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- . Moreover we make contact with the Modified Newtonian Dynamics (MOND) approach for gravity

One poster is a strong promoter of Deur and Deur theory of how to get MOND out of GR via self-interaction and analogy to QCD.

There is intense skepticism of Deur's approach, which has 0 citations other than the author.

I saw this paper,

[Submitted on 8 Oct 2022]

Patrick Concha, Evelyn Rodríguez, Gustavo Rubio

on section 3.3 page 8- 9 the authors derive MOND from the cosmological constant and generalized non-relativistic MacDowell-Mansouri gravity theory,

the observed cosmological constant is an input, is this convincing way to derive MOND from MacDowell-Mansouri gravity theory?

for background,

General Relativity and Quantum Cosmology

[Submitted on 30 Nov 2006 (v1), last revised 15 May 2009 (this version, v2)]

MacDowell-Mansouri gravity and Cartan geometry

Derek K. Wise

The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physical field. The Cartan perspective allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous "model spacetime", including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti de Sitter, or other models. A "Cartan connection" gives a prescription for parallel transport from one "tangent model spacetime" to another, along any path, giving a natural interpretation of the MacDowell-Mansouri connection as "rolling" the model spacetime along physical spacetime. I explain Cartan geometry, and "Cartan gauge theory", in which the gauge field is replaced by a Cartan connection. In particular, I discuss MacDowell-Mansouri gravity, as well as its more recent reformulation in terms of BF theory, in the context of Cartan geometry.

Comments: 34 pages, 5 figures. v2: many clarifications, typos corrected

Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Differential Geometry (math.DG)

Cite as: arXiv:gr-qc/0611154

There is intense skepticism of Deur's approach, which has 0 citations other than the author.

I saw this paper,

### High Energy Physics - Theory

[Submitted on 8 Oct 2022]

### Non-relativistic gravity theories in four spacetime dimensions

Patrick Concha, Evelyn Rodríguez, Gustavo Rubio

In this work we present a non-relativistic gravity theory defined in four spacetime dimensions using the MacDowell-Mansouri geometrical formulation. We obtain a Newtonian gravity action which is constructed from the curvature of a Newton-Hooke version of the so-called Newtonian algebra. We show that the non-relativistic gravity theory presented here contains the Poisson equation in presence of a cosmological constant. Moreover we make contact with the Modified Newtonian Dynamics (MOND) approach for gravity by considering a particular ansatz for a given gauge field. We extend our results to a generalized non-relativistic MacDowell-Mansouri gravity theory by considering a generalized Newton-Hooke algebra.

Comments: | 20 pages |

Subjects: | High Energy Physics - Theory (hep-th); General Relativity and Quantum Cosmology (gr-qc) |

Cite as: | arXiv:2210.04101 [hep-th] |

the observed cosmological constant is an input, is this convincing way to derive MOND from MacDowell-Mansouri gravity theory?

for background,

General Relativity and Quantum Cosmology

[Submitted on 30 Nov 2006 (v1), last revised 15 May 2009 (this version, v2)]

MacDowell-Mansouri gravity and Cartan geometry

Derek K. Wise

The geometric content of the MacDowell-Mansouri formulation of general relativity is best understood in terms of Cartan geometry. In particular, Cartan geometry gives clear geometric meaning to the MacDowell-Mansouri trick of combining the Levi-Civita connection and coframe field, or soldering form, into a single physical field. The Cartan perspective allows us to view physical spacetime as tangentially approximated by an arbitrary homogeneous "model spacetime", including not only the flat Minkowski model, as is implicitly used in standard general relativity, but also de Sitter, anti de Sitter, or other models. A "Cartan connection" gives a prescription for parallel transport from one "tangent model spacetime" to another, along any path, giving a natural interpretation of the MacDowell-Mansouri connection as "rolling" the model spacetime along physical spacetime. I explain Cartan geometry, and "Cartan gauge theory", in which the gauge field is replaced by a Cartan connection. In particular, I discuss MacDowell-Mansouri gravity, as well as its more recent reformulation in terms of BF theory, in the context of Cartan geometry.

Comments: 34 pages, 5 figures. v2: many clarifications, typos corrected

Subjects: General Relativity and Quantum Cosmology (gr-qc); High Energy Physics - Theory (hep-th); Differential Geometry (math.DG)

Cite as: arXiv:gr-qc/0611154