Table of Contents
Preface v
1 Non-linear gravitational clustering in an expanding universe Jasjeet Singh Bagla 1
1.1 Introduction 1
1.2 Gravitational clustering 2
1.2.1 Linear approximation 3
1.2.2 Quasi-linear approximations 4
1.3 In search of universalities 6
1.3.1 Mode coupling: Effect of small scale perturbations 8
1.3.2 Mode coupling: Effect of large scale perturbations 11
1.4 Conclusions 12
References 13
2 Dark ages and cosmic reionization Tirthankar Roy Choudhury 15
2.1 Introduction 16
2.2 Theoretical formalism 18
2.2.1 Cosmological radiation transfer 19
2.2.2 Post-reionization epoch 20
2.2.3 Pre-overlap epoch 25
2.2.4 Reionization of the inhomogeneous IGM 27
2.3 Modelling of reionization 30
2.3.1 Reionization sources 30
2.3.2 Illustration of a semi-analytical model 35
2.4 Current status and future 37
2.4.1 Simulations 37
2.4.2 Various observational probes 38
2.5 Concluding remarks 43
References 43
3 Probing fundamental constant evolution with redshifted spectral lines Nissim Kanekar 51
3.1 Introduction 51
3.2 Redshifted spectral lines: Background 54
3.3 Optical techniques 55
3.3.1 The alkali doublet method 55
3.3.2 The many-multiplet method 56
3.3.3 Molecular hydrogen lines 60
3.4 "Radio" techniques 60
3.4.1 Radio-optical comparisons 61
3.4.2 Radio comparisons 62
3.4.3 Ammonia inversion transitions 63
3.5 "Conjugate" Satellite OH lines 64
3.6 Results from the different techniques 65
3.7 Future studies 67
3.8 Summary 69
3.9 Acknowledgments 70
References 70
4 Averaging the inhomogeneous universe Aseem Paranjape 77
4.1 Introduction 78
4.2 History of the averaging problem 80
4.2.1 Noonan's averaging scheme 81
4.2.2 Futamase's scheme 82
4.2.3 Boersma's scheme 82
4.2.4 Kasai's scheme 83
4.2.5 Conventional wisdom and controversy 83
4.3 Buchert's spatial averaging of scalars 86
4.4 Zalaletdinov's Macroscopic Gravity (MG) 88
4.4.1 A spatial averaging limit 92
4.5 Backreaction in cosmological perturbation theory 95
4.5.1 Lessons from linear theory 98
4.5.2 The nonlinear regime 101
4.5.3 Calculations in an exact model 103
4.6 Conclusions 104
4.6.1 The "Special Observer" assumption 105
References 106
5 Signals of cosmic magnetic fields from the cosmic microwave background radiation T. R. Seshadri 115
5.1 Introduction 115
5.2 Origin of CMBR 116
5.2.1 Homogeneous universe 117
5.3 Origin of CMBR and the homogeneity of the universe 119
5.4 Finer features of the CMBR: A brief introduction 122
5.4.1 Temperature anisotropy 123
5.5 Origin of temperature anisotropy in the CMBR 125
5.6 Characterizing the nature of CMBR polarization anisotropy 126
5.7 Origin of CMBR polarization anisotropy 129
5.8 Cosmic magnetic fields 131
5.9 Polarization in CMBR due to magnetic fields 132
5.10 Non-Gaussianity from magnetic fields 137
References 143
6 Quantum corrections to Bekenstein-Hawking entropy S. Shankaranarayanan 147
6.1 Paddy 148
6.2 Prologue 148
6.3 Entropy and the choice of system states 149
6.3.1 Thought experiment by von Neumann 150
6.4 An intriguing feature of black hole entropy 153
6.5 Quantum corrections 155
6.6 Quantum entanglement 157
6.6.1 Relevance of entanglement for black hole entropy 157
6.6.2 Rapid review of entanglement 158
6.7 Entanglement entropy: Assumptions and setup 160
6.8 Entanglement entropy: Microcanonical 162
6.9 Entanglement entropy: Canonical 167
6.10 Conclusions and discussion 168
6.11 Acknowledgments 169
6.12 Appendix 170
References 172
7 Quantum measurement and quantum gravity: many worlds or collapse of the wave function? T. P. Singh 177
7.1 The quantum measurement problem 178
7.1.1 First explanation: The many-worlds interpretation 178
7.1.2 Second explanation: Collapse of the wave-function 179
7.1.3 Goal of the present paper 180
7.2 A toy model for non-linear quantum mechanics and collapse of the wave-function 182
7.2.1 Introduction 182
7.2.2 The toy model 184
7.2.3 The Doebner-Goldin equation 186
7.3 Quantum gravity suggests that quantum mechanics is non-linear 186
7.3.1 Outline of the approach 186
7.3.2 Why quantum mechanics without classical space-time? 186
7.3.3 A reformulation based on noncommutative differential geometry 189
7.3.4 ' Quantum Minkowski spacetime 190
7.3.5 Including self-gravity 192
7.3.6 A non-linear Schrodinger equation 193
7.3.7 Explaining quantum measurement 194
7.3.8 Ideas for an experimental test of the model 197
7.4 Other models for collapse of the wave-function 198
7.4.1 Models that do not involve gravity 199
7.4.2 Models that involve gravity 200
7.5 Discussion 201
References 203
8 On the generation and evolution of perturbations during inflation and reheating L. Sriramkumar 207
8.1 Inflation and reheating 207
8.2 Inflating the universe 210
8.2.1 Drawing the modes back inside the Hubble radius 210
8.2.2 Propelling accelerated expansion with scalar fields 212
8.2.3 Slow roll inflation 213
8.2.4 Solutions in the slow roll approximation 215
8.3 Gauge invariant, linear, perturbation theory 216
8.3.1 Scalar perturbations 217
8.3.2 Vector perturbations 223
8.3.3 Tensor perturbations 224
8.4 Generation of perturbations during inflation 225
8.4.1 Equation of motion for the curvature perturbation 226
8.4.2 Quantization of the perturbations and the definition of the power spectra 227
8.4.3 The scalar and tensor spectra in slow roll inflation 229
8.5 Reheating the universe 232
8.5.1 Behavior of the scalar field at the end of inflation 233
8.5.2 Transferring the energy from the inflation to radiation 235
8.6 Evolution of perturbations during reheating 238
8.6.1 Equations governing the evolution of perturbations 239
8.6.2 Effects of reheating on the perturbations 242
8.7 Non-trivial post-inflationary dynamics: Modulated reheating and the curvaton scenarios 243
8.7.1 Modulated or the inhomogeneous reheating scenario 243
8.7.2 The curvaton scenario 244
8.8 Summary and discussion 245
References 246
9 Patterns in neural processing Sunu Engineer 251
9.1 Introduction 251
9.2 The brain-the neuron 252
9.3 The model 257
9.4 Evolution of the neural system 260
9.5 Conclusions 261
References 261
Articles co-authored by the contributors with T. Padmanabhan 263
Index 269
