Inflation of small true vacuum bubble by quantization of Einstein-Hilbert action

TL;DR

This paper investigates how quantizing the Einstein-Hilbert action for a small vacuum bubble leads to exponential expansion similar to inflation, with quantum potential acting as the inflation-driving scalar field, and explores particle creation during this process.

Contribution

It introduces a novel approach where quantum potential from quantization induces inflationary expansion in vacuum bubbles, providing a new perspective on early universe inflation.

Findings

Quantum potential causes exponential expansion of small vacuum bubbles.

Expansion persists for about a Planck time, ending spontaneously as the bubble grows.

Particle creation during inflation can reheat the universe.

Abstract

We study the quantization of the Einstein-Hilbert action for a small true vacuum bubble without matter or scalar field. The quantization of action induces an extra term of potential called quantum potential in Hamilton-Jacobi equation, which gives expanding solutions including the exponential expansion solutions of the scalar factor $a$ for the bubble. We show that exponential expansion of the bubble continues with a short period (about a Planck time $t_p$), no matter whether the bubble is closed, flat or open. The exponential expansion ends spontaneously when the bubble becomes large, i.e., the scalar factor $a$ of the bubble approaches a Planck length $l_p$. We show that it is quantum potential of the small true vacuum bubble that plays the role of the scalar field potential suggested in the slow-roll inflation model. With the picture of quantum tunneling, we calculate particle creation rate during inflation, which shows that particles created by inflation have the capability of reheating the universe.