# Extended theories of gravity

Distribution of astronomical systems in the phase space diagram or gravity, plotted by X. Hernández

Extended theories of gravity are alternative theories of gravity developed from the exact starting points investigated first by Einstein and Hilbert. These are theories describing gravity, which are metric theory, "a linear connection" or related affine theories, or metric-affine gravitation theory. Rather than trying to discover correct calculations for the matter side of the Einstein field equations; which include inflation, dark energy, dark matter, large-scale structure, and possibly quantum gravity; it is proposed, instead, to change the gravitational side of the equation.[1][2]

## Proposed theories

### Hernández et al.

One such theory is also an extension to general relativity and Newton's Universal gravity law (${\displaystyle f(\chi )=\chi ^{\frac {3}{2}}}$), first proposed in 2010 by the Mexican astronomers Xavier Hernández Doring, Sergio Mendoza Ramos et al., researchers at the Astronomy Institute, at the National Autonomous University of Mexico.[3][4] This theory is in accordance with observations of kinematics of the solar system, extended binary stars,[5] and all types of galaxies and galactic groups and clouds.[6] It also reproduces the gravitational lensing effect with out the need of postulating dark matter.[7]

There is some evidence that it could also explain the dark energy phenomena[8][9] and give a nice solution to the initial conditions problem.[10]

These results can be classified as a metric f(R) gravity theory, more properly an f(R,T) theory, derived from an action principle. This approach to solve the dark matter problem takes into account the Tully–Fisher relation as an empirical law that applies always at scales larger than the Milgrom radius.[11]

## References

1. ^ Capozziello, S.; De Laurentis, M. (2011). "Extended Theories of Gravity". Physics Reports. 509 (4–5): 167–321. arXiv:. Bibcode:2011PhR...509..167C. doi:10.1016/j.physrep.2011.09.003.
2. ^ Capozziello, S.; Francaviglia, M. (2008). "Extended theories of gravity and their cosmological and astrophysical applications". General Relativity and Gravitation. 40 (2–3): 357–420. arXiv:. Bibcode:2008GReGr..40..357C. doi:10.1007/s10714-007-0551-y.
3. ^ Mendoza, S.; Hernandez, X.; Hidalgo, J. C.; Bernal, T. (2011). "A natural approach to extended Newtonian gravity: Tests and predictions across astrophysical scales". Monthly Notices of the Royal Astronomical Society. 411 (411): 226–234. arXiv:. Bibcode:2011MNRAS.411..226M. doi:10.1111/j.1365-2966.2010.17685.x.
4. ^ Hidalgo, J. C.; Mendoza, S.; Hernandez, X.; Bernal, T.; Jimenez, M. A.; Allen, C. (2012). "Non-relativistic Extended Gravity and its applications across different astrophysical scales". AIP Conference Proceedings. AIP Conference Proceedings. 1458: 427–430. arXiv:. Bibcode:2012AIPC.1458..427H. doi:10.1063/1.4734451.
5. ^ Hernandez, X.; Jiménez, M. A.; Allen, C. (2012). "Wide binaries as a critical test of Classical Gravity". European Physical Journal C. 72 (2): 1884. arXiv:. Bibcode:2012EPJC...72.1884H. doi:10.1140/epjc/s10052-012-1884-6.
6. ^ Hernandez, X. (2012). "A Phase Space Diagram for Gravity". Entropy. 14 (12): 848. arXiv:. Bibcode:2012Entrp..14..848H. doi:10.3390/e14050848.
7. ^ Mendoza, S.; Bernal, T.; Hernandez, X.; Hidalgo, J. C.; Torres, L. A. (2013). "Gravitational lensing with f(χ)=χ3/2 gravity in accordance with astrophysical observations". Monthly Notices of the Royal Astronomical Society. 433 (3): 1802–1812. arXiv:. Bibcode:2013MNRAS.433.1802M. doi:10.1093/mnras/stt752.
8. ^ Mendoza, S. (2012). "Extending Cosmology: The Metric Approach". In Olmo, G. J. Open Questions in Cosmology. INTECH. pp. 133–156. arXiv:. doi:10.5772/53878. ISBN 978-953-51-0880-1.
9. ^ Carranza, D. A.; Mendoza, S.; Torres, L. A. (2012). "A cosmological dust model with extended f(χ) gravity". European Physical Journal C. 73: 2282. arXiv:. Bibcode:2013EPJC...73.2282C. doi:10.1140/epjc/s10052-013-2282-4.
10. ^ Hernandez, X.; Jimenez, M. A. (2013). "A first linear cosmological structure formation scenario under extended gravity". arXiv: [astro-ph.CO].
11. ^ Capozziello, S.; De Laurentis, M. (2013). "Extended Gravity: State of the Art and Perspectives". In Rosquist, K.; Jantzen, R. T.; Ruffini, R. Proceedings of the Thirteenth Marcel Grossman Meeting on General Relativity. World Scientific. arXiv:.