Extended theories of gravity

{{Short description|none}}

Extended theories of gravity are alternative theories of gravity developed from the starting points investigated first by Albert 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 instead proposed to change the gravitational side of the equation.

{{cite journal

|last1=Capozziello |first1=S.

|last2=De Laurentis |first2=M.

|year=2011

|title=Extended Theories of Gravity

|journal=Physics Reports

|volume=509 |issue=4–5 |pages=167–321

|arxiv=1108.6266

|bibcode=2011PhR...509..167C

|doi=10.1016/j.physrep.2011.09.003

|s2cid=119296243

}}

{{cite journal

|last1=Capozziello |first1=S.

|last2=Francaviglia |first2=M.

|year=2008

|title=Extended theories of gravity and their cosmological and astrophysical applications

|journal=General Relativity and Gravitation

|volume=40 |issue=2–3 |pages=357–420

|arxiv=0706.1146

|bibcode=2008GReGr..40..357C

|doi=10.1007/s10714-007-0551-y

|s2cid=119587409

}}{{cite journal

|last1=Wands |first1=D.

|year=1994

|title=Extended gravity theories and the Einstein–Hilbert action

|journal=Classical and Quantum Gravity

|volume=11 |issue=1 |pages=269–279

|arxiv=gr-qc/9307034

|bibcode=1994CQGra..11..269W

|doi=10.1088/0264-9381/11/1/025

|s2cid=15060182

}}{{cite journal

|last1=Allemandi |first1=G.

|last2=Capone |first2=M.

|last3=Capozziello |first3=S.

|last4=Francaviglia |first4=M.

|year=2006

|title=Conformal aspects of the Palatini approach in Extended Theories of Gravity

|journal=General Relativity and Gravitation

|volume=38 |issue=1 |pages=33–60

|arxiv=hep-th/0409198

|bibcode=2006GReGr..38...33A

|doi=10.1007/s10714-005-0208-7

|s2cid=33278891

}}

Core concepts of RAQUAL such as a weak field limit that follows $f(\backslash chi)\backslash approx\backslash chi^\backslash frac\{3\}\{2\}$ have been adopted under the name "extended gravity", by Hernández and Mendoza at the National Autonomous University of Mexico.

{{cite journal

|last1=Mendoza |first1=S.

|last2=Hernandez |first2=X.

|last3=Hidalgo |first3=J. C.

|last4=Bernal |first4=T.

|year=2011

|title=A natural approach to extended Newtonian gravity: Tests and predictions across astrophysical scales

|journal=Monthly Notices of the Royal Astronomical Society

|volume=411 |issue=1 |pages=226–234

|arxiv=1006.5037

|bibcode=2011MNRAS.411..226M

|doi=10.1111/j.1365-2966.2010.17685.x

|doi-access=free

|s2cid=118640139

}}

{{cite journal

|last1=Hidalgo |first1=J. C.

|last2=Mendoza |first2=S.

|last3=Hernandez |first3=X.

|last4=Bernal |first4=T.

|last5=Jimenez |first5=M. A.

|last6=Allen |first6=C.

|year=2012

|title=Non-relativistic Extended Gravity and its applications across different astrophysical scales

|journal=AIP Conference Proceedings

|volume=1458 |pages=427–430

|arxiv=1202.4189

|bibcode=2012AIPC.1458..427H

|doi=10.1063/1.4734451

|s2cid=118566737

}} This theory is an 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 and MOND.

{{cite conference

|last1=Capozziello |first1=S.

|last2=De Laurentis |first2=M.

|year=2013

|title=Extended Gravity: State of the Art and Perspectives

|editor1-last=Rosquist |editor1-first=K.

|editor2-last=Jantzen |editor2-first=R. T.

|editor3-last=Ruffini |editor3-first=R.

|book-title=Proceedings of the Thirteenth Marcel Grossman Meeting on General Relativity

|publisher=World Scientific

|arxiv=1307.4523

|bibcode = 2013arXiv1307.4523C }} This matches gravitational lensing observations without the need for dark matter.

{{cite journal

|last1=Mendoza |first1=S.

|last2=Bernal |first2=T.

|last3=Hernandez |first3=X.

|last4=Hidalgo |first4=J. C.

|last5=Torres |first5=L. A.

|year=2013

|title=Gravitational lensing with f(χ)=χ^3/2 gravity in accordance with astrophysical observations

|journal=Monthly Notices of the Royal Astronomical Society

|volume=433 |issue=3 |pages=1802–1812

|arxiv=1208.6241

|bibcode=2013MNRAS.433.1802M

|doi=10.1093/mnras/stt752

|doi-access=free

}} There is some evidence that it could also explain the dark energy phenomena

{{cite journal

|last1=Carranza |first1=D. A.

|last2=Mendoza |first2=S.

|last3=Torres |first3=L. A.

|year=2012

|title=A cosmological dust model with extended f(χ) gravity

|journal=European Physical Journal C

|volume=73 |page=2282

|arxiv=1208.2502

|bibcode=2013EPJC...73.2282C

|doi=10.1140/epjc/s10052-013-2282-4

|s2cid=118644910

}} and give a solution to the initial conditions problem.

{{cite arXiv

|last1=Hernandez |first1=X.

|last2=Jimenez |first2=M. A.

|year=2013

|title=A first linear cosmological structure formation scenario under extended gravity

|eprint=1307.0777

|class=astro-ph.CO

}}