Fermions in loop quantum cosmology and the role of parity

Bojowald, Martin; Das, Rupam

doi:10.1088/0264-9381/25/19/195006

Cited by 28 publications

(42 citation statements)

References 64 publications

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“…The consideration of fermions in LQC has been limited to the study of a homogeneous and anisotropic model coupled to a homogeneous fermion field [54], where the focus was placed in the role played by parity. In this work we aim to analyzing a fermion field with local degrees of freedom in the context of hybrid LQC.…”

Section: Introductionmentioning

confidence: 99%

Fermions in hybrid loop quantum cosmology

2017

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This work pioneers the quantization of primordial fermion perturbations in hybrid Loop Quantum Cosmology (LQC). We consider a Dirac field coupled to a spatially flat, homogeneous, and isotropic cosmology, sourced by a scalar inflaton, and treat the Dirac field as a perturbation. We describe the inhomogeneities of this field in terms of creation and annihilation variables, chosen to admit a unitary evolution if the Dirac fermion were treated as a test field. Considering instead the full system, we truncate its action at quadratic perturbative order and construct a canonical formulation. In particular this implies that, in the global Hamiltonian constraint of the model, the contribution of the homogeneous sector is corrected with a quadratic perturbative term. We then adopt the hybrid LQC approach to quantize the full model, combining the loop representation of the homogeneous geometry with the Fock quantization of the inhomogeneities. We assume a Born-Oppenheimer ansatz for physical states and show how to obtain a Schrödinger equation for the quantum evolution of the perturbations, where the role of time is played by the homogeneous inflaton. We prove that the resulting quantum evolution of the Dirac field is indeed unitary, despite the fact that the underlying homogeneous geometry has been quantized as well. Remarkably, in such evolution, the fermion field couples to an infinite sequence of quantum moments of the homogeneous geometry. Moreover, the evolved Fock vacuum of our fermion perturbations is shown to be an exact solution of the Schrödinger equation. Finally, we discuss in detail the quantum backreaction that the fermion field introduces in the global Hamiltonian constraint. For completeness, our quantum study includes since the beginning (gauge-invariant) scalar and tensor perturbations, that were studied in previous works.

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Section: Introductionmentioning

confidence: 99%

Fermions in hybrid loop quantum cosmology

2017

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“…[13], the role of a parity violating 4-fermion self-interaction in a torsion-free theory has been studied. In this work, we propose both a nonminimal coupling of fermions (as analyzed in Refs [14][15][16]) and a topological gravitational term endowed with torsion (see for instance Ref. [17]).…”

Section: Introductionmentioning

confidence: 99%

Fermi-bounce cosmology and scale-invariant power spectrum

et al. 2014

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We develop a non-singular bouncing cosmology using a non-trivial coupling of general relativity to fermionic fields. The usual Big Bang singularity is avoided thanks to a negative energy density contribution from the fermions. Our theory is ghost-free since the fermionic operator that generates the bounce is equivalent to torsion, which has no kinetic terms. The physical system consists of standard general relativity plus a topological sector for gravity, and fermionic matter described by Dirac fields with a non-minimal coupling. We show that a scale invariant power-spectrum generated in the contracting phase can be recovered by suitable choices of fermion number density and bare mass, thus providing a possible alternative to the inflationary scenario.

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“…This fact has an interesting implication if we wish to describe the gravitational sector of the theory by using the Holst action, instead of the usual Hilbert-Palatini one. It turns out that in fact, in this more general case, the Holst modification no longer vanishes on-shell; consequently, the effective action differs from that of the Einstein-Cartan theory [17][18][19][20][21]. Specifically, the new effective action depends explicitly on the BI parameter, which, consequently, acquires a classical meaning [18].…”

Section: Introductionmentioning

confidence: 99%

Interaction of the Barbero-Immirzi field with matter and pseudoscalar perturbations

2009

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In loop quantum gravity the classical point of departure is the Einstein-Hilbert action modified by the addition of the so-called Holst term. Classically, this term does not affect the equations of motion, but it induces a well-known quantization ambiguity in the quantum theory, parametrized by the BarberoImmirzi parameter. Recently, it has been suggested to promote the Barbero-Immirzi parameter to a field. The resulting theory, obtainable starting from the usual Holst action, is general relativity coupled to a pseudoscalar field. However, this theory turns out to have an unconventional kinetic term for the BarberoImmirzi field and a rather unnatural coupling with fermions. The main goal of this work is twofold: First, to propose a further generalization of the Holst action, which yields a theory of gravity and matter with a more natural coupling to the Barbero-Immirzi field; second, to study the possible implications for cosmology correlated to the existence of this new pseudoscalar field.

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Fermions in loop quantum cosmology and the role of parity

Cited by 28 publications

References 64 publications

Fermions in hybrid loop quantum cosmology

Fermions in hybrid loop quantum cosmology

Fermi-bounce cosmology and scale-invariant power spectrum

Interaction of the Barbero-Immirzi field with matter and pseudoscalar perturbations

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