## From Quantum to Emergent Gravity: Theory and Phenomenology (2007)

### BibTeX

@MISC{Volovik07fromquantum,

author = {G. E. Volovik},

title = {From Quantum to Emergent Gravity: Theory and Phenomenology},

year = {2007}

}

### OpenURL

### Abstract

Let us assume that gravity is an emergent low-energy phenomenon arising from a topologically stable defect in momentum space – the Fermi point. What are the consequences? We discuss the natural values of fermion masses and cosmological constant; flatness of the Universe; bounds on Lorentz violation; etc.

### Citations

130 |
The Universe in a Helium Droplet
- Volovik
- 2003
(Show Context)
Citation Context ...deed, the momentum space topology suggests that, both in relativistic quantum field theories and in fermionic condensed matter, there are several universality classes of quantum vacua (ground states) =-=[1, 2, 3]-=-. One of them contains vacua with trivial topology, whose fermionic excitations are massive (gapped) fermions. The natural mass of these fermions is on the order of EP. 3Fermi-point scenario for emer... |

60 |
Kosmologische Betrachtungen zur allgemeinen Relativitätstheorie, Sitzungsberichte der Preussischen Akad. d. Wissenschaften
- Einstein
- 1917
(Show Context)
Citation Context ...or example, emergent gravity is not able to incorporate the geodesically-complete Einstein Universe with spatial section S 3 [6]. It, therefore, appears that the original static S 3 Einstein Universe =-=[7]-=- can exist only within the context of fundamental general relativity. Some coordinate transformations in GR are not allowed in emergent gravity: these are either singular transformations of the origin... |

30 | Anyons in an exactly solved model and beyond
- Kitaev
- 2006
(Show Context)
Citation Context ...acuum will be only revealed at much higher Lorentzviolating scale ELorentz. The opposite situation, when fermionic degrees of freedom emerge in the underlying bosonic quantum vacuum, is possible (see =-=[15, 16]-=- and especially Ref. [17], where the Fermi points emerge in some model of spins on a three-dimensional lattice), but at the moment the generic mechanism for the emergence of gravity and matter in boso... |

15 | Emergent CPT violation from the splitting of Fermi point
- Klinkhamer, Volovik
- 2005
(Show Context)
Citation Context ...iolated or spontaneously broken, there are two topologically different scenarios: (bottom left) either Fermi point annihilate each other and Dirac mass is formed; (bottom right) or Fermi points split =-=[12]-=-. It is possible that actually the splitting exists at the microscopic level, but in our low energy corner we cannot observe it because of the emergent gauge symmetry: in some cases splitting can be r... |

10 |
Stability of Fermi surfaces and K
- Horava
- 2005
(Show Context)
Citation Context ...deed, the momentum space topology suggests that, both in relativistic quantum field theories and in fermionic condensed matter, there are several universality classes of quantum vacua (ground states) =-=[1, 2, 3]-=-. One of them contains vacua with trivial topology, whose fermionic excitations are massive (gapped) fermions. The natural mass of these fermions is on the order of EP. 3Fermi-point scenario for emer... |

8 | Emergent gauge bosons
- Bjorken
(Show Context)
Citation Context ...ati-Salam models. (9) Lorentz symmetry must persist well above the Planck energy. The requirement for two well separated energy scales follows from the high precision of physical laws in our Universe =-=[9]-=-, and it represents the most crucial test of the emergent scenario. In the case when the Lorentz violating scale ELorentz < EP, the metric field does not obey Einstein equations; instead it is governe... |

7 | Black hole entropy in induced gravity: Reduction to 2D quantum field theory on the horizon, Phys
- Frolov, Fursaev
- 1998
(Show Context)
Citation Context ...stein equations emerge in the limit ELorentz ≫ EP, and their accuracy is determined by the small parameter E2 P /E2 Lorentz ≪ 1. For example, in the Frolov-Fursaev version of Sakharov induced gravity =-=[10]-=-, the ultraviolet cut-off is much larger than the Planck energy, and Einstein equations are reproduced. The observed bounds on the violation of Lorentz symmetry can be obtained from ultra-high-energy ... |

7 |
Ultra-high-energy cosmic-ray bounds on nonbirefringent modified-Maxwell theory, Phys
- Klinkhamer, Risse
- 2008
(Show Context)
Citation Context ...mmetry can be obtained from ultra-high-energy cosmic rays. For example, according to conservative estimations the relative value of the Lorentz violating terms in the Maxwell equations is below 10−18 =-=[11]-=-. This suggests that ELorentz > 109EP, which is in favor of emergent scenario. All this implies that physics continues far beyond the Planck scale, and this opens new possibilities for construction of... |

6 |
Merging gauge coupling constants without Grand Unification
- Klinkhamer, Volovik
(Show Context)
Citation Context ...nergy, gives rise to topological defects in real space (e.g., a hedgehog-like object) and life (e.g., a real hedgehog). composite objects, the ultraviolet cut-off is different for fermions and bosons =-=[13]-=- (a similar situation occurs in condensed matter [14]). The smaller (composite) scale can be associated with EP, while the "atomic" structure of the quantum vacuum will be only revealed at much higher... |

5 |
Metric fluctuations of an evaporating black hole from back reaction of stress tensor fluctuations
- Hu, Roura
(Show Context)
Citation Context ...uantize gravitational waves to obtain their quanta – gravitons; it is possible to obtain some quantum corrections to Einstein equation; to extend classical gravity to the semiclassical and stochastic =-=[5]-=- levels, etc. But one cannot cannot obtain “quantum gravity” by full quantization of Einstein equations. (4) Effective gravity may essentially differ from fundamental gravity even in principle. Since ... |

4 |
Self-tuning vacuum variable and cosmological constant; arXiv:0711.3170; G.E. Volovik, Emergent physics: Fermi point scenario
- Klinkhamer, Volovik
(Show Context)
Citation Context ...does not depend on the microscopic structure of the vacuum from which gravity emerges, and is actually the final result of the renormalization dictated by macroscopic physics (more on that see in Re. =-=[4]-=-). 3. Emergent gravity vs fundamental gravity The Fermi-point scenario gives a particular mechanism of emergent gravity. This mechanism has many consequences, and some of them can be used to falsify t... |

4 |
Coexisting vacua and effective gravity, Phys
- Klinkhamer, Volovik
- 2005
(Show Context)
Citation Context ...e metrics, which are natural in general relativity, are simply forbidden. For example, emergent gravity is not able to incorporate the geodesically-complete Einstein Universe with spatial section S 3 =-=[6]-=-. It, therefore, appears that the original static S 3 Einstein Universe [7] can exist only within the context of fundamental general relativity. Some coordinate transformations in GR are not allowed i... |

4 |
Cosmology as a search for overall equilibrium
- Barcelo
- 2007
(Show Context)
Citation Context ...nt, and thus its smallness requires fine-tuning. Thus observations are in favor of emergent gravity. The unsolved problem is: what is the physical mechanism of relaxation of Λ towards zero? (See Ref. =-=[8]-=- and references therein.) The present small value of Λ indicates that the Universe is so close to equilibrium that the current relaxation rate is very slow. (7) In the Fermi point scenario space-time ... |

4 | From new states of matter to a unification of light and electrons
- Wen
- 2006
(Show Context)
Citation Context ...acuum will be only revealed at much higher Lorentzviolating scale ELorentz. The opposite situation, when fermionic degrees of freedom emerge in the underlying bosonic quantum vacuum, is possible (see =-=[15, 16]-=- and especially Ref. [17], where the Fermi points emerge in some model of spins on a three-dimensional lattice), but at the moment the generic mechanism for the emergence of gravity and matter in boso... |

3 |
Specific heat of a one-dimensional interacting Fermi system: the role of anomalies, arXiv:0707.4422
- Chubukov, Maslov, et al.
(Show Context)
Citation Context ...e (e.g., a hedgehog-like object) and life (e.g., a real hedgehog). composite objects, the ultraviolet cut-off is different for fermions and bosons [13] (a similar situation occurs in condensed matter =-=[14]-=-). The smaller (composite) scale can be associated with EP, while the "atomic" structure of the quantum vacuum will be only revealed at much higher Lorentzviolating scale ELorentz. The opposite situat... |

3 |
Exactly soluble spin-1/2 models on three-dimensional lattices and non-abelian statistics of closed string excitations
- Si, Yu
(Show Context)
Citation Context ...t much higher Lorentzviolating scale ELorentz. The opposite situation, when fermionic degrees of freedom emerge in the underlying bosonic quantum vacuum, is possible (see [15, 16] and especially Ref. =-=[17]-=-, where the Fermi points emerge in some model of spins on a three-dimensional lattice), but at the moment the generic mechanism for the emergence of gravity and matter in bosonic vacuum has not yet be... |