STRING COSMOLOGICAL MODELS IN BIANCHI TYPE-III SPACE-TIME WITH BULK VISCOSITY AND Λ TERM
|
|
- Lucas Higgins
- 5 years ago
- Views:
Transcription
1 Jan. 05. Vol. 6. No ES & F. ll rights reserved ISSN STIN OSMOLOIL MODELS IN BINHI TYPE-III SPE-TIME WITH BULK VISOSITY ND Λ TEM PEETI SONI SPN SHIMLI search Scholar Department of Mathematics Pacific cademy of Higher Education & esearch University Udaipur (ajasthan)india ssoc. Prof. Department of Mathematics Pacific cademy of Higher Education & esearch University Udaipur (ajasthan)india preeti00ni@gmail.com shrimalisapna@gmail.com BSTT The present study deals with exact solution of Einstein field equations in Bianchi type-iii string cosmological models with bulk viscosity and variable cosmological term Λ. Exact solutions of the field equations are obtained by assuming the conditions: the coefficient of the viscosity is proportional to the expansion scalar expansion scalar is proportional to shear scalar and Λ is proportional to the Hubble parameter. The physical implications of the models are also discussed in detail. Keywords: Bianchi-III space-time Bulk Viscosity Variable Λ expansion scalar shear Hubble parameter. INODUTION osmic string in recent years have drawn considerable attention among researchers for various aspects such that the study of the early universe. It is well known that in an earlier stage of the universe when the radiation in the form of photons as well as neutrinos decoupled from matter it behaved like a viscous fluid. Misner [ ] have studied the effect of viscosity on the evolution of cosmological models. Nightingale [] has investigated the role of viscosity in cosmology. Thus we should consider the presence of a material distribution other than a perfect fluid to have realistic cosmological models. Heller and Klimek [] emphasized that the introduction of bulk viscosity effectively removes the initial singularities with in a certain class of cosmological models. The effect of bulk viscosity on the cosmological evolution has been studied by a number of authors in the fram work of general theory of relativity viz. Pavon et al. [5] Maartens [6] Kalyani and Singh [7] Singh et al. [8]. 7 On other hand one outstanding problem in cosmology is the cosmological constant problem [9 0]. Since its introduction and its significance has been studied from time to time by various workers [-]. In modern cosmological theories the cosmological constant remains a focal point of interest. wide range of observations now suggests compellingly that the universe possesses a non-zero cosmological constant []. ecently Singh et al. [5] investigated Bianchi type- III cosmological models with gravitational constant and the cosmological constant Λ. In this chapter we have investigated Bianchi type-iii string cosmological models with bulk viscosity and cosmological term Λ(t). To obtain an explicit solution we assume that the coefficient of the viscosity is proportional to the expansion scalar and the expansion scalar is proportional to the shear scalar and for the cosmological term Λ we assume that it is proportional the Hubble parameter Λ H.
2 Jan. 05. Vol. 6. No ES & F. ll rights reserved ISSN B B (a). DEIVITON OF FIELD EQUTION. THE VITTIONL FIELD: In our case we consider the Bianchi type- III metric in the form ds dt dx B e dy dz x () where B and are functions of time alone and a is a constant. The metric () has the following non-zero christoffel symbols. B x e B B B B B B B B B B B B (b) (c) (d) B B (e) From () one finds the following icci scalar for the Bianchi type-iiii universe B B B B B B () The non-vanishing components of Einstein j j tensor i i are given by B B B B (a) BBe x. (b) Where dots on B represents the ordinary differentiation with respect to t. The surviving components of the mixed icci tensor j i are as follows: B B B B (c) 8
3 Jan. 05. Vol. 6. No ES & F. ll rights reserved ISSN B B B B (d) T (8d) B B (e) T 0. (8e) B. VISOUS FLUID: The energy momentum tensor for a cloud of string dust with a bulk viscous fluid of string is given by T = u u x x u ; l g u u j j j l j j i i i i i Where u i and x i satisfy the condition. i i i uu = x x = u x = 0 (6) i i i In equation (5) is the proper energy density for a cloud string with particle attached them is the coefficient of bulk viscosity is the string tension density of particles u i is the cloud four-velocity vector and x i is a unit space-like vector representing the direction of string. If the particle density of the configuration is denoted by p then we have ρ = ρ + p (5) (7) In a co-moving system of references such that ui = (0 0 0 ) we have T (8a). FIELD EQUTION: Einstein s field equations with 8 = and variable cosmological term Λ (t) in suitable units are ij gij Tij t g (9) The field equation (9) and (8) subsequently lead to the following system of equations: B B B B (0a) (0b) B B B B B B B B (0c) (0d) T (8b) B 0 B (0e) T (8c) 9 The scalar expansion and components of shear ij are given by
4 Jan. 05. Vol. 6. No ES & F. ll rights reserved ISSN B B () scalar is proportional to the shear scalar which leads to the B = n (7) B B () x B e B B () Where n is a constant and the second condition is Λ = ah (8) Where H is Hubble parameter and a is a positive constant. From equation (0e) we have = B (9) where B B. () = 0 (5) Therefore B B B B B B (6) From equation (9) without any loss of generality we can take = B (0) In order to obtain the more general solution we assume that the coefficient of bulk viscosity is inversely proportional to the expansion therefore we have = K () Substituting equation (7) into equation () we have = n () By the use of the equation (7) (9) (0) and () the field equation (0a) reduces to. SOLUTIONS OF THE FIELD EQUTION: s the field equations (0) are a system of five equations with seven unknown parameters B and Λ. Thus two more relations are needed to solve the system completely. We assume that one condition is that the expansion a nn K n Equation () can be rewritten as () / n n n K n a n () On integrating equation () we obtain 0
5 Jan. 05. Vol. 6. No ES & F. ll rights reserved ISSN Kn an t n n e (5) Where is constant of integration. gain integrating equation () we get n K n n n e an n K n n n a n t K n n n (6) Where is constant of integration Therefore from equation (7) (9) and (5) we obtain ds K n n dt n n e an nn K n n nn an t K n n n x K n n dx e dy n n K n n an n t K n n n e dz an n (9) For the model (8) the expressions for the energy density the string tension density the particle density p the expansion scalar the shear scalar and the cosmological term are respectively given by B n K n n n e an K n n n n e an n n K n n n n a n t K n n n n n K n n (7) n n a n t K n n n (8) K n n n n n a n a n t t n n n e e an n n K n n K n n n n e an an t n a n K n n n n n K n n a n a n t t n n n e e an (0) Hence the metric () reduces to form
6 Jan. 05. Vol. 6. No ES & F. ll rights reserved ISSN n a 5na a K n n n n n e an an t n an t n n n n K n n n n n e an n n K n n K n n 8na a K n n n n an n t n n e K an n eferences [] Misner.W. (967) : Nature. 0. () [] Misner.W. (968) : J. strophys. 5. [] Nightingale J.P. (97) : J. strophys. K n n n n [] Heller M. and Klimek M. (975) : strophys. Space Sci. 6. a n a n [5] Pavon D. Bafaluy J.and Jou D. (99) : n t t n n e e lass Quantum ravity an [6] Maartens. (995) : lass Quantum ravity. 55. () [7] Kalyani D. and Singh.P. (997) : In new direction in elativity and osmology. a n K n N n n e e an a n a n t t n n K n n n n () a n a n t t n n n e e an n n (5) n an K n n n t n n e K a n n In summery we have presented a new class of Bianchi type-iiii string cosmological () models with bulk viscosity and cosmological term Λ(t). To obtain an explicit solution we adopt the conditions and Λ H. Thus the cosmological model for a string n n n K n n p cosmology with bulk viscosity and n n cosmological term is obtained. The model describes a shearing non-rotating continuously a n a n n t t expanding universe with a big-bang start. The n n e e physical and geometrical aspects of the model an are also discussed. In the absences of cosmological term Λ the model reduces to the string model with bulk viscosity investigated by Bali and Pradhan (007).
7 Jan. 05. Vol. 6. No ES & F. ll rights reserved ISSN [8] Singh T. Beesham. and Mbokazi W.S. (998) : en. ela. ravit [9] Ng Y. J. (99) : Int. J. Mod. Phys. D 5. [0] Weinberg S. (989) : ev. Mod. Phys. 6. [] Zeldovich Ya. B. (968) :Sov. Phys. Usp. 8. [] Linde. D. (97) : ZETP. Lett [] Krauss L. M. and Turner M. S. (995) : en. el. rav [].. eiss et al. (00) : stron. J [5] Singh J. P. Tiwari. K.and Pratibha Shukla (007) : hin. Phys. Lett. ().
International Journal of Applied and Universal Research E-ISSN No: Volume III, Issue V, Sept-Oct Available online at:
COSMOLOGICAL MODELS BIANCHI TYPE II WITH BULK VISCOSITY IN GENERAL THEORY OF RELATIVITY R.K. Dubey 1, Shishir Kumar Srivastava 2, Dhirendra Tripathi 3 1 Department of Mathematics Govt. S.K.N.P.G. College,
More informationBianchi Type-VI Bulk Viscous Fluid String Cosmological Model in General Relativity
Bulg. J. Phys. 38 2011 14 14 Bianchi Type-VI Bulk Viscous Fluid String Cosmological Model in General Relativity S.P. Kandalkar 1, P.P. Khade 2, S.P. Gawande 1 1 Department of Mathematics, Government Vidarbha
More informationBianchi Type VIII Inflationary Universe with Massless Scalar Field in General Relativity
August 05 Volume 6 Issue 8 pp. 679-68 Bali,. & Swati, Bianchi Type VIII Inflationary Universe with Massless Scalar Field in General elativity Bianchi Type VIII Inflationary Universe with Massless Scalar
More informationMagnetized Anisotropic Bianchi Type-VI Cosmological Model Containing Dark Energy
IOSR Journal of pplied Physics (IOSR-JP) e-issn: 78-486Volume 0, Issue Ver II (Jan eb 08), PP 3-35 wwwiosrjournalsorg Magnetized nisotropic Bianchi Type-VI Cosmological Model Containing Dark Energy Mukunda
More informationString Fluid Cosmological Model with Magnetic Field in Bimetric Theory of Gravitation
Available at http://pvamu.edu/aam Appl. Appl. Math. ISSN: 1932-9466 Vol. 9, Issue 1 (June 2014), pp. 246-259 Applications and Applied Mathematics: An International Journal (AAM) String Fluid Cosmological
More informationBianchi Type-III Inflationary Universe with Constant Deceleration Parameter in General Relativity
Bulg. J. Phys. 38 2011 139 1 Bianchi Type-III Inflationary Universe with Constant Deceleration Parameter in General Relativity S.D. Katore Department of Mathematics, S.G.B. Amravati University, Amravati
More informationLRS Bianchi Type I Cosmological Model with Bulk Viscosity in Lyra Geometry
Bulg. J. Phys. 4 (5 4 5 LRS Bianchi Type I Cosmological Model with Bulk Viscosity in Lyra Geometry S.P. Kandalkar, S. Samdurkar Department of Mathematics, Govt. Vidarbha Institute of Science & Humanities,
More informationBianchi Type VI0 Inflationary Universe with Constant Deceleration Parameter and Flat Potential in General Relativity
Advances in Astrophysics, Vol., No., May 7 https://dx.doi.org/.66/adap.7. 67 Bianchi ype VI Inflationary Universe with Constant Deceleration Parameter and Flat Potential in General Relativity Raj Bali
More informationInternational Journal of Applied and Universal Research ISSN No: Volume III, Issue II, Mar-Apr Available online at:
BIANCHI TYPE III ELECTRO MAGNETIZED COSMOLOGICAL MODEL WITH NAMBU STRINGS IN GENERAL THEORY OF RELATIVITY R.K.Dubey 1, Anil Saini 2, Neelam Yadav 3 1 Department of Mathematics, Govt. SKN PG College Mauganj
More informationINFLATIONARY SOLUTIONS OF BIANCHI TYPE I STRING MODELS WITH BULK VISCOUS FLUID IN BIMETRIC THEORY OF GRAVITATION
International Journal of Researches In iosciences, griculture & Technology May 06 ISSN No. Online 347-57X INFLTIONRY SOLUTIONS OF INCHI TYPE I STRING MODELS WITH ULK VISCOUS FLUID IN IMETRIC THEORY OF
More informationBianchi-IX string cosmological model in Lyra geometry
PRAMANA cfl Indian Academy of Sciences Vol. 60, No. 6 journal of June 200 physics pp. 115 1159 Bianchi-IX string cosmological model in Lyra geometry F RAHAMAN 1;2, S CHAKRABORTY 2, N BEGUM 1, M HOSSAIN
More informationBianchi Type-VI Inflationary Universe in General Relativity
March 01 Vol. 3 Issue 5 pp. 7-79 Katore S. D. & Chopade B. B. Bianchi Type-VI Inflationary Universe in General Relativity Bianchi Type-VI Inflationary Universe in General Relativity 7 Article Shivdas.
More informationNEW EXACT SOLUTION OF BIANCHI TYPE V COSMOLOGICAL STIFF FLUID MODEL IN LYRA S GEOMETRY
ASTROPHYSICS NEW EXACT SOLUTION OF BIANCHI TYPE V COSMOLOGICAL STIFF FLUID MODEL IN LYRA S GEOMETRY VINEET K. YADAV 1,, LALLAN YADAV 2, ANIL KUMAR YADAV 3 1,2 Department of Physics, D. D. U. Gorahpur University,
More informationLocally-rotationally-symmetric Bianchi type-v cosmology in general relativity
PRAMANA c Indian Academy of Sciences Vol. 72, No. 2 journal of February 2009 physics pp. 429 443 Locally-rotationally-symmetric Bianchi type-v cosmology in general relativity C P SINGH Department of Applied
More informationInflationary Universe Scenario in Bianchi Type VI 0 Space Time with Flat Potential and Bulk Viscosity in General Relativity
IOS Journal of pplied Physics (IOS-JP) e-issn: 78-86.Volume 9, Issue Ver. I (Jan. Feb. 07), PP -0 www.iosrjournals.org Inflationary Universe Scenario in ianchi Type VI 0 Space Time with Flat Potential
More informationA higher-dimensional Bianchi type-i inflationary Universe in general relativity
PRAMANA c Indian Academy of Sciences Vol. 78, No. 1 journal of January 01 physics pp. 101 107 A higher-dimensional Bianchi type-i inflationary Universe in general relativity SDKATORE 1,, K S ADHAV 1, V
More informationSOME LRS BIANCHI TYPE-I COSMOLOGICAL MODELS WITH ZERO-MASS SCALAR FIELD
SOME LRS BIANCHI TYPE-I COSMOLOGICAL MODELS WITH ZERO-MASS SCALAR FIELD By Purushottam R.B.S. Yadav Manish Kumar Deptt. of Mathematics P.G. Deptt. of Mathematics P.G. Deptt. of Mathematics Nalanda College
More informationAnisotropic Lyra cosmology
PRAMANA c Indian Academy of Sciences Vol. 62, No. 6 journal of June 2004 physics pp. 87 99 B B BHOWMIK and A RAJPUT 2 Netaji Subhas Vidyaniketan Higher Secondary School, Basugaon 783 372, Dist. Kokrajhar,
More informationBianchi Type V Magnetized String Dust Universe with Variable Magnetic Permeability
EJTP 5, No. 19 (008) 105 114 Electronic Journal of Theoretical Physics Bianchi Type V Magnetized String Dust Universe with Variable Magnetic Permeability Raj Bali Department of Mathematics, University
More informationKANTOWSKI-SACHS INFLATIONARY UNIVERSE IN GENERAL RELATIVITY
KNTOWSKI-SCHS INFLTIONY UNIVESE IN GENEL ELTIVITY ------------------------------------------------------------------------------------ This wor has been published in Internional J. of Theoretical Physics
More informationA Magnetized Kantowski-Sachs Inflationary Universe in General Relativity
Bulg. J. Phys. 37 (2010) 144 151 A Magnetized Kantowski-Sachs Inflationary Universe in General Relativity S.D. Katore PG Department of Mathematics, SGB Amravati University, Amravati, India Received 10
More informationTHE DARK SIDE OF THE COSMOLOGICAL CONSTANT
THE DARK SIDE OF THE COSMOLOGICAL CONSTANT CAMILO POSADA AGUIRRE University of South Carolina Department of Physics and Astronomy 09/23/11 Outline 1 Einstein s Greatest Blunder 2 The FLRW Universe 3 A
More informationBRANE COSMOLOGY and Randall-Sundrum model
BRANE COSMOLOGY and Randall-Sundrum model M. J. Guzmán June 16, 2009 Standard Model of Cosmology CMB and large-scale structure observations provide us a high-precision estimation of the cosmological parameters:
More informationNew Non-Diagonal Singularity-Free Cosmological Perfect-Fluid Solution
New Non-Diagonal Singularity-Free Cosmological Perfect-Fluid Solution arxiv:gr-qc/0201078v1 23 Jan 2002 Marc Mars Departament de Física Fonamental, Universitat de Barcelona, Diagonal 647, 08028 Barcelona,
More informationPLANE SYMMETRIC UNIVERSE WITH COSMIC STRING AND BULK VISCOSITY IN SCALAR TENSOR THEORY OF GRAVITATION 1. INTRODUCTION
PLANE SYMMETRIC UNIVERSE WITH COSMIC STRING AND BULK VISCOSITY IN SCALAR TENSOR THEORY OF GRAVITATION S.D. KATORE, A.Y. SHAIKH Department of Mathematics, S.G.B. Amravati University, Amravati-60, India
More informationGravitational collapse and the vacuum energy
Journal of Physics: Conference Series OPEN ACCESS Gravitational collapse and the vacuum energy To cite this article: M Campos 2014 J. Phys.: Conf. Ser. 496 012021 View the article online for updates and
More informationClassical and Quantum Bianchi type I cosmology in K-essence theory
Classical and Quantum Bianchi type I cosmology in K-essence theory Luis O. Pimentel 1, J. Socorro 1,2, Abraham Espinoza-García 2 1 Departamento de Fisica de la Universidad Autonoma Metropolitana Iztapalapa,
More informationTheoretical Models of the Brans-Dicke Parameter for Time Independent Deceleration Parameters
Theoretical Models of the Brans-Dicke Parameter for Time Independent Deceleration Parameters Sudipto Roy 1, Soumyadip Chowdhury 2 1 Assistant Professor, Department of Physics, St. Xavier s College, Kolkata,
More informationA Mathematical Aspect of Higher Dimensional. Cosmological Models with Varying G and ΛTerm
Int. J. Contemp. Math. Sciences, Vol. 7, 01, no. 1, 1005-101 A Mathematical Aspect of Higher Dimensional Cosmological Models with Varying G and ΛTerm. K. Dubey Department of Mathematics, Govt. Science
More informationResearch Article Bianchi Types II, VIII, and IX String Cosmological Models with Bulk Viscosity in a Theory of Gravitation
International cholarly Research Network IRN Mathematical Physics Volume 2012, Article ID 341612, 15 pages doi:10.5402/2012/341612 Research Article Bianchi Types II, VIII, and IX tring Cosmological Models
More informationarxiv:gr-qc/ v1 20 May 2005
EMERGENT UNIVERSE IN STAROBINSKY MODEL arxiv:gr-qc/0505103v1 20 May 2005 S. Mukherjee and B.C. Paul Physics Department, North Bengal University Dist : Darjeeling, PIN : 734 430, India. S. D. Maharaj Astrophysics
More informationBianchi Type-IX Bulk Viscous String Cosmological Model in f(r,t) Gravity with Special Form of Deceleration Parameter
International Journal of heoretical and Mathematical Physics 0, (6): 0-7 DOI: 0593/jijtmp00060 Bianchi ype-ix Bul Viscous String Cosmological Model in f(r,) Gravity with Special Form of Deceleration Parameter
More informationMASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.286: The Early Universe October 27, 2013 Prof. Alan Guth PROBLEM SET 6
MASSACHUSETTS INSTITUTE OF TECHNOLOGY Physics Department Physics 8.86: The Early Universe October 7, 013 Prof. Alan Guth PROBLEM SET 6 DUE DATE: Monday, November 4, 013 READING ASSIGNMENT: Steven Weinberg,
More informationNonsingular big-bounce cosmology from spin and torsion
Nonsingular big-bounce cosmology from spin and torsion Nikodem J. Popławski Department of Physics, Indiana University, Bloomington, IN 22 nd Midwest Relativity Meeting University of Chicago, Chicago, IL
More informationGeometrical Behaviuors of LRS Bianchi Type-I Cosmological Model
EJTP 6, No. 22 (2009) 79 84 Electronic Journal of Theoretical Physics Geometrical Behaviuors of LRS Bianchi Type-I Cosmological Model Hassan Amirhashchi 1, Hishamuddin Zainuddin 2 and Hamid Nil Saz Dezfouli
More informationSteady-State Cosmology in the Yilmaz Theory of Gravitation
Steady-State Cosmology in the Yilmaz Theory of ravitation Abstract H. E. Puthoff Institute for Advanced Studies at Austin 43 W. Braker Ln., Suite 3 Austin, Texas 78759 Yilmaz has proposed a modification
More informationFRW UNIVERSE WITH VARIABLE G AND Λ TERM IN f(r,t ) GRAVITY
FRW UNIVERSE WITH VARIABLE G AND Λ TERM IN f(r,t ) GRAVITY G. P. SINGH a, BINAYA K. BISHI b Department of Mathematics, Visvesvaraya National Institute of Technology Nagpur, Nagpur-440010, India E-mail:
More informationDYNAMIC COSMOLOGICAL CONSTANT IN BRANS DICKE THEORY
DYNAMIC COSMOLOGICAL CONSTANT IN BRANS DICKE THEORY G P SINGH, AY KALE, J TRIPATHI 3 Department of Mathematics, Visvesvaraya National Institute of Technology, Nagpur - 44, India Department of Mathematics,
More informationBianchi Type-VI0Dark Energy Cosmological Models in General Relativity
Global Journal of Science Frontier Research Mathematics and Decision Sciences Volume 12 Issue 12 Version 1.0 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals
More informationON VARIATION OF THE METRIC TENSOR IN THE ACTION OF A PHYSICAL FIELD
ON VARIATION OF THE METRIC TENSOR IN THE ACTION OF A PHYSICAL FIELD L.D. Raigorodski Abstract The application of the variations of the metric tensor in action integrals of physical fields is examined.
More informationAdS/CFT and Second Order Viscous Hydrodynamics
AdS/CFT and Second Order Viscous Hydrodynamics Micha l P. Heller Institute of Physics Jagiellonian University, Cracow Cracow School of Theoretical Physics XLVII Course Zakopane, 20.06.2007 Based on [hep-th/0703243]
More informationBIANCHI TYPE I ANISOTROPIC UNIVERSE WITHOUT BIG SMASH DRIVEN BY LAW OF VARIATION OF HUBBLE S PARAMETER ANIL KUMAR YADAV
BIANCHI TYPE I ANISOTROPIC UNIVERSE WITHOUT BIG SMASH DRIVEN BY LAW OF VARIATION OF HUBBLE S PARAMETER ANIL KUMAR YADAV Department of Physics, Anand Engineering College, Keetham, Agra -282 007, India E-mail:
More informationDynamics of Bianchi type-vi 0 holographic dark energy models in general relativity and Lyra s geometry
Pramana J. Phys. (2017) 88: 0 DOI 10.1007/s1204-016-18-z c Indian Academy of Sciences Dynamics of Bianchi type-vi 0 holographic dark energy models in general relativity and Lyra s geometry S D KATORE and
More informationInternational Journal of Emerging Technologies in Computational and Applied Sciences (IJETCAS)
International Association of Scientific Innovation and Research (IASIR) (An Association Unifying the Sciences, Engineering, and Applied Research) International Journal of Emerging Technologies in Computational
More informationarxiv:gr-qc/ v1 9 Mar 2000
CAN A KASNER UNIVERSE WITH A VISCOUS COSMOLOGICAL FLUID BE ANISOTROPIC? I. Brevik 1 arxiv:gr-qc/0003039v1 9 Mar 2000 Division of Applied Mechanics, Norwegian University of Science and Technology, N-7491
More informationFundamental Theories of Physics in Flat and Curved Space-Time
Fundamental Theories of Physics in Flat and Curved Space-Time Zdzislaw Musielak and John Fry Department of Physics The University of Texas at Arlington OUTLINE General Relativity Our Main Goals Basic Principles
More informationMATHEMATICAL TRIPOS Part III PAPER 53 COSMOLOGY
MATHEMATICAL TRIPOS Part III Wednesday, 8 June, 2011 9:00 am to 12:00 pm PAPER 53 COSMOLOGY Attempt no more than THREE questions. There are FOUR questions in total. The questions carry equal weight. STATIONERY
More informationOddities of the Universe
Oddities of the Universe Koushik Dutta Theory Division, Saha Institute Physics Department, IISER, Kolkata 4th November, 2016 1 Outline - Basics of General Relativity - Expanding FRW Universe - Problems
More informationCanadian Journal of Physics. Anisotropic solution in phantom cosmology via Noether symmetry approach
Anisotropic solution in phantom cosmology via Noether symmetry approach Journal: Canadian Journal of Physics Manuscript ID cjp-2017-0765.r2 Manuscript Type: Article Date Submitted by the Author: 07-Dec-2017
More informationNon-gravitating waves
Non-gravitating waves D C Robinson Mathematics Department King s College London Strand London WC2R 2LS United Kingdom email: david.c.robinson@kcl.ac.uk October 6, 2005 Abstract: It is pointed out that
More informationarxiv:gr-qc/ v3 17 Jul 2003
REGULAR INFLATIONARY COSMOLOGY AND GAUGE THEORIES OF GRAVITATION A. V. Minkevich 1 Department of Theoretical Physics, Belarussian State University, av. F. Skoriny 4, 0050, Minsk, Belarus, phone: +37517095114,
More informationCurved Spacetime III Einstein's field equations
Curved Spacetime III Einstein's field equations Dr. Naylor Note that in this lecture we will work in SI units: namely c 1 Last Week s class: Curved spacetime II Riemann curvature tensor: This is a tensor
More informationBianchiTypeVICosmologicalModelwithQuadraticformofTimeDependentTerminGeneralRelativity
Global Journal of Science Frontier Research: A Physics and Space Science Volume 16 Issue 6 Version 1.0 Year 2016 Type : Double Blind Peer Reviewed International Research Journal Publisher: Global Journals
More informationGeneral Relativity. Einstein s Theory of Gravitation. March R. H. Gowdy (VCU) General Relativity 03/06 1 / 26
General Relativity Einstein s Theory of Gravitation Robert H. Gowdy Virginia Commonwealth University March 2007 R. H. Gowdy (VCU) General Relativity 03/06 1 / 26 What is General Relativity? General Relativity
More informationLecture 1 General relativity and cosmology. Kerson Huang MIT & IAS, NTU
A Superfluid Universe Lecture 1 General relativity and cosmology Kerson Huang MIT & IAS, NTU Lecture 1. General relativity and cosmology Mathematics and physics Big bang Dark energy Dark matter Robertson-Walker
More informationProblem Set #4: 4.1, 4.3, 4.5 (Due Monday Nov. 18th) f = m i a (4.1) f = m g Φ (4.2) a = Φ. (4.4)
Chapter 4 Gravitation Problem Set #4: 4.1, 4.3, 4.5 (Due Monday Nov. 18th) 4.1 Equivalence Principle The Newton s second law states that f = m i a (4.1) where m i is the inertial mass. The Newton s law
More informationNumber-Flux Vector and Stress-Energy Tensor
Massachusetts Institute of Technology Department of Physics Physics 8.962 Spring 2002 Number-Flux Vector and Stress-Energy Tensor c 2000, 2002 Edmund Bertschinger. All rights reserved. 1 Introduction These
More informationStrings, gauge theory and gravity. Storrs, Feb. 07
Strings, gauge theory and gravity Storrs, Feb. 07 Outline Motivation - why study quantum gravity? Intro to strings Gravity / gauge theory duality Gravity => gauge: Wilson lines, confinement Gauge => gravity:
More informationHypersurface-homogeneous cosmological models with anisotropic dark energy in Saez Ballester theory of gravitation
Pramana J. Phys. (207) 88: 8 DOI 0.007/s204-06-7-4 c Indian Academy of Sciences Hypersurface-homogeneous cosmological models with anisotropic dark energy in Saez Ballester theory of gravitation MVERMA,
More informationBIANCHI TYPE-III COSMOLOGICAL MODEL WITH VARIABLE G AND Λ-TERM IN GENERAL RELATIVITY
BIANCHI TYPE-III COSMOLOGICAL MODEL WITH VARIABLE G AND Λ-TERM IN GENERAL RELATIVITY HASSAN AMIRHASHCHI 1, H. ZAINUDDIN 2,a, ANIRUDH PRADHAN 2,3 1 Young Researchers Club, Mahshahr Branch, Islamic Azad
More informationarxiv:gr-qc/ v1 1 Nov 2002
International Journal of Modern Physics D, c World Scientific Publishing Company Vol. 0, No. 0 (2002 000 000 PLANE-SYMMETRIC INHOMOGENEOUS BULK VISCOUS COSMOLOGICAL MODELS WITH VARIABLEΛ arxiv:gr-qc/0211002v1
More informationA Study of the Variable Equation-of-State Parameter in the Framework of Brans-Dicke Theory
International Journal of Pure and Applied Physics. ISSN 0973-1776 Volume 13, Number 3 (2017), pp. 279-288 Research India Publications http://www.ripublication.com A Study of the Variable Equation-of-State
More informationarxiv:gr-qc/ v1 2 Apr 2002
ENERGY AND MOMENTUM OF A STATIONARY BEAM OF LIGHT Thomas Bringley arxiv:gr-qc/0204006v1 2 Apr 2002 Physics and Mathematics Departments, Duke University Physics Bldg., Science Dr., Box 90305 Durham, NC
More informationTachyon scalar field in DBI and RSII cosmological context
Tachyon scalar field in DBI and RSII cosmological context Neven Bilic, Goran S. Djordjevic, Milan Milosevic and Dragoljub D. Dimitrijevic RBI, Zagreb, Croatia and FSM, University of Nis, Serbia 9th MATHEMATICAL
More informationarxiv:gr-qc/ v1 9 Aug 2006
Nonlinear spinor field in Bianchi type-i cosmology: accelerated regimes Bijan Saha arxiv:gr-qc/0608047v1 9 Aug 2006 Laboratory of Information Technologies Joint Institute for Nuclear Research, Dubna 141980
More informationGeneral relativity and the Einstein equations
April 23, 2013 Special relativity 1905 Let S and S be two observers moving with velocity v relative to each other along the x-axis and let (t, x) and (t, x ) be the coordinate systems used by these observers.
More informationModern Cosmology / Scott Dodelson Contents
Modern Cosmology / Scott Dodelson Contents The Standard Model and Beyond p. 1 The Expanding Universe p. 1 The Hubble Diagram p. 7 Big Bang Nucleosynthesis p. 9 The Cosmic Microwave Background p. 13 Beyond
More informationViscosity Effects on Anisotropic Universe in Curvature-Matter Coupling Gravity
Commun. Theor. Phys. 69 08) 537 543 Vol. 69, No. 5, May, 08 Viscosity Effects on Anisotropic Universe in Curvature-Matter Coupling Gravity M. Sharif and Aisha Siddiqa Department of Mathematics, University
More informationSome geometrical aspects of Bianchi type-i space time
THEORETIAL AND APPLIED MEHANIS vol. 27, pp. 79-86, 2002 Some geometrical aspects of Bianchi type-i space time G.Mohanty, R..Sahu, P.K.Sahoo Submitted 1 March, 2000 Abstract A problem of spatially homogeneous
More informationRelativity, Gravitation, and Cosmology
Relativity, Gravitation, and Cosmology A basic introduction TA-PEI CHENG University of Missouri St. Louis OXFORD UNIVERSITY PRESS Contents Parti RELATIVITY Metric Description of Spacetime 1 Introduction
More informationRelic Gravitons, Dominant Energy Condition and Bulk Viscous Stresses
TUPT-03-99 april 1999 arxiv:gr-qc/9903113v1 31 Mar 1999 Relic Gravitons, Dominant Energy Condition and Bulk Viscous Stresses Massimo Giovannini 1 Institute of Cosmology, Department of Physics and Astronomy
More informationarxiv: v2 [gr-qc] 1 Oct 2009
On the cosmological effects of the Weyssenhoff spinning fluid in the Einstein-Cartan framework Guilherme de Berredo-Peixoto arxiv:0907.1701v2 [gr-qc] 1 Oct 2009 Departamento de Física, ICE, Universidade
More informationCosmological Issues. Consider the stress tensor of a fluid in the local orthonormal frame where the metric is η ab
Cosmological Issues 1 Radiation dominated Universe Consider the stress tensor of a fluid in the local orthonormal frame where the metric is η ab ρ 0 0 0 T ab = 0 p 0 0 0 0 p 0 (1) 0 0 0 p We do not often
More informationOutline. Covers chapter 2 + half of chapter 3 in Ryden
Outline Covers chapter + half of chapter 3 in Ryden The Cosmological Principle I The cosmological principle The Cosmological Principle II Voids typically 70 Mpc across The Perfect Cosmological Principle
More informationGeneral Relativity Lecture 20
General Relativity Lecture 20 1 General relativity General relativity is the classical (not quantum mechanical) theory of gravitation. As the gravitational interaction is a result of the structure of space-time,
More informationVanishing Dimensions in Four Dimensional Cosmology with Nonminimal Derivative Coupling of Scalar Field
Advanced Studies in Theoretical Physics Vol. 9, 2015, no. 9, 423-431 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/astp.2015.5234 Vanishing Dimensions in Four Dimensional Cosmology with Nonminimal
More informationHypersurface-homogeneous Universe filled with perfect fluid in f(r, T) theory of gravity
Pramana J. Phys. (6) 87: 83 DOI.7/s43-6-99- c Indian Academy of Sciences Hypersurface-homogeneous Universe filled with perfect fluid in f(r, T) theory of gravity A Y SHAIKH, and S D KATORE Department of
More informationarxiv:gr-qc/ v1 24 Dec 2001
CIRI/01-swkg02 Naked Singularities in Spherically Symmetric, Self-Similar Spacetimes Sanjay M. Wagh Central India Research Institute, Post Box 606, Laxminagar, Nagpur 440 022, India E-mail:ciri@vsnl.com
More informationEmergent Universe by Tunneling. Pedro Labraña, ICC, Universidad de Barcelona and Facultad de Ciencias, Universidad del Bío-Bío, Chile.
Emergent Universe by Tunneling Pedro Labraña, ICC, Universidad de Barcelona and Facultad de Ciencias, Universidad del Bío-Bío, Chile. The Emergent Universe scenario Is Eternal Inflation, past eternal?
More informationAn introduction to General Relativity and the positive mass theorem
An introduction to General Relativity and the positive mass theorem National Center for Theoretical Sciences, Mathematics Division March 2 nd, 2007 Wen-ling Huang Department of Mathematics University of
More informationNew exact cosmological solutions to Einstein s gravity minimally coupled to a Quintessence field
New exact cosmological solutions to Einstein s gravity minimally coupled to a Quintessence field Olga Arias, Tame Gonzalez and Israel Quiros Physics Department. Las Villas Central University. Santa Clara
More informationResearch Article Axially Symmetric Bulk Viscous String Cosmological Models in GR and Brans-Dicke Theory of Gravitation
ISRN stronomy and strophysics Volume 2013, rticle ID 543483, 5 pages http://dx.doi.org/10.1155/2013/543483 Research rticle xially Symmetric Bulk Viscous String Cosmological Models in GR and Brans-Dicke
More informationarxiv:gr-qc/ v1 14 Jul 1994
LINEAR BIMETRIC GRAVITATION THEORY arxiv:gr-qc/9407017v1 14 Jul 1994 M.I. Piso, N. Ionescu-Pallas, S. Onofrei Gravitational Researches Laboratory 71111 Bucharest, Romania September 3, 2018 Abstract A general
More informationDark Matter as a consequence of electric charge non-conservation - will it remain dark forever?
Dark Matter as a consequence of electric charge non-conservation - will it remain dark forever? Richard M. Weiner Laboratoire de Physique Théorique, Univ. Paris-Sud, Orsay, France and Physics Department,
More informationGENERAL RELATIVISTIC SINGULARITY-FREE COSMOLOGICAL MODEL
GENERAL RELATIVISTIC SINGULARITY-FREE COSMOLOGICAL MODEL arxiv:0904.3141v2 [physics.gen-ph] 16 Aug 2009 Marcelo Samuel Berman 1 1 Instituto Albert Einstein / Latinamerica - Av. Candido Hartmann, 575 -
More informationTowards a future singularity?
BA-TH/04-478 February 2004 gr-qc/0405083 arxiv:gr-qc/0405083v1 16 May 2004 Towards a future singularity? M. Gasperini Dipartimento di Fisica, Università di Bari, Via G. Amendola 173, 70126 Bari, Italy
More informationCOSMOLOGY The Origin and Evolution of Cosmic Structure
COSMOLOGY The Origin and Evolution of Cosmic Structure Peter COLES Astronomy Unit, Queen Mary & Westfield College, University of London, United Kingdom Francesco LUCCHIN Dipartimento di Astronomia, Universita
More informationarxiv: v1 [gr-qc] 9 Jun 2008
VISCOUS DARK COSMOLOGY WITH ACCOUNT OF QUANTUM EFFECTS I. BREVIK 1 and O. GORBUNOVA 2 arxiv:0806.1399v1 [gr-qc] 9 Jun 2008 Department of Energy and Process Engineering, Norwegian University of Science
More informationDecaying Dark Matter, Bulk Viscosity, and Dark Energy
Decaying Dark Matter, Bulk Viscosity, and Dark Energy Dallas, SMU; April 5, 2010 Outline Outline Standard Views Dark Matter Standard Views of Dark Energy Alternative Views of Dark Energy/Dark Matter Dark
More informationThe Perfect Cosmological Principle
Cosmoloy AS7009, 0 Lecture Outline The cosmoloical principle: Isotropy Homoeneity Bi Ban vs. Steady State cosmoloy Redshift and Hubble s law Scale factor, Hubble time, Horizon distance Olbers paradox:
More informationCosmological Implications of Spinor-Torsion Coupling
Cosmological Implications of Spinor-Torsion Coupling Nikodem J. Popławski Department of Physics, Indiana University, Bloomington, IN Astrophysics-Relativity Seminar Department of Physics and Astronomy
More informationarxiv: v1 [physics.gen-ph] 9 May 2014
arxiv:1407.6624v1 [physics.gen-ph] 9 May 2014 Vanishing Dimensions in Four Dimensional Cosmology with Nonminimal Derivative Coupling of Scalar Field Agus Suroso and Freddy P. Zen Theoretical Physics Laboratory,
More informationLate-time oscillatory behaviour for self-gravitating scalar fields
arxiv:gr-qc/0611088 v2 27 Nov 2006 Late-time oscillatory behaviour for self-gravitating scalar fields Alan D. Rendall Max-Planck-Institut für Gravitationsphysik Albert-Einstein-Institut Am Mühlenberg 1
More informationExamining the Viability of Phantom Dark Energy
Examining the Viability of Phantom Dark Energy Kevin J. Ludwick LaGrange College 11/12/16 Kevin J. Ludwick (LaGrange College) Examining the Viability of Phantom Dark Energy 11/12/16 1 / 28 Outline 1 Overview
More informationPAPER 71 COSMOLOGY. Attempt THREE questions There are seven questions in total The questions carry equal weight
MATHEMATICAL TRIPOS Part III Friday 31 May 00 9 to 1 PAPER 71 COSMOLOGY Attempt THREE questions There are seven questions in total The questions carry equal weight You may make free use of the information
More informationCosmology (Cont.) Lecture 19
Cosmology (Cont.) Lecture 19 1 General relativity General relativity is the classical theory of gravitation, and as the gravitational interaction is due to the structure of space-time, the mathematical
More informationElectromagnetic spikes
Electromagnetic spikes Ernesto Nungesser (joint work with Woei Chet Lim) Trinity College Dublin ANZAMP, 29th of November, 2013 Overview Heuristic picture of initial singularity What is a Bianchi spacetime?
More informationBrane in the Relativistic Theory of Gravitation
Brane in the Relativistic Theory of Gravitation arxiv:gr-qc/0009v Jan 00 Ramy Naboulsi March 0, 008 Tokyo Institute of Technology, Department of Physics, O-Okoyama, Meguro-ku, Tokyo Abstract It was proven
More informationSome LRS Bianchi Type VI 0 Cosmological Models with Special Free Gravitational Fields
EJTP 6, No. 21 (2009 165 174 Electronic Journal of Theoretical Physics Some LRS ianchi Type VI 0 Cosmological Models with Special Free Gravitational Fields Raj ali 1, Ratna anerjee 2 and S.K.anerjee 3
More informationReconstructed standard model of cosmology in the Earth-related coordinate system
Reconstructed standard model of cosmology in the Earth-related coordinate system Jian-Miin Liu Department of Physics, Nanjing University Nanjing, The People s Republic of China On leave. E-mail: liu@phys.uri.edu
More information