Modified Teleparallel theories of gravity [PhD Thesis]

Preface......Page 1
Conventions......Page 16
A theory of curved spacetime......Page 19
 Weak equivalence principle......Page 20
Strong equivalence principle......Page 24
General Covariance principle......Page 31
Causality and relativity principles......Page 33
Mach's Principle......Page 34
Important mathematical quantities......Page 35
Metric tensor......Page 36
Geodesic equation......Page 38
Covariant derivative, connections and parallel transportation......Page 40
Curvature tensor, Ricci scalar, scalar curvature and torsion tensor......Page 44
Newton's law of Universal Gravitation......Page 53
Einstein field equations......Page 57
Friedmann-Lemaître-Robertson-Walker cosmology......Page 64
Newtonian Cosmology......Page 68
FLRW Cosmology and CDM model......Page 72
FLRW cosmology......Page 73
A very brief history of the Universe......Page 78
CDM model......Page 80
The Cosmological constant problem......Page 84
An alternative description of gravity: Teleparallel gravity......Page 88
Tetrads and linear frames......Page 90
Gravitational gauge theory of the translations......Page 91
Action, field equations and equivalence with GR......Page 97
The Teleparallel force equation......Page 104
Why do we want to modify TEGR (or GR)?......Page 107
Lorentz transformations......Page 110
Action and field equations......Page 114
Good and bad tetrads......Page 116
FLRW Cosmology......Page 119
Brans-Dicke and scalar-tensor theories......Page 123
Teleparallel scalar-tensor theories......Page 127
Teleparallel quintom models......Page 132
General equations......Page 142
Some important special theories......Page 146
Lorentz covariance......Page 149
Conservation equations......Page 151
FLRW Cosmology......Page 152
Noether symmetry approach......Page 155
f(T,B)=f(T)......Page 159
f(T,B)=f(-T+B)=f(R)......Page 161
f(T,B)=T+F(B)......Page 164
Reconstruction method in f(T,B) gravity......Page 167
Power-law Cosmology......Page 168
de-Sitter reconstruction......Page 170
CDM reconstruction......Page 171
Reconstruction method in f(T,B)=T+F(B) cosmology......Page 174
Generalised non-minimally gravity matter-coupled theory......Page 176
Torsion decomposition and other Teleparallel gravity theories......Page 182
New class of modified Teleparallel gravity models......Page 185
Variations of T_vec and T_ax......Page 186
Variations of T_ten......Page 187
Field equations......Page 188
Inclusion of parity violating terms and higher-order invariants......Page 189
Inclusion of the boundary term and derivatives of torsion......Page 190
Conformal transformations......Page 191
Basic equations......Page 192
Minimal and non-minimal couplings......Page 194
Connection with other theories......Page 197
Gauss-Bonnet term......Page 199
Example: FLRW spacetime with diagonal tetrad......Page 202
Example: static spherically symmetric spacetime – isotropic coordinates......Page 203
Example: FLRW spacetime – good tetrad......Page 204
Modified Teleparallel theory: Gauss-Bonnet and trace extension......Page 207
Variation of B_G......Page 208
Variation of T_G......Page 211
Equations of motion and FLRW example......Page 214
Energy-momentum trace extension and connection with other theories......Page 217
Teleparallel non-local gravity......Page 223
Action and field equations......Page 227
Teleparallel non-local cosmology......Page 230
Generalised non-local gravity and cosmology......Page 234
The Noether symmetry approach......Page 238
Noether symmetries in Teleparallel non-local gravity with coupling Tf(^-1T)......Page 241
Finding Noether symmetries......Page 242
Cosmological solutions......Page 243
Noether symmetries in curvature non-local gravity with coupling Rf(^-1R)......Page 246
Appendix......Page 249