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1 Bibliography Abbott, B. P. et al. (2016). Observation of gravitational waves from a binary black hole merger, Phys. Rev. Lett. 116, Ade, P. A. R. et al. (2015). Planck 2015 results. XIII. Cosmological parameters, arxiv: Aldrovandi, R. and Pereira, J. G. (2013). Teleparallel Gravity An Introduction (Springer, Heidelberg). Ashtekar, A., Berger, B. K., Isenberg, J. and MacCallum, M. (2015). General Relativity and Gravitation A Centennial Perspective (Cambridge University Press, Cambridge). Bishop, R. L. and Goldberg, S. I. (1980). Tensor Analysis on Manifolds (Dover Publications, New York). Blagojevic, M. (2001). Gravitation and Gauge Symmetries (CRC Press, Taylor & Francis, New York). Blagojevic, M. and Hehl, F. W. (2012). Gauge Theories of Gravitation A Reader with Commentaries (Imperial College Press, World Scientific, London). Choquet-Bruhat, Y. (2008). General Relativity and the Einstein Equations (Oxford University Press, Oxford). do Carmo, M. (1992). Riemannian Geometry (Birkhäuser, Boston). Dodelson, S. (2003). Modern Cosmology (Academic Press, San Diego). Eisenhart, L. P. (1997). Riemannian Geometry (Princeton University Press, Princeton). Escher, M. C. (2015). Gallery recognition & success, com/gallery/recognition-success/. Last accessed on 30th June Felice, A. D. and Tsujikawa, S. (2010). f(r) Theories, Living Rev. Relativ. 13, 3, doi: /lrr , Last accessed on 30th June Frankel, T. (2012). The Geometry of Physics (Cambridge University Press, Cambridge). Gorbunov, D. S. and Rubakov, V. A. (2011). Introduction to the Theory of the Early Universe: Cosmological Perturbations and Inflationary Theory (World Scientific, Singapore). Hawking, S. W. and Ellis, G. F. R. (1973). The Large Scale Structure of Space- Time (Cambridge University Press, Cambridge). Hogg, D. W. (1999). Distance measures in cosmology, eprint astro-ph/ Isham, C. J. (2001). Modern Differential Geometry for Physicists (World Scientific, Singapore). Liddle, A. R. (2015). An Introduction to Modern Cosmology (John Wiley & Sons, Chichester). 265

2 266 Bibliography Lightman, A. P., Press, W. H., Price, R. H. and Teukolsky, S. A. (1975). Problem Book in Relativity and Gravitation (Princeton University Press, Princeton), Last accessed on 30th June Maggiore, M. (2007). Gravitational Waves Volume 1: Theory and Experiments (Oxford University Press, Oxford). Maluf, J. W. (2013). The teleparallel equivalent of general relativity, Annalen Phys. 525, Misner, C. W., Thorne, K. S. and Wheeler, J. A. (1973). Gravitation (W. H. Freeman and Company, San Francisco). Nakahara, M. (2003). Geometry, Topology and Physics (CRC Press, Taylor & Francis, New York). NASA (1999). Mars climate orbiter, Last accessed on 30th June Rowan-Robinson, M. (2004). Cosmology (Oxford University Press, Oxford). Ryan, M. P. and Shepley, L. C. (1975). Homogeneous Relativistic Cosmologies (Princeton University Press, Princeton), edu/members/larry/ryanshepley.pdf. Last accessed on 30th June Sotiriou, T. P. and Faraoni, V. (2010). f(r) Theories of gravity, Rev. Mod. Phys. 82, Stephani, H., Kramer, D., MacCallum, M. A. H., Hoenselaers, C. and Hertl, E. (2003). Exact Solutions of Einstein s Field Equations (Cambridge University Press, Cambridge). Wald, R. M. (1984). General Relativity (The University of Chicago Press, Chicago). Weinberg, S. (1972). Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity (John Wiley & Sons, New York). Weinberg, S. (2008). Cosmology (Oxford University Press, Oxford). Will, C. M. (2014). The confrontation between general relativity and experiment, Living Rev. Relativ. 17, 4, doi: /lrr , reviews.org/lrr Last accessed on 30th June Zwiebach, B. (2009). A First Course in String Theory (Cambridge University Press, Cambridge).

3 Index A affine parameter, 10 angular diameter distance, 176, 178 arc length, 26 autoparallel, 41 B Bianchi identity, 49 twice contracted, 55 Birkhoff s theorem, 112 black hole, 113, 117, 123, 144 Buchdahl inequality, 121 C chart, 19 Christoffel symbol, 27 trace, 33 transformation, 33 classical tests, 127 gravitational redshift, 136 light deflection, 132 perihelion precession, 127 radar echo delay, 138 conformal tensor, 53 conservation equation charge, 77 cosmological, 161 energy, 78 energy momentum, 87 momentum, 78 contravariant vector, 13 coordinate system, 19 coordinate transformation, 12 cosmological constant, 160 cosmological principle, 153, 155 cosmology, 153 covariant derivative, 34, 37 covariant vector, 13 critical density, 171, 183 cross product, see vector product curl, 15 curvature, 42 curve, 10 cylindrical coordinates, 24 D dark energy, 183 dark matter, 183 de Sitter solution, 168 deceleration parameter, 170 decoupling, see recombination density parameter, 171 differential, 15 directional derivative, 15 distance redshift relations, 177 div, 15 dual basis vector, 15 dual vector space, 14 E e-foldings, 194 Eddington Finkelstein coordinates, 142 Einstein field equations, 88, 103 Einstein summation convention, 8 Einstein tensor, 54 Einstein Hilbert action, 100, 102 energy-momentum tensor, 78 electromagnetic field, 82 ideal fluid, 79 variational, 103 equivalence principle, 69 Euler equation, 81 Euler Lagrange equations,

4 268 Index event, 70 event horizon, 144 F Faraday tensor, 18, 76 field equations linearised, 95 cosmological, 89, Einstein, 88 flatness problem, 185, 189 Friedmann Lemaître Robertson Walker metric, 157 G geodesic, 28, geodesic deviation equation, 56, 98 grad, 15 gravitational radar echo delay, 138 radiation, 97 redshift, time delay, 138 waves, 97 H Hawking radiation, 146 Hawking temperature, 146 horizon problem, 185, 189 Hubble function, 170 law, 174 length, 182, 188 length comoving, 188 parameter, 170, 181 time, 182 hyperbolic disk, 25, 54 I index notation, 7 scalar product, 7 vector, 8 vector product, 9 inflation, 187, 191 J Jacobian, 12 K Kerr solution, 146 Klein Gordon equation, 191 Kronecker delta, 7 Kruskal Szekeres coordinates, 144 L Lagrangian, 57, 60 length contraction, 74 Levi-Civita symbol, 9 Lie derivative, 60 light deflection, 132, 135 Newtonian, 135 line element, 22 linearised Einstein field equations, 95 Einstein tensor, 93 Ricci tensor, 93 Riemann scalar, 93 Riemann tensor, 93 lookback time, 180 Lorentz boosts, 71 force, 76 transformations, 71 Lorenz gauge, 78, 90, luminosity distance, 174, 178 M manifold, 19 mass, 118 gravitational, 68 inertial, 68 matter action, 103 Maxwell equations, 75, 90 homogeneous, 75 inhomogeneous, 75 metric, 22 Lorentzian, 22 signature, 22 metricity, 35

5 Index 269 minimal gravitational coupling, 89 Minkowski space, 25, 71 N Newton s theory of gravity, 67 Newtonian potential, non-metricity, 35 null geodesics, 123 cosmology, 172 incoming, 142 outgoing, 142 radial, 141 P parallel transport, 38 particle horizon, 158 perihelion precession, 127, 131 photon sphere, 125 Planck mass, 192 polar coordinates, 23 power-law inflation, 197 projection, 3 R radar echo delay, 138 recombination, 184 redshift cosmological, 153, 172 gravitational, 136 Ricci scalar, 52 tensor, 52 Riemann tensor, 47 identities, 49 Riemann curvature tensor, 47 S scalar field, 190 scalar product, 3 scale factor, 157 Schwarzschild, 113 effective potential, 124 geodesics, 123 interior metric, 122 interior solution, 117 radius, 116, 141 solution, 115 shortest lines, 26, 41 skew-symmetric part, 17 slow-roll approximation, 193 inflation, 192 parameters, 193 special relativity, 70 spherical coordinates, 24 spherical symmetry, 111 straightest lines, 41 symmetric part, 17 T tangent space, 11 tangent vector, 10 temperature, 183 tensor, 16 contraction, 17 definition, 16 rank, 16 time dilation, 74 Tolman Oppenheimer Volkoff equation, 120 torsion, 35, 46 transverse-traceless, 98 U universe age, 180 de Sitter, 167 Einstein static, 166 matter dominated, 163 radiation dominated, 165 V variational approach, 100 vector, 1 addition, 2 basis, 4 contravariant, 13 covariant, 13 direction, 1

6 270 Index field, 12 index notation, 8 magnitude, 1 unit, 1 zero, 1 vector product, 3 volume, 24 W weak gravity, 92 Weyl tensor, see conformal tensor world line, 75

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