Kaluza-Klein dark energy model in Lyra manifold in the presence of massive scalar field
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ORIGINAL ARTICLE
Kaluza-Klein dark energy model in Lyra manifold in the presence of massive scalar field Y. Aditya1
· K. Deniel Raju2,3 · V.U.M. Rao3 · D.R.K. Reddy3
Received: 31 August 2019 / Accepted: 30 October 2019 © Springer Nature B.V. 2019
Abstract In this investigation we intend to study the dynamics of an anisotropic dark energy cosmological model in the presence of a massive scalar field in a modified Riemannian manifold proposed by Lyra (Math. Z. 54:52, 1951) in the background of a five dimensional Kaluza-Klein space time. We solve the Einstein field equations using some physically significant conditions and present a deterministic dark energy cosmological model. We use here the time dependent displacement vector field of the Lyra manifold. All the dynamical parameters of the model, namely, average Hubble parameter, anisotropy parameter, equation of state parameter, dark energy density, deceleration parameter and statefinders are evaluated for our model and their physical relevance to modern cosmology is discussed in detail. Keywords Kaluza-Klein model · DE model · Lyra manifold · Massive scalar meson field
1 Introduction The subject that is attracting several researchers, in modern cosmology, is the accelerated expansion of the universe (Riess et al. 1998; Perlmutter et al. 1999). It has been said
B Y. Aditya
[email protected] D.R.K. Reddy [email protected]
1
Department of Mathematics, GMR Institute of Technology, Rajam 532127, India
2
Department of Mathematics, ANITS (A), Visakhapatnam 531162, India
3
Department of Applied Mathematics, Andhra University, Visakhapatnam 530003, India
that this is caused by an exotic negative pressure which is known as dark energy (DE). Several DE models have been proposed to explain this phenomenon which even today remains as mystery. The cosmological constant is supposed to account for this DE. But it has some serious problems. Hence two approaches have been suggested to describe this mysterious concept. One method is to construct DE model and study their significance in relation to this cosmic inflation. Another way is to modify Einstein’s theory of gravitation and to construct DE models with a special reference to the observations of modern cosmology which throws a better light to explain this scenario. For this purpose, there have been several modifications of Einstein’s theory of gravitation by modifying the EinsteinHilbert action of general relativity and introducing Scalar Fields (SFs) into Einstein theory. Introduction of SFs leads to the well known quintessence models which help to explain the accelerated expansion of the universe. Thus the modified theories of gravitation are f (R) and f (R, T ) theories (Nojiri and Odintsov 2003; Harko et al. 2011) and scalar-tensor theories proposed by Brans and Dicke (1961) and Saez and Ballester (1986). Anisotropic DE models in the above modified theories of gravitation were investigated by numerous researchers (Copeland et al. 2006; Nojiri et al. 2005; Kiran et al. 2014; Reddy et al. 2014; Aditya et al
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