Geodesic deviation in Sáez–Ballester theory

TY - JOUR

T1 - Geodesic deviation in Sáez–Ballester theory

AU - Rasouli, S. M.M.

AU - Sakellariadou, M.

AU - Moniz, Paulo Vargas

N1 - Funding Information: We would like to thank the anonymous referee for valuable comments, which have led to improve the manuscript. PVM and SMMR acknowledge the FCT grants UID-B-MAT/00212/2020 and UID-P-MAT/00212/2020 at CMA-UBI plus the COST Action CA18108 (Quantum gravity phenomenology in the multi–messenger approach). The work of M.S. is supported in part by the Science and Technology Facility Council (STFC), United Kingdom , under the research grant ST/P000258/1 . Publisher Copyright: © 2022 Elsevier B.V.

PY - 2022/9

Y1 - 2022/9

N2 - We study the geodesic deviation (GD) equation in a generalized version of the Sáez–Ballester (SB) theory in arbitrary dimensions. We first establish a general formalism and then restrict to particular cases, where (i) the matter-energy distribution is that of a perfect fluid, and (ii) the spacetime geometry is described by a vanishing Weyl tensor. Furthermore, we consider the spatially flat FLRW universe as the background geometry. Based on this setup, we compute the GD equation as well as the convergence condition associated with fundamental observers and past directed null vector fields. Moreover, we extend that framework and extract the corresponding geodesic deviation in the modified Sáez–Ballester theory (MSBT), where the energy–momentum tensor and potential emerge strictly from the geometry of the extra dimensions. In order to examine our herein GD equations, we consider two novel cosmological models within the SB framework. Moreover, we discuss a few quintessential models and a suitable phantom dark energy scenario within the mentioned SB and MSBT frameworks. Noticing that our herein cosmological models can suitably include the present time of our Universe, we solve the GD equations analytically and/or numerically. By employing the correct energy conditions plus recent observational data, we consistently depict the behavior of the deviation vector η(z) and the observer area distance r0(z) for our models. Concerning the Hubble constant problem, we specifically focus on the observational data reported by the Planck collaboration and the SH0ES collaboration to depict η(z) and r0(z) for our herein phantom model. Subsequently, we contrast our results with those associated with the ΛCDM model. We argue that the MSBT can be considered as a fitting candidate for a proper description of the late evolution of the universe.

AB - We study the geodesic deviation (GD) equation in a generalized version of the Sáez–Ballester (SB) theory in arbitrary dimensions. We first establish a general formalism and then restrict to particular cases, where (i) the matter-energy distribution is that of a perfect fluid, and (ii) the spacetime geometry is described by a vanishing Weyl tensor. Furthermore, we consider the spatially flat FLRW universe as the background geometry. Based on this setup, we compute the GD equation as well as the convergence condition associated with fundamental observers and past directed null vector fields. Moreover, we extend that framework and extract the corresponding geodesic deviation in the modified Sáez–Ballester theory (MSBT), where the energy–momentum tensor and potential emerge strictly from the geometry of the extra dimensions. In order to examine our herein GD equations, we consider two novel cosmological models within the SB framework. Moreover, we discuss a few quintessential models and a suitable phantom dark energy scenario within the mentioned SB and MSBT frameworks. Noticing that our herein cosmological models can suitably include the present time of our Universe, we solve the GD equations analytically and/or numerically. By employing the correct energy conditions plus recent observational data, we consistently depict the behavior of the deviation vector η(z) and the observer area distance r0(z) for our models. Concerning the Hubble constant problem, we specifically focus on the observational data reported by the Planck collaboration and the SH0ES collaboration to depict η(z) and r0(z) for our herein phantom model. Subsequently, we contrast our results with those associated with the ΛCDM model. We argue that the MSBT can be considered as a fitting candidate for a proper description of the late evolution of the universe.

KW - Extra dimensions

KW - FLRW cosmology

KW - Focusing condition

KW - Geodesic deviation

KW - Hubble tension

KW - Induced–matter theory

KW - Mattig relation

KW - Phantom dark energy

KW - Quintessence

KW - Sáez–Ballester theory

UR - http://www.scopus.com/inward/record.url?scp=85138422481&partnerID=8YFLogxK

U2 - 10.1016/j.dark.2022.101112

DO - 10.1016/j.dark.2022.101112

M3 - Article

AN - SCOPUS:85138422481

SN - 2212-6864

VL - 37

JO - Physics of the Dark Universe

JF - Physics of the Dark Universe

M1 - 101112

ER -