BIANCHI-ICOSMOLOGICALMODEL IN f(R,T) GRAVITY
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Date
2020
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University of Zululand
Abstract
Cosmology today is often described as being a ‘precision’ science, which reflects that cosmology had not always been seen as such. The enormous theoretical and experimental data from the cosmic microwave background (CMB), type Ia supernovae (SNe Ia), the Wilkinson Microwave Anisotropy Probe (WMAP), large scale structure (LSS), gravitational lensing, the Sloan Digital Sky Survey (SDSS), baryonic acoustic oscillations (BAO), and PLANCK, has drastically ameliorated cosmology; thus, providing a deeper understanding of the universe. These observations suggest that the universe is currently undergoing an accelerated expansion, where two thirds of its critical energy densityisreservedintheformofanenergycalleddarkenergy(DE).Thisenergyisusually associated with a cosmological constant, and the resulting standard cosmological model is called the ΛCDM model. This humongous episode confronted the fundamental theories of cosmology and astrophysics. Due to some shortcomings of the ΛCDM model, various alternatives have been proposed, which include modifications of general relativity itself, by imposing extra terms in the Einstein-Hilbert action (EH), or by considering dynamical candidates. These modified theories of gravity include GaussBonnet, f(G),higherderivative(HD)theories, f(R) theories, f(T) and f(R,T) gravity theories, while dynamical candidates include the cosmological constant, quintessence, phantom, quintom, k-essence, tachyon and Chaplygin gas, among others.
Thoughthepresentuniverseishomogenousandisotropic,theoreticalstudiesandobservationaldatasupporttheexistenceofananisotropicphaseatearlyevolution,leading to the consideration of anisotropic- background models of the universe. Many authors have explored the features of modified theories of gravity in anisotropic background to studytheearlyuniverse. Amongstthevariousfamiliesofhomogeneous,butanisotropic geometries, the most well-known are the Bianchi type I -IX space-time line elements. However,earlierstudiesonthepossibleeffectsofanisotropicuniversemaketheBianchi type-I model a prime alternative. In particular, a locally-rotationally-symmetric (LRS)
xii
or a plane symmetric spacetime is the simplest version of Bianchi-I models.
Most studies on standard gravity, as well as on modified gravity, assume the cosmic fluid to be prefect, i.e. non-viscous. From a hydrodynamicist’s point of view, this is somewhat visionary, since there are several mechanisms in fluid mechanics, even in homogeneous space without boundaries, it is where bulk viscous fluid come into play. Dissipativeeffects, includingbothbulkandshearviscosity, aresupposedtoplayavery important role in the early evolution of the universe. The bulk viscous pressure term in the matter energy-momentum tensor may lead to an accelerating universe.
This dissertation primarily investigates exact solutions of LRS Bianchi-I cosmological model with and without viscous matter in f(R,T) theory of gravity, where f(R,T) is an arbitrary function of the Ricci scalar R and the trace T of the energy-momentum tensor. In particular, we have studied f(R,T) = R+2f(T), where f(T) = λT with λ being an arbitrary constant. The function f(R,T) = R+2f(T) is used with two noninteracting fluids: one the perfect fluid, and the other from modified f(R,T) gravity. The characteristic of the dynamical evolution of each cosmological model has been performed. A number of viability criteria, such as the existence of exact real solutions and physical viability, have been taken care of from each cosmological model.
This is a four-chapter dissertation comprising the first introductory chapter; chapters two and three, being the actual research work, carried out by the authors; and the concluding chapter.
Description
A dissertation submitted in fulfilment of the requirement for the Degree of Masters of Science in the department of Mathematical Sciences, Faculty of Science, Agriculture and Engineering, at the University of Zululand, 2020.
Keywords
General Relativity and Cosmology, The standardΛCDM model, Cosmological Principle (Homogeneous and Isotropic space-time)., Friedmann-Robertson-Walker (FRW) space-time