Spontaneously Induced Gravity: From Rippled Dark Matter to Einstein Corpuscles

TL;DR

This paper proposes a model where gravity is spontaneously induced via a scalar field, leading to observable ripples in cosmological evolution and novel dark core structures, with potential testable signatures.

Contribution

It introduces a spontaneous induction mechanism for gravity using a Brans-Dicke scalar, linking cosmological evolution and static solutions with new testable predictions.

Findings

Cosmological evolution mimics dark radiation, dark matter, and dark energy sequence.

Static solutions include a dark core with a varying Newton constant.

Predicted gravitational corpuscles become point-like in the GR limit.

Abstract

Suppose General Relativity, provocatively governed by a dimensional coupling constant, is a spontaneously induced theory of Gravity. Invoking Zee's mechanism, we represent the reciprocal Newton constant by a Brans Dicke scalar field, and let it damped oscillating towards its General Relativistic VEV. The corresponding cosmological evolution, in the Jordan frame, averagely resembles the familiar dark radiation -> dark matter -> dark energy domination sequence. The fingerprints of the theory are fine ripples, hopefully testable, in the FRW scale factor; they die away at the strict General Relativity limit. Also derived is the spherically symmetric static configuration associated with spontaneously induced General Relativity. At the stiff scalar potential limit, the exterior Schwarzschild solution is recovered. However, due to level crossing at the would have been horizon, it now connects with a novel dark core characterized by a locally varying Newton constant. The theory further predicts light Einstein-style gravitational corpuscles (elementary particles?) which become point-like at the GR-limit.