Calculations in induced gravity from higher-derivative field theories

TL;DR

This paper explores how Einstein's gravity can emerge from higher-derivative scalar field theories, providing formulas for induced constants and demonstrating finiteness in certain infinite-derivative models.

Contribution

It introduces an effective multi-field approach to derive induced gravity from higher-derivative theories, including explicit expressions for induced constants in various dimensions.

Findings

Explicit formulas for induced cosmological and gravitational constants.

Finite induced constants can be obtained in specific infinite-derivative theories.

The approach applies to theories in arbitrary dimensions.

Abstract

In this paper, we investigate Einstein's gravity induced from higher-derivative scalar field theories. We develop an approach utilizing an effective theory of multiple fields for the higher-derivative theory. The expressions for induced cosmological constant and the induced gravitational constant are obtained in the present scenario of induced gravity in D dimensions. We also show that finite values for the induced constants can be extracted in certain infinite-derivative theories.