Anomaly freedom in perturbative loop quantum gravity

Bojowald, Martin; Hossain, Golam Mortuza; Kagan, Mikhail; Shankaranarayanan, S.

doi:10.1103/physrevd.78.063547

Cited by 146 publications

(254 citation statements)

References 71 publications

(146 reference statements)

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“…The unstable solution corresponds to ξ = ξ 0 , while φ rolls down the exponential potential in (101). The resulting equation of state parameter satisfies w 1.…”

Section: Basics Of Cosmological Perturbation Theorymentioning

confidence: 98%

“…A consistent treatment of perturbations in LQC has been proposed in Refs. [100][101][102]. The most common approach consists in taking a modified Friedmann equation containing a −ρ 2 contribution to the right hand side [89,[103][104][105][106] (see also, [88]).…”

Section: Loop Quantum Cosmologymentioning

confidence: 99%

“…It has been argued in the LQG literature that LQC is not the homogeneous and isotropic limit of LQG [113], and thus, the operation of quantization and taking the mini-superspace approximation might not commute. For recent works on perturbations, which aim to go beyond the mini-superspace approximation, see [100][101][102].…”

Section: Loop Quantum Cosmologymentioning

confidence: 99%

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A critical review of classical bouncing cosmologies

2015

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Given the proliferation of bouncing models in recent years, we gather and critically assess these proposals in a comprehensive review. The PLANCK data shows an unmistakably red, quasi scaleinvariant, purely adiabatic primordial power spectrum and no primary non-Gaussianities. While these observations are consistent with inflationary predictions, bouncing cosmologies aspire to provide an alternative framework to explain them. Such models face many problems, both of the purely theoretical kind, such as the necessity of violating the NEC and instabilities, and at the cosmological application level, as exemplified by the possible presence of shear. We provide a pedagogical introduction to these problems and also assess the fitness of different proposals with respect to the data. For example, many models predict a slightly blue spectrum and must be fine-tuned to generate a red spectral index; as a side effect, large non-Gaussianities often result.We highlight several promising attempts to violate the NEC without introducing dangerous instabilities at the classical and/or quantum level. If primordial gravitational waves are observed, certain bouncing cosmologies, such as the cyclic scenario, are in trouble, while others remain valid. We conclude that, while most bouncing cosmologies are far from providing an alternative to the inflationary paradigm, a handful of interesting proposals have surfaced, which warrant further research. The constraints and lessons learned as laid out in this review might guide future research.

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“…The unstable solution corresponds to ξ = ξ 0 , while φ rolls down the exponential potential in (101). The resulting equation of state parameter satisfies w 1.…”

Section: Basics Of Cosmological Perturbation Theorymentioning

confidence: 98%

Section: Loop Quantum Cosmologymentioning

confidence: 99%

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A critical review of classical bouncing cosmologies

2015

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“…3 Quadratic expressions of spatial derivatives in (9) then provide interaction terms that can be written as depending on either the patch geometries in product form, such as…”

Section: Classical Modelmentioning

confidence: 99%

“…First, effective equations have been successful in addressing the anomaly problem [3,4] and in including all relevant quantum effects in sufficiently general form. (For details, see [5].)…”

Section: Introductionmentioning

confidence: 99%

Nonlinear (loop) quantum cosmology

et al. 2012

Self Cite

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Inhomogeneous quantum cosmology is modeled as a dynamical system of discrete patches, whose interacting many-body equations can be mapped to a non-linear minisuperspace equation by methods analogous to Bose-Einstein condensation. Complicated gravitational dynamics can therefore be described by more-manageable equations for finitely many degrees of freedom, for which powerful solution procedures are available, including effective equations. The specific form of non-linear and non-local equations suggests new questions for mathematical and computational investigations, and general properties of non-linear wave equations lead to several new options for physical effects and tests of the consistency of loop quantum gravity. In particular, our quantum cosmological methods show how sizeable quantum corrections in a lowcurvature universe can arise from tiny local contributions adding up coherently in large regions.

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Observational effects from quantum cosmology

Calcagni

2013

Annalen der Physik

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The status of quantum cosmologies as testable models of the early universe is assessed in the context of inflation. While traditional Wheeler-DeWitt quantization is unable to produce sizable effects in the cosmic microwave background, the more recent loop quantum cosmology can generate potentially detectable departures from the standard cosmic spectrum. Thus, present observations constrain the parameter space of the model, which could be made falsifiable by near-future experiments.

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Anomaly freedom in perturbative loop quantum gravity

Cited by 146 publications

References 71 publications

A critical review of classical bouncing cosmologies

A critical review of classical bouncing cosmologies

Nonlinear (loop) quantum cosmology

Observational effects from quantum cosmology

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