Weak field and slow motion limits in energy–momentum powered gravity

Özgür Akarsu, A. Kazım Çamlıbel, Nihan Katırcı, İbrahim Semiz, N. Merve Uzun*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

We explore the weak field and slow motion limits, Newtonian and Post-Newtonian limits, of the energy–momentum powered gravity (EMPG), viz., the energy–momentum squared gravity (EMSG) of the form f(TμνTμν)=α(TμνTμν)η with α and η being constants. We have shown that EMPG with η≥0 and general relativity (GR) are not distinguishable by local tests, say, the Solar System tests; as they lead to the same gravitational potential form, PPN parameters, and geodesics for the test particles. However, within the EMPG framework, Mast, the mass of an astrophysical object inferred from astronomical observations such as planetary orbits and deflection of light, corresponds to the effective mass Meff(α,η,M)=M+Mempg(α,η,M), M being the actual physical mass and Mempg being the modification due to EMPG. Accordingly, while in GR we simply have the relation Mast=M, in EMPG we have Mast=M+Mempg. Within the framework of EMPG, if there is information about the values of {α,η} pair or M from other independent phenomena (from cosmological observations, structure of the astrophysical object, etc.), then in principle it is possible to infer not only Mast alone from astronomical observations, but M and Mempg separately. For a proper analysis within EMPG framework, it is necessary to describe the slow motion condition (also related to the Newtonian limit approximation) by |peffeff|≪1 (where peff=p+pempg and ρeff=ρ+ρempg), whereas this condition leads to |p/ρ|≪1 in GR.

Original languageEnglish
Article number101305
JournalPhysics of the Dark Universe
Volume42
DOIs
Publication statusPublished - Dec 2023

Bibliographical note

Publisher Copyright:
© 2023 Elsevier B.V.

Funding

Valuable comments and suggestions by the referees are gratefully acknowledged. The authors thank Elham Nazari for useful discussions. Ö.A. acknowledges the support by the Turkish Academy of Sciences in the scheme of the Outstanding Young Scientist Award ( TÜBA-GEBİP ). N.K. thanks Doğuş University for the financial support provided by the Scientific Research (BAP) project number 2021-22-D1-B01 . Ö.A. and N.K. are supported in part by TÜBİTAK grant 122F124 . N.M.U. is supported by Boğaziçi University Research Fund Grant Number 18541P . Ö.A. and N.K. acknowledge the COST Action CA21136 (CosmoVerse). Valuable comments and suggestions by the referees are gratefully acknowledged. The authors thank Elham Nazari for useful discussions. Ö.A. acknowledges the support by the Turkish Academy of Sciences in the scheme of the Outstanding Young Scientist Award (TÜBA-GEBİP). N.K. thanks Doğuş University for the financial support provided by the Scientific Research (BAP) project number 2021-22-D1-B01. Ö.A. and N.K. are supported in part by TÜBİTAK grant 122F124. N.M.U. is supported by Boğaziçi University Research Fund Grant Number 18541P. Ö.A. and N.K. acknowledge the COST ActionCA21136 (CosmoVerse).

FundersFunder number
COST ActionCA21136
Doğuş University2021-22-D1-B01
TÜBA-GEBİP
Türkiye Bilimsel ve Teknolojik Araştırma Kurumu122F124
Türkiye Bilimler Akademisi
Boğaziçi Üniversitesi18541P

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