Contents -- Preface -- 1. Non-linear gravitational clustering in an expanding universe Jasjeet Singh Bagla -- 1.1 Introduction -- 1.2 Gravitational clustering -- 1.2.1 Linear approximation -- 1.2.2 Quasi-linear approximations -- 1.3 In search of universalities -- 1.3.1 Mode coupling: Effect of small scale perturbations -- 1.3.2 Mode coupling: Effect of large scale perturbations -- 1.4 Conclusions -- Acknowledgments -- References -- 2. Dark ages and cosmic reionization Tirthankar Roy Choudhury -- 2.1 Introduction -- 2.2 Theoretical formalism -- 2.2.1 Cosmological radiation transfer -- 2.2.2 Post-reionization epoch -- 2.2.2.1 Resonant Lyman series absorption -- 2.2.2.2 Continuum absorption -- 2.2.3 Pre-overlap epoch -- 2.2.4 Reionization of the inhomogeneous IGM -- 2.3 Modelling of reionization -- 2.3.1 Reionization sources -- 2.3.1.1 Mass function of collapsed haloes -- 2.3.1.2 Star formation rate -- 2.3.1.3 Production of ionizing photons -- 2.3.1.4 Feedback processes -- 2.3.1.5 Quasars -- 2.3.2 Illustration of a semi-analytical model -- 2.4 Current status and future -- 2.4.1 Simulations -- 2.4.2 Various observational probes -- 2.4.2.1 Absorption spectra of high redshift sources -- 2.4.2.2 CMBR observations -- 2.4.2.3 Ly emitters -- 2.4.2.4 Sources of reionization -- 2.4.2.5 21cm observations -- 2.5 Concluding remarks -- References -- 3. Probing fundamental constant evolution with redshifted spectral lines Nissim Kanekar -- 3.1 Introduction -- 3.2 Redshifted spectral lines: Background -- 3.3 Optical techniques -- 3.3.1 The alkali doublet method -- 3.3.2 The many-multiplet method -- 3.3.3 Molecular hydrogen lines -- 3.4 "Radio" techniques -- 3.4.1 Radio-optical comparisons -- 3.4.2 Radio comparisons -- 3.4.3 Ammonia inversion transitions -- 3.5 "Conjugate" Satellite OH lines -- 3.6 Results from the different techniques -- 3.7 Future studies.

3.8 Summary -- 3.9 Acknowledgments -- References -- 4. Averaging the inhomogeneous universe Aseem Paranjape -- 4.1 Introduction -- 4.2 History of the averaging problem -- 4.2.1 Noonan's averaging scheme -- 4.2.2 Futamase's scheme -- 4.2.3 Boersma's scheme -- 4.2.4 Kasai's scheme -- 4.2.5 Conventional wisdom and controversy -- 4.3 Buchert's spatial averaging of scalars -- 4.4 Zalaletdinov's Macroscopic Gravity (MG) -- 4.4.1 A spatial averaging limit -- 4.5 Backreaction in cosmological perturbation theory -- 4.5.1 Lessons from linear theory -- 4.5.2 The nonlinear regime -- 4.5.2.1 Dimensional arguments, and why they fail -- 4.5.3 Calculations in an exact model -- 4.6 Conclusions -- 4.6.1 The "Special Observer" assumption -- References -- 5. Signals of cosmic magnetic fields from the cosmic microwave background radiation T. R. Seshadri -- 5.1 Introduction -- 5.2 Origin of CMBR -- 5.2.1 Homogeneous universe -- 5.3 Origin of CMBR and the homogeneity of the universe -- 5.4 Finer features of the CMBR: A brief introduction -- 5.4.1 Temperature anisotropy -- 5.5 Origin of temperature anisotropy in the CMBR -- 5.6 Characterizing the nature of CMBR polarization anisotropy -- 5.7 Origin of CMBR polarization anisotropy -- 5.8 Cosmic magnetic fields -- 5.9 Polarization in CMBR due to magnetic fields -- 5.10 Non-Gaussianity from magnetic fields -- References -- 6. Quantum corrections to Bekenstein-Hawking entropy S. Shankaranarayanan -- 6.1 Paddy -- 6.2 Prologue -- 6.3 Entropy and the choice of system states -- 6.3.1 Thought experiment by von Neumann -- 6.4 An intriguing feature of black hole entropy -- 6.5 Quantum corrections -- 6.6 Quantum entanglement -- 6.6.1 Relevance of entanglement for black hole entropy -- 6.6.2 Rapid review of entanglement -- 6.7 Entanglement entropy: Assumptions and setup -- 6.8 Entanglement entropy: Microcanonical.

6.9 Entanglement entropy: Canonical -- 6.10 Conclusions and discussion -- 6.11 Acknowledgments -- 6.12 Appendix -- References -- 7. Quantum measurement and quantum gravity: many worlds or collapse of the wave function? T. P. Singh -- 7.1 The quantum measurement problem -- 7.1.1 First explanation: The many-worlds interpretation -- 7.1.2 Second explanation: Collapse of the wave-function -- 7.1.3 Goal of the present paper -- 7.2 A toy model for non-linear quantum mechanics and collapse of the wave-function -- 7.2.1 Introduction -- 7.2.2 The toy model -- 7.2.3 The Doebner-Goldin equation -- 7.3 Quantum gravity suggests that quantum mechanics is nonlinear -- 7.3.1 Outline of the approach -- 7.3.2 Why quantum mechanics without classical spacetime? -- 7.3.3 A reformulation based on noncommutative differential geometry -- 7.3.4 Quantum Minkowski spacetime -- 7.3.5 Including self-gravity -- 7.3.6 A non-linear Schrodinger equation -- 7.3.7 Explaining quantum measurement -- 7.3.8 Ideas for an experimental test of the model -- 7.4 Other models for collapse of the wave-function -- 7.4.1 Models that do not involve gravity -- 7.4.2 Models that involve gravity -- 7.5 Discussion -- Acknowledgements -- References -- 8. On the generation and evolution of perturbations during inflation and reheating L. Sriramkumar -- 8.1 Inflation and reheating -- 8.2 Inflating the universe -- 8.2.1 Drawing the modes back inside the Hubble radius -- 8.2.2 Propelling accelerated expansion with scalar fields -- 8.2.3 Slow roll inflation -- 8.2.4 Solutions in the slow roll approximation -- 8.3 Gauge invariant, linear, perturbation theory -- 8.3.1 Scalar perturbations -- 8.3.1.1 Equations of motion governing the scalar perturbations -- 8.3.1.2 A conserved quantity at super-Hubble scales -- 8.3.1.3 Evolution of the Bardeen potential at super-Hubble scales -- 8.3.2 Vector perturbations.

8.3.3 Tensor perturbations -- 8.4 Generation of perturbations during inflation -- 8.4.1 Equation of motion for the curvature perturbation -- 8.4.2 Quantization of the perturbations and the definition of the power spectra -- 8.4.3 The scalar and tensor spectra in slow roll inflation -- 8.5 Reheating the universe -- 8.5.1 Behavior of the scalar field at the end of inflation -- 8.5.2 Transferring the energy from the inflation to radiation -- 8.6 Evolution of perturbations during reheating -- 8.6.1 Equations governing the evolution of perturbations -- 8.6.2 Effects of reheating on the perturbations -- 8.7 Non-trivial post-inflationary dynamics: Modulated reheating and the curvaton scenarios -- 8.7.1 Modulated or the inhomogeneous reheating scenario -- 8.7.2 The curvaton scenario -- 8.8 Summary and discussion -- Acknowledgements -- References -- 9. Patterns in neural processing Sunu Engineer -- 9.1 Introduction -- 9.2 The brain-the neuron -- 9.3 The model -- 9.4 Evolution of the neural system -- 9.5 Conclusions -- References -- Articles co-authored by the contributors with T. Padmanabhan -- Index.