Frame Dependence in Scalar-tensor Theory

TL;DR

This paper investigates how the choice of frame in scalar-tensor theories affects the geometric and physical properties, highlighting differences between Jordan and Einstein frames through theoretical analysis and application to cosmology.

Contribution

It clarifies the relationship between Jordan and Einstein frames, showing how frame choice influences the connection, equations, and conservation laws in scalar-tensor theories.

Findings

Jordan frame contains more geometric information than Einstein frame.

Transforming to Einstein frame simplifies field equations and stress conservation.

Application to Robertson-Walker spacetime illustrates differences in cosmological models.

Abstract

Palatini variation of Jordan frame lagrangians gives an equation relating the dilaton to the object of non-metricity and hence the existence of the dilaton implies that the spacetime connection is more general than that given soley by the Christoffel symbol of general relativity. Transferring from Jordan to Einstein frame, which connection, lagrangian, field equations and stress conservation equations occur are discussed: it is found that the Jordan frame has more information, this can be expressed in several ways, the simplest is that the extra information corresponds to the function multiplying the Ricci scalar in the action. The Einstein frame has the advantages that stress conservation implies no currents and that the field equations are easier to work with. This is illustrated by application to Robertson-Walker spacetime.