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As I understand the crisis instigated by the realization that a QFT of gravity is non-renormalizable, it is that such calculations are divergent (as are simliar calculations in QCD and other Yang-Mills QFTs). In other theories the divergences can be regularized and via renormalization relative values obtained that are physically meaningful. But in the case of gravity there are an infinite number of degrees of freedom in the process that must be resolved via empirical measurements so that the concept of "calculation" becomes meaningless. I am not familiar anymore with the details of this argument however and may have missed a point or misrepresented one.

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haushofer

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https://arxiv.org/abs/0907.4238

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ohwilleke

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Alexandre Deur argues that this is the case, and I have cut and pasted an annotated bibliography of his quantum gravity publications and a couple of closely related papers by others below.

Mannheim argues in his work on conformal gravity that his approach (which works from fourth derivatives rather than the second derivatives of GR and make a couple of other assumptions relative to conformal symmetry) makes quantum gravity calculations feasible. See, e.g. Philip D. Mannheim, "Is dark matter fact or fantasy? -- clues from the data" (March 27, 2019) (especially Section IX).

Until somebody does it in a way that can reach wide agreement, it is hard to know if that is the only issue. The fact that there is graviton self-interaction is definitely one of the things that makes both quantum gravity and QCD calculations (gluons also have that property) very difficult. Gravitons are hypothetically spin-2 unlike gluons which are spin-1 and that also makes graviton calculations more difficult (Deur overcomes this difficulty by approximating quantum gravity with spin-0 gravitons which represent the static case of a spin-2 graviton theory.)

There is also dispute over whether quantum gravity should be about quantizing a graviton carrier boson, about quantizing space-time, or if it is necessary at all (i.e. if there is actually some way to meld a non-quantum theory of gravity with quantum theories of everything else).

__Annotated Bibliography__

The first article in the series by Deur on gravity is:

The first of his papers published in a peer reviewed journal is:

Deur also makes a theoretical prediction which neither dark matter nor MOND suggest, which is born out by observation. This prediction is that non-spherical elliptical galaxies have greater deviations from general relativity without dark matter than more spherically symmetric elliptical galaxies do. This is found in a 2014 paper:

Deur argues that most or all of observed dark energy phenomena results from gravitons being confined in galaxy and galactic cluster scale systems, which is what gives rise to the dark matter phenomena in this systems. The diversion of gravitons to more strongly bind matter in the galaxies leads to a small deficit of gravitons which escape the galaxy and cause galaxies and galactic clusters to bind to each other. It also neatly explains the "cosmic coincidence problem." He spells out this analysis in a 2018 pre-print (with an original pre-print date in 2017) which also examines cosmology implications of his approach more generally:

The use of a scalar graviton approximation used by Deur is justified in a published 2017 paper:

A paper in the same journal by independent authors confirms that scalar approximations can reproduce experimental tests:

Mannheim argues in his work on conformal gravity that his approach (which works from fourth derivatives rather than the second derivatives of GR and make a couple of other assumptions relative to conformal symmetry) makes quantum gravity calculations feasible. See, e.g. Philip D. Mannheim, "Is dark matter fact or fantasy? -- clues from the data" (March 27, 2019) (especially Section IX).

Until somebody does it in a way that can reach wide agreement, it is hard to know if that is the only issue. The fact that there is graviton self-interaction is definitely one of the things that makes both quantum gravity and QCD calculations (gluons also have that property) very difficult. Gravitons are hypothetically spin-2 unlike gluons which are spin-1 and that also makes graviton calculations more difficult (Deur overcomes this difficulty by approximating quantum gravity with spin-0 gravitons which represent the static case of a spin-2 graviton theory.)

There is also dispute over whether quantum gravity should be about quantizing a graviton carrier boson, about quantizing space-time, or if it is necessary at all (i.e. if there is actually some way to meld a non-quantum theory of gravity with quantum theories of everything else).

The first article in the series by Deur on gravity is:

A. Deur, “Non-Abelian Effects in Gravitation” (September 17, 2003) (not published).The non-abelian symmetry of a lagrangian invalidates the principle of superposition for the field described by this lagrangian.A consequence in QCD is that non-linear effects occur, resulting in the quark-quark linear potential that explains the quark confinement, the quarkonia spectra or the Regge trajectories. Following a parallel between QCD and gravitation,we suggest that these non-linear effects should create an additional logarithmic potential in the classical newtonian description of gravity. The modified potential may account for the rotation curve of galaxies and other problems, without requiring dark matter.

The first of his papers published in a peer reviewed journal is:

A. Deur, “Implications of Graviton-Graviton Interaction to Dark Matter” (May 6, 2009) (published at 676 Phys. Lett. B 21 (2009)).Our present understanding of the universe requires the existence of dark matter and dark energy. We describe here a natural mechanism that could make exotic dark matter and possibly dark energy unnecessary.Graviton-graviton interactions increase the gravitational binding of matter. This increase, for large massive systems such as galaxies, may be large enough to make exotic dark matter superfluous. Within a weak field approximation we compute the effect on the rotation curves of galaxies and find the correct magnitude and distribution without need for arbitrary parameters or additional exotic particles. The Tully-Fisher relation also emerges naturally from this framework. The computations are further applied to galaxy clusters.

Deur also makes a theoretical prediction which neither dark matter nor MOND suggest, which is born out by observation. This prediction is that non-spherical elliptical galaxies have greater deviations from general relativity without dark matter than more spherically symmetric elliptical galaxies do. This is found in a 2014 paper:

Alexandre Deur, “A correlation between the amount of dark matter in elliptical galaxies and their shape” (July 28, 2014).We discuss the correlation between the dark matter content of elliptical galaxies and their ellipticities. We then explore a mechanism for which the correlation would emerge naturally. Such mechanism leads to identifying the dark matter particles to gravitons.A similar mechanism is known in Quantum Chromodynamics (QCD) and is essential to our understanding of the mass and structure of baryonic matter.

Deur argues that most or all of observed dark energy phenomena results from gravitons being confined in galaxy and galactic cluster scale systems, which is what gives rise to the dark matter phenomena in this systems. The diversion of gravitons to more strongly bind matter in the galaxies leads to a small deficit of gravitons which escape the galaxy and cause galaxies and galactic clusters to bind to each other. It also neatly explains the "cosmic coincidence problem." He spells out this analysis in a 2018 pre-print (with an original pre-print date in 2017) which also examines cosmology implications of his approach more generally:

A. Deur, “A possible explanation for dark matter and dark energy consistent with the Standard Model of particle physics and General Relativity” (August 14, 2018) (Proceeding for a presentation given at Duke University, Apr. 2014. Based on A. D. PLB B676, 21 (2009); A.D, MNRAS, 438, 1535 (2014)). The body text of this paper explains at greater length that:Numerical calculations have shown thatthe increase of binding energy in massive systems due to gravity's self-interaction can account for galaxy and cluster dynamics without dark matter.Such approach is consistent with General Relativity and the Standard Model of particle physics.The increased binding implies an effective weakening of gravity outside the bound system. In this article, this suppression is modeled in the Universe's evolution equations and its consequence for dark energy is explored. Observations are well reproduced without need for dark energy.The cosmic coincidence appears naturally and the problem of having a de Sitter Universe as the final state of the Universe is eliminated.

Reference [9] in that paper is worth noting because is provides a simple and analogous solution to the gross disparity between the quantum mechanical expectation for the cosmological constant and its actual, tiny value. It is as follows:The framework used in Refs. [3, 4] is analogous to the well-studied phenomenology of Quantum Chromodynamics (QCD) in its strong regime. Both GR and QCD Lagrangians comprise field self-interaction terms. In QCD, their effect is important because of the large value of QCD’s coupling, typically αs ' 0.1 at the transition between QCD’s weak and strong regimes [8]. In GR, self-interaction becomes important for p GM/L large enough (G is Newton’s constant, M the mass of the system and p L its characteristic scale), typically for GM/L & 10−3 [4].In QCD, a crucial consequence of self-interaction associated with a large αs is an increased binding of quarks, which leads to their confinement. Refs. [3, 4] show that GR’s self-interaction terms lead to a similar phenomenon for p GM/L large enough, which can explain observations suggestive of dark matter.Beside confinement,the other principal feature of QCD is a dearth of strong interaction outside of hadrons, the bound states of QCD. This is due to the confinement of the color field in hadrons. While the confined field produces a constant force between quarks that is more intense than the 1/r2 force expected from a theory without self-interaction, this concentration of the field inside the hadron means a depletion outside. If such phenomenon occurs for gravity because of trapping of the gravitational field in massive structures such as galaxies or clusters of galaxies, the suppression of gravity at large scale can be mistaken for a repulsive pressure, i.e. dark energy.Specifically, the Friedman equation for the Universe expansion is (assuming a matter-dominated flat Universe) H2 = 8πGρ/3, with H the Hubble parameter and ρ the density.If gravity is effectively suppressed at large scale as massive structures coalesce, the Gρ factor, effectively decreasing with time, would imply a larger than expected value of H at early times, as seen by the observations suggesting the existence of dark energy.Incidentally,beside dark matter and dark energy, QCD phenomenology also suggests a solution to the problem of the extremely large value of Λ predicted by Quantum Field Theory[9].

Stanley J. Brodsky and Robert Shrock, "Condensates in quantum chromodynamics and the cosmological constant" 108(1) PNAS 45 (January 4, 2011).Casher and Susskind [Casher A, Susskind L (1974) Phys Rev 9:436–460] have noted that in the light-front description, spontaneous chiral symmetry breaking is a property of hadronic wavefunctions and not of the vacuum. Here we show from several physical perspectives that,because of color confinement, quark and gluon condensates in quantum chromodynamics (QCD) are associated with the internal dynamics of hadrons.We discuss condensates using condensed matter analogues, the Anti de Sitter/conformal field theory correspondence, and the Bethe–Salpeter–Dyson–Schwinger approach for bound states. Our analysis is in agreement with the Casher and Susskind model and the explicit demonstration of “in-hadron” condensates by Roberts and coworkers [Maris P, Roberts CD, Tandy PC (1998) Phys Lett B 420:267–273], using the Bethe–Salpeter–Dyson–Schwinger formalism for QCD-bound states. These results imply thatQCD condensates give zero contribution to the cosmological constant, because all of the gravitational effects of the in-hadron condensates are already included in the normal contribution from hadron masses.

The use of a scalar graviton approximation used by Deur is justified in a published 2017 paper:

A. Deur, “Self-interacting scalar fields at high temperature” (June 15, 2017) (published at Eur. Phys. J. C77 (2017) no.6, 412).We study two self-interacting scalar field theories in their high-temperature limit using path integrals on a lattice. We first discuss the formalism and recover known potentials to validate the method.We then discuss how these theories can model, in the high-temperature limit, the strong interaction and General Relativity.For the strong interaction, the model recovers the known phenomenology of the nearly static regime of heavy quarkonia.The model also exposes a possible origin for the emergence of the confinement scale from the approximately conformal Lagrangian. Aside from such possible insights,the main purpose of addressing the strong interaction here --given that more sophisticated approaches already exist-- is mostly to further verify the pertinence of the model in the more complex case of General Relativity for which non-perturbative methods are not as developed. The results have important implications on the nature of Dark Matter. In particular, non-perturbative effects naturally provide flat rotation curves for disk galaxies, without need for non-baryonic matter, and explain as well other observations involving Dark Matter such as cluster dynamics or the dark mass of elliptical galaxies.

A paper in the same journal by independent authors confirms that scalar approximations can reproduce experimental tests:

Diogo P. L. Bragança, José P. S. Lemos “Stratified scalar field theories of gravitation with self-energy term and effective particle Lagrangian” (June 29, 2018) (open access).We construct a general stratified scalar theory of gravitation from a field equation that accounts for the self-interaction of the field and a particle Lagrangian, and calculate its post-Newtonian parameters. Using this general framework, we analyze several specific scalar theories of gravitation and check their predictions for the solar system post-Newtonian effects.

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ohwilleke

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For convenience, the linked article and its abstract are as follows:

https://arxiv.org/abs/0907.4238

R. P. Woodard (University of Florida)

(Submitted on 24 Jul 2009)

I give a pedagogical explanation of what it is about quantization that makes general relativity go from being a nearly perfect classical theory to a very problematic quantum one. I also explain why some quantization of gravity is unavoidable, why quantum field theories have divergences, why the divergences of quantum general relativity are worse than those of the other forces, what physicists think this means and what they might do with a consistent theory of quantum gravity if they had one. Finally, I discuss the quantum gravitational data that have recently become available from cosmology.

Comments: | 106 page review article solicited by Reports on Progress in Physics |

Subjects: | General Relativity and Quantum Cosmology (gr-qc); Cosmology and Nongalactic Astrophysics (astro-ph.CO); High Energy Physics - Theory (hep-th) |

DOI: | 10.1088/0034-4885/72/12/126002 |

Report number: | UFIFT-QG-09-06 |

Cite as: | arXiv:0907.4238 [gr-qc] |

(or arXiv:0907.4238v1 [gr-qc] for this version) |

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