# Conformal Gravity: Dark Matter and Dark Energy

## Abstract

**:**

## 1. Introduction

## 2. Postulates and Formalism

## 3. Dark Matter: Galactic Rotation Velocities

## 4. Dark Matter: Hubble Expansion

## 5. Dark Energy

## 6. Galactic Halos

## 7. Open Questions

## 8. Conclusions

## References

- Dodelson, S. Modern Cosmology; Academic Press: New York, NY, USA, 2003. [Google Scholar]
- Weyl, H. Gravitation und elektrizität. Sitzungber. Preuss. Akad. Wiss.
**1918**, 465, 465–480. [Google Scholar] - Mannheim, P.D. Conformal cosmology with no cosmological constant. Gen. Rel. Grav.
**1990**, 22, 289–298. [Google Scholar] [CrossRef] - Mannheim, P.D. Alternatives to dark matter and dark energy. Prog. Part. Nucl. Phys.
**2006**, 56, 340–445. [Google Scholar] [CrossRef] - Nesbet, R.K. Cosmological implications of conformal field theory. Mod. Phys. Lett. A
**2011**, 26, 893–900. [Google Scholar] [CrossRef] - DeWitt, B.S. Relativity, Groups, and Topology; DeWitt, C., DeWitt, B.S., Eds.; Gordon and Breach: New York, NY, USA, 1964. [Google Scholar]
- Mannheim, P.D. Comprehensive solution to the cosmological constant, zero-point energy, and quantum gravity problems. Gen. Rel. Grav.
**2011**, 43, 703–750. [Google Scholar] [CrossRef] - Nesbet, R.K. Conformal higgs model of dark energy. arXiv:1004.5097v2 [physics.gen-ph].
- Mannheim, P.D.; Kazanas, D. Exact vacuum solution to conformal weyl gravity and galactic rotation curves. Astrophys. J.
**1989**, 342, 635–638. [Google Scholar] [CrossRef] - Flanagan, E.E. Fourth order weyl gravity. Phys. Rev. D
**2006**, 74, 023002:1–023002:4. [Google Scholar] [CrossRef] - Mannheim, P.D. Schwarzschild limit of conformal gravity in the presence of macroscopic scalar fields. Phys. Rev. D
**2007**, 75, 124006:1–124006:15. [Google Scholar] [CrossRef] - Mannheim, P.D. Are galactic rotation curves really flat? Astrophys. J.
**1997**, 479, 659–664. [Google Scholar] [CrossRef] - Mannheim, P.D.; O’Brien, J.G. Impact of a global quadratic potential on galactic rotation curves. Phys. Rev. Lett.
**2011**, 106, 121101:1–121101:4. [Google Scholar] [CrossRef] [PubMed] - Mannheim, P.D.; O’Brien, J.G. Fitting galactic rotation curves with conformal gravity and a global quadratic potential. Phys. Rev. D
**2012**, 85, 124020:1–124020:26. [Google Scholar] [CrossRef] - O’Brien, J.G.; Mannheim, P.D. Fitting dwarf galaxy rotation curves with conformal gravity. Mon. Not. R. Astron. Soc.
**2012**, 421, 1273–1282. [Google Scholar] [CrossRef] - Nesbet, R.K. Proposed explanation of galactic halos. arXiv:1109.3626v3 [physics.gen-ph].
- Peskin, M.E.; Schroeder, D.V. Introduction to Quantum Field Theory; Westview Press: Boulder, CO, USA, 1995. [Google Scholar]
- Cottingham, W.N.; Greenwood, D.A. An Introduction to the Standard Model of Particle Physics; Cambridge University Press: New York, NY, USA, 1998. [Google Scholar]
- Nesbet, R.K. Variational Principles and Methods in Theoretical Physics and Chemistry; Cambridge University Press: New York, NY, USA, 2003. [Google Scholar]
- Deser, S.; Franklin, J. Schwarzschild and birkhoff a la weyl. Am. J. Phys.
**2005**, 73, 261–264. [Google Scholar] [CrossRef] - Ostriker, J.P.; Peebles, P.J.E. A numerical study of the stability of flattened galaxies: Or, can cold galaxies survive? Astrophys. J.
**1973**, 186, 467–480. [Google Scholar] [CrossRef] - Ostriker, J.P.; Peebles, P.J.E.; Yahil, A. The size and mass of galaxies and the mass of the universe. Astrophys. J.
**1974**, 193, L1–L4. [Google Scholar] [CrossRef] - Sanders, R.H. The Dark Matter Problem; Cambridge University Press: New York, NY, USA, 2010. [Google Scholar]
- Rogstad, D.H.; Shostak, G.S. Gross properties of five SCD galaxies. Astrophys. J.
**1972**, 176, 315–321. [Google Scholar] [CrossRef] - Bosma, A. 21-cm line studies of spiral galaxies. Astron. J.
**1981**, 86, 1825–1846. [Google Scholar] [CrossRef] - Walsh, D.; Carswell, R.F.; Weymann, R.J. Twin quasistellar objects or gravitational lens. Nature
**1979**, 279, 381–384. [Google Scholar] [CrossRef] [PubMed] - Paczynski, B. Giant luminous arcs discovered in two clusters of galaxies. Nature
**1987**, 325, 572–573. [Google Scholar] [CrossRef] - Bartelmann, M. Gravitational lensing. Class. Quantum Gravity
**2010**, 27. [Google Scholar] [CrossRef] - Persic, M.; Salucci, P.; Stel, F. The universal rotation curve of spiral galaxies. I. Mon. Not. R. Astron. Soc.
**1996**, 281, 27–48. [Google Scholar] [CrossRef] - Salucci, P.; Lapi, A.; Tonini, C.; Gentile, G.; Yegorova, I.; Klein, U. The universal rotation curve of spiral galaxies. II. Mon. Not. R. Astron. Soc.
**2007**, 378, 41–51. [Google Scholar] [CrossRef] - Milgrom, M. A modification of newtonian dynamics. Astrophys. J.
**1983**, 270, 365–370. [Google Scholar] [CrossRef] - Sanders, R.H.; McGaugh, S.S. Modified newtonian dynamics as an alternative to dark matter. Ann. Rev. Astron. Astrophys.
**2002**, 40, 263–317. [Google Scholar] [CrossRef] - Tully, R.B.; Fisher, J.R. A new method for determining the distances to galaxies. Astron. Astrophys.
**1977**, 54, 661–673. [Google Scholar] - McGaugh, S.S. Novel test of MOND with gas rich galaxies. Phys. Rev. Lett.
**2011**, 106, 121303:1–121303:4. [Google Scholar] [CrossRef] [PubMed] - Bekenstein, J.D. Relativistic gravitation theory for the MOND paradigm. Phys. Rev. D
**2004**, 70, 083509:1–083509:28. [Google Scholar] [CrossRef] - Moffat, J.W. Scalar-tensor-vector gravity theory. J. Cosmol. Astropart. Phys.
**2006**, 2006, 4–23. [Google Scholar] [CrossRef] - Brownstein, J.R.; Moffat, J.W. Galaxy rotation curves without non-baryonic dark matter. Astrophys. J.
**2006**, 636, 721–761. [Google Scholar] [CrossRef] - Moffat, J.W.; Rahvar, S.; Toth, V.T. Applying MOG to lensing: Einstein rings, abell 520 and the bullet cluster. arXiv:1204.2985v1[astro-ph.CO].
- Hubble, E. A relation between distance and radial velocity among extra-galactic nebulae. Proc. Nat. Acad. Sci. USA
**1929**, 15, 168–173. [Google Scholar] [CrossRef] [PubMed] - Riess, A.G.; Filippenko, A.V.; Challis, P.; Clocchiatti, A.; Diercks, A.; Garnavich, P.M.; Gilliland, R.L.; Hogan, C.J.; Jha, S.; Kirshner, R.P.; et al. Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J.
**1998**, 116, 1009–1038. [Google Scholar] [CrossRef] - Perlmutter, S.; Aldering, G.; Goldhaber, G.; Knop, R.A.; Nugent, P.; Castro, P.G.; Deustua, S.; Fabbro, S.; Goobar, A.; Groom, D.E.; et al. Measurement of Ω and Λ from 42 high-redshift supernovae. Astrophys. J.
**1999**, 517, 565–586. [Google Scholar] [CrossRef] - Friedmann, A. Über die Krümmung des raumes. Zeits. Phys.
**1922**, 10, 377–386. [Google Scholar] [CrossRef] - Friedmann, A. Über die Möglichkeit einer welt mit konstanter negativer krümmung des raumes. Zeits. Phys.
**1924**, 21, 326–332. [Google Scholar] [CrossRef] - LeMaître, G. Un univers homogène de masse constante et de rayon croissant. Ann. Soc. Sci. Bruxelles
**1927**, A47, 49–59. [Google Scholar] - Mannheim, P.D. How recent is cosmic acceleration? Int. J. Mod. Phys. D
**2003**, 12, 893–904. [Google Scholar] [CrossRef] - Komatsu, E.; Dunkley, J.; Nolta, M.R.; Bennett, C.L.; Gold, B.; Hinshaw, G.; Jarosik, N.; Larson, D.; Limon, M.; Page, L.; et al. Five-year WMAP Observations. Astrophys. J. Supp.
**2009**, 180, 330–381. [Google Scholar] [CrossRef] - Komatsu, E.; Smith, K.M.; Dunkley, J.; Bennett, C.L.; Gold, B.; Hinshaw, G.; Jarosik, N.; Larson, D.; Nolta, M.R.; Page, L.; et al. Seven-year WMAP Observations. Astrophys. J. Supp.
**2011**, 192, 18–74. [Google Scholar] [CrossRef] - Wang, Y.; Mukherjee, P. Observational constraints on dark energy and cosmic curvature. Phys. Rev. D
**2007**, 76, 103533:1–103533:11. [Google Scholar] [CrossRef] - Nesbet, R.K. The higgs scalar field with no massive higgs particle. arXiv:1009.1372v3 [physics.gen-ph].
- Cho, A. Higgs boson makes its debut after decades-long search. Science
**2012**, 337, 141–143. [Google Scholar] [CrossRef] [PubMed] - Nesbet, R.K. Theory of spin-dependent conductivity in GMR materials. IBM J. Res. Dev.
**1998**, 42, 53–71. [Google Scholar] [CrossRef] - McGaugh, S.S. Balance of dark and luminous mass in rotating galaxies. Phys. Rev. Lett.
**2005**, 95, 171302:1–171302:4. [Google Scholar] [CrossRef] [PubMed] - Allen, S.W.; Evrard, A.E.; Mantz, A.B. Cosmological parameters from observations of galaxy clusters. Ann. Rev. Astron. Astrophys.
**2011**, 49, 409–470. [Google Scholar] [CrossRef]

© 2013 by the author; licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution license (http://creativecommons.org/licenses/by/3.0/).

## Share and Cite

**MDPI and ACS Style**

Nesbet, R.K.
Conformal Gravity: Dark Matter and Dark Energy. *Entropy* **2013**, *15*, 162-176.
https://doi.org/10.3390/e15010162

**AMA Style**

Nesbet RK.
Conformal Gravity: Dark Matter and Dark Energy. *Entropy*. 2013; 15(1):162-176.
https://doi.org/10.3390/e15010162

**Chicago/Turabian Style**

Nesbet, Robert K.
2013. "Conformal Gravity: Dark Matter and Dark Energy" *Entropy* 15, no. 1: 162-176.
https://doi.org/10.3390/e15010162