Barbero-Immirzi parameter as a scalar field:K-inflation from loop quantum gravity?

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.

Observational issues in loop quantum cosmology

“…Simulations [21,22,23] have shown that effective equations approximate very well the full quantum dynamics (in the sense of expectation values of Dirac observables). The effective Hamiltonian constraint is, for N=1 corresponding to cosmic time t,…”

Qualitative study in loop quantum cosmology

“…In particular, in [55] it was verified for ω = 1. Equation (19) corresponds to an ellipse in the plane (ρ, H), that we can parametrize in the following form…”

Erratum: Perturbations of Schwarzschild black holes in dynamical Chern-Simons modified gravity [Phys. Rev. D80, 064008 (2009)]

“…We studied only two limiting regimes: βM 4 ≫ 1 and βM 4 1. Before proceeding to the analysis of these two cases, we mention that, since Q, Θ exponentially diverge in the r * → ±∞ limits, it is not at all obvious that equations (17), (18) reduce to the form (19) and then that their solutions, in these limits, have the form (20), as we have assumed at the beginning of this section. Actually, Eq.…”