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Linearized field equations and extra force in $f (R, T^{(n)})$ extended gravity

Department of Physics, University of Tehran, North Kargar Avenue, 14399-55961 Tehran, Iran

E-mail Address: h.abedi@ut.ac.ir

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,

Francesco Bajardi

Scuola Superiore Meridionale, Largo San Marcellino 10, 80138 Napoli, Italy

INFN Sezione di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy

E-mail Address: francesco.bajardi@unina.it

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, and

Salvatore Capozziello

https://orcid.org/0000-0003-4886-2024

Scuola Superiore Meridionale, Largo San Marcellino 10, 80138 Napoli, Italy

INFN Sezione di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy

Dipartimento di Fisica “Ettore Pancini”, Università degli Studi di Napoli “Federico II”, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, I-80126, Napoli, Italy

Laboratory for Theoretical Cosmology, International Centre of Gravity and Cosmos, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050 Tomsk, Russia

E-mail Address: capozziello@na.infn.it

Corresponding author.

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https://doi.org/10.1142/S0218271822400156Cited by:2 (Source: Crossref)

This article is part of the issue:

Selected papers of the 4th PU International Conference on Gravitation and Cosmology
Guest editors: Muhammad Sharif, Francesco De Paolis, Gonzalo J. Olmo and M. Zaeem Ul Haq Bhatti

Abstract

We consider an extended theory of gravity with Lagrangian $ℒ = f (R, T^{(n)})$ , with $T^{(n)}$ being a $2 n$ th-order invariant made of contractions of the energy–momentum tensor. When $n = 1$ , this theory reduces to $f (R, T)$ gravity, where $T$ accounts for the trace of the energy–momentum tensor. We study the gravitational wave polarization modes, from which it results that when the matter Lagrangian contains dynamical scalar fields minimally coupled to the geometry, further polarization modes arise with respect to General Relativity. Finally, we show that the motion for test particles is nongeodesic and we explicitly obtain the extra force.

Keywords:

PACS: 04.50.−h, 04.20.Cv, 98.80.Jk

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Vol. 31, No. 11

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Received 12 February 2022

Accepted 23 March 2022

Published: 22 April 2022

Keywords