The Barbero-Immirzi Parameter as a Scalar Field: K-Inflation from Loop Quantum Gravity?

TL;DR

This paper explores a loop-quantum gravity inspired modification of general relativity where the Barbero-Immirzi parameter becomes a scalar field, potentially driving k-inflation through its kinetic energy.

Contribution

It introduces a dynamic BI scalar field into the Holst action, linking loop quantum gravity concepts with cosmological inflation models.

Findings

The modified theory maintains general relativity solutions for constant BI field.

Time-varying BI field behaves like a pressureless perfect fluid in cosmology.

Potential for natural k-inflation driven by BI field's kinetic energy.

Abstract

We consider a loop-quantum gravity inspired modification of general relativity, where the Holst action is generalized by making the Barbero-Immirzi (BI) parameter a scalar field, whose value could be dynamically determined. The modified theory leads to a non-zero torsion tensor that corrects the field equations through quadratic first-derivatives of the BI field. Such a correction is equivalent to general relativity in the presence of a scalar field with non-trivial kinetic energy. This stress-energy of this field is automatically covariantly conserved by its own dynamical equations of motion, thus satisfying the strong equivalence principle. Every general relativistic solution remains a solution to the modified theory for any constant value of the BI field. For arbitrary time-varying BI fields, a study of cosmological solutions reduces the scalar field stress-energy to that of a pressureless perfect fluid in a comoving reference frame, forcing the scale factor dynamics to be equivalent to those of a stiff equation of state. Upon ultraviolet completion, this model could provide a natural mechanism for k-inflation, where the role of the inflaton is played by the BI field and inflation is driven by its non-trivial kinetic energy instead of a potential.