglie-Bohm quantum trajectory theory, we show explicitly that it is the quantum potential that plays the role of the cosmological constant and provides the power for the exponential expansion of the true vacuum bubble. So it is clear that the birth of the early universe completely depends on the quantum nature of the theory. PACS numbers: 98.80.Cq, 98.80.Qc I. INTRODUCTION With the lambda-cold dark matter (􀀃CDM) model and all available observations (cosmic microwave background, abundance of light elements), it has been widely accepted that the universe was created in a big bang. However, there are still some puzzles, such as problems of the 􀀍atness, the horizon, the monopole, and the singularity [1] . Quantum mechanics has been applied to cosmology to study the formation of the universe and its early evolution. In particular, in􀀍ation theories, which suggest that the universe experienced an exponential expansion period, were proposed to solve puzzles of the early universe [2–4] . In quantum cosmology theory, the universe is described by a wave function rather than the classical spacetime. The wave function of the universe should satisfy the Wheeler-DeWitt equation (WDWE) [5] . With the development of quantum cosmology theory, it has been suggested that the universe can be created spontaneously from nothing, where “nothing” means there is neither matter nor space or time [6], and the problem of singularity can be avoided naturally. Although the picture of the universe created spontaneously from nothing has emerged for a long time, a rigorous mathematical foundation for such a picture is still missing. According to Heisenberg’s uncertainty principle, a small empty space, also called a small true vacuum bubble, can be created probabilistically by quantum 􀀍uctuations of the metastable false vacuum. But if the small bubble cannot expand rapidly, it will disappear soon due to quantum 􀀍uctuations. In this case, the early universe would disappear before it grows up. On the other side, if the small bubble expands rapidly to a large enough size, the universe can then be created irreversibly. In this paper, we obtain analytic solutions of the 􀀃 Corresponding author. Electronic address: [qycai@wipm.ac](qycai@wipm.ac).cn WDWE of the true vacuum bubble. With the de BroglieBohm quantum trajectory theory, we prove that once a small true vacuum bubble is created, it has the chance to expand exponentially when it is very small, i. e. , a ≪ 1. The exponential expansion will end when the true vacuum bubble becomes very large, i. e. , a ≫ 1. It is the quantum potential of the small true vacuum bubble that plays the role of the cosmological constant and provides the power for its exponential expansion. This explicitly shows that the universe can be created spontaneously by virtue of a quantum mechanism. II. WDWE FOR THE SIMPLEST MINISUPERSPACE MODEL Heisenberg’s uncertainty principle indicates that a small true v

FAQs

What problem does the paper address about “spontaneous creation from nothing”?

It addresses the lack of a rigorous mathematical foundation showing how a universe could emerge from a state with neither matter nor space-time, resolving whether the small vacuum bubble can grow rather than disappear.

How are analytic solutions obtained in the paper?

Analytic solutions of the Wheeler–DeWitt equation are derived within a minisuperspace description where the bubble radius is the single degree of freedom.

What determines the exponential expansion of the true vacuum bubble?

Using the de Broglie–Bohm quantum trajectory theory, the paper shows that the quantum potential functions as an effective cosmological constant and provides the power for exponential expansion.

Jul 6, 2026

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