Trans-Planckian Redshifts and the Substance of the Space-Time River

Jacobson, Ted

doi:10.1143/ptps.136.1

Cited by 167 publications

(178 citation statements)

References 40 publications

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“…In more realistic models, the number N of patches should change in time, either by a fundamental process of discrete geometries being refined [32,33], or by an approximation procedure akin to adaptive mesh refinement that maintains the decomposition into isotropic patches as a good model. (A time-dependent number of degrees of freedom is a general problem, studied for instance in [34,35,36,37,38]. )…”

Section: Classical Modelmentioning

confidence: 99%

Nonlinear (loop) quantum cosmology

et al. 2012

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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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Section: Classical Modelmentioning

confidence: 99%

Nonlinear (loop) quantum cosmology

et al. 2012

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“…As before we take the field to be in the free fall vacuum state. A number of studies have demonstrated that in this state, to leading order in κ/Λ, models with UV dispersion reproduce the relativistic result that the outgoing modes at infinity are thermally populated at the Hawking temperature [30,31,32,33]. To evaluate the entanglement entropy we need to know whether thermality extends to the near-horizon modes that contribute to the entropy.…”

Section: Dispersion Induced Cut-offmentioning

confidence: 99%

Black hole entanglement entropy regularized in a freely falling frame

Jacobson

Renaud

2007

Phys. Rev. D

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We compute the black hole horizon entanglement entropy S E for a massless scalar field, first with a hard cutoff and then with high frequency dispersion, both imposed in a frame that falls freely across the horizon. Using WKB methods, we find that S E is finite for a hard cutoff or super-luminal dispersion, because the mode oscillations do not diverge at the horizon and the contribution of high transverse momenta is cut off by the angular momentum barrier. For sub-luminal dispersion the entropy depends on the behavior at arbitrarily high transverse momenta. In all cases it scales with the horizon area. For the hard cutoff it is linear in the cutoff, rather than quadratic. This discrepancy from the familiar result arises from the difference between the free-fall frame and the static frame in which a cutoff is usually imposed. In the superluminal case the entropy scales with a fractional power of the cutoff that depends on the index of the dispersion relation. Implications for the possible relation between regularized entanglement entropy and the Bekenstein-Hawking entropy are discussed. An appendix provides an explicit derivation of the entangled, thermal nature of the near-horizon free fall vacuum for a dispersive scalar field in four dimensions.

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“…The validity of these assumptions is unclear; this is known as the trans-Planckian question of inflationary cosmology [4].…”

Section: Introductionmentioning

confidence: 99%

Minimal modifications of the primordial power spectrum from an adiabatic short distance cutoff

2002

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As a simple model for unknown Planck scale physics, we assume that the quantum modes responsible for producing primordial curvature perturbations during inflation are placed in their instantaneous adiabatic vacuum when their proper momentum reaches a fixed high energy scale M . The resulting power spectrum is derived and presented in a form that exhibits the amplitude and frequency of the superimposed oscillations in terms of H/M and the slow roll parameter ǫ.The amplitude of the oscillations is proportional to the third power of H/M . We argue that these small oscillations give the lower bound of the modifications of the power spectrum if the notion of free mode propagation ceases to exist above the critical energy scale M .

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Trans-Planckian Redshifts and the Substance of the Space-Time River

Cited by 167 publications

References 40 publications

Nonlinear (loop) quantum cosmology

Nonlinear (loop) quantum cosmology

Black hole entanglement entropy regularized in a freely falling frame

Minimal modifications of the primordial power spectrum from an adiabatic short distance cutoff

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