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Cosmological and Astrophysical Observables from Field Theory in Curved Backgrounds

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Cosmological and Astrophysical Observables from Field Theory in Curved Backgrounds Cosmological and astrophysical observables from field theory in curved backgrounds by José Tomás Gálvez Ghersi M.Sc., Imperial College London, 2013 B.Sc., Universidad Nacional de Ingeniería, 2011 Thesis Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy in the Department of Physics Faculty of Science c José Tomás Gálvez Ghersi 2019 SIMON FRASER UNIVERSITY Summer 2019 Copyright in this work rests with the author. Please ensure that any reproduction or re-use is done in accordance with the relevant national copyright legislation. Approval Name: José Tomás Gálvez Ghersi Degree: Doctor of Philosophy (Physics) Title: Cosmological and astrophysical observables from field theory in curved backgrounds Examining Committee: Chair: John Bechhoefer Professor Andrei Frolov Senior Supervisor Associate Professor Levon Pogosian Supervisor Professor Malcolm Kennett Supervisor Associate Professor David Sivak Internal Examiner Assistant Professor Robert Brandenberger External Examiner Professor Department of Physics McGill University Date Defended: May 3, 2019 ii Abstract The framework of effective field theory has provided valuable insights needed to understand the evolution of physical systems at different energy scales. In particular, when comparing the near-equilibrium phenomena at astrophysical scales with effects at cosmological dis- tances. The objective of this thesis is to introduce useful tools for the evaluation of (a) the observational consistency of an effective field theory of gravity, and (b) the potential modifications of theories, equipped with diffeomorphism invariance. We calculate the evo- lution of gravitational observables relevant in early universe field configurations, and also in effective theories modified by contributions from higher curvature terms or semiclassical effects testable at astrophysical scales. To do so, we develop efficient numerical routines to resolve the dynamic two-point correlation functions of primordial fluctuations in infla- tionary and bouncing cosmologies, the accretion of scalar fields and spacetime curvature in modified gravity, and the evolution of scattering processes involving scalar and gravitational radiation. Additionally, we investigate the viability of defining gauge-invariant quantities in theories of gravity, where the canonical coordinates are deformed to incorporate extra de- grees of freedom. Keywords: Effective field theory (EFT); Single and multifield models of Inflation; IS- Bounce; Constraint Algebra and deformations; Scalar accretion; Modified Gravity; Worm- holes; Gravitational Waves; coalescence of exotic compact objects (ECOs). iii Acknowledgements I would like to thank Alex Zucca, Alexander Vikman, Sabir Ramazanov, Mason Protter, Levon Pogosian, Justine Munich, Claire Maulit, Malcolm Kennett, Jun-Qi Guo, Ghazal Geshnizjani, David Dobre, Aditya Dhumuntarao, Michael Desrochers, Andrew DeBenedic- tis, David Broun and Niayesh Afshordi for their time and their valuable advice, comments and discussions. In particular, I have a large debt of gratitude with my supervisor, Andrei Frolov, for his guidance and patience throughout the completion of my PhD. My work was partly funded by the Discovery Grants program of the Natural Sciences and Engineering Re- search Council of Canada and the Billy Jones Graduate Scholarship, granted by the Physics Department at SFU. Part of my research was done at the Perimeter Institute for Theoretical Physics. Research at the Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development Canada. This research was enabled in part by support provided by WestGrid (www.westgrid.ca) and Compute Canada Calcul Canada (www.computecanada.ca). iv Table of Contents Approval ii Abstract iii Acknowledgements iv Table of Contentsv List of Tables viii List of Figures ix 1 Introduction1 I Early Universe Cosmology: Inflationary and bouncing scenarios9 2 Single-field Inflation: observational constraints on Constant-Roll Inflation 10 2.1 Model and background dynamics........................ 12 2.2 Perturbations................................... 14 2.3 Planck constraints ................................ 18 2.4 Discussion..................................... 20 3 Two-point correlators revisited: fast and slow scales in multifield models of inflation 22 3.1 Perturbation theory: a lightning review..................... 23 3.2 Two-point correlators revisited ......................... 24 3.3 Initial conditions and spectral evolution scheme................ 28 3.4 Results....................................... 32 3.5 Discussion..................................... 37 4 Unbraiding the bounce: superluminality around the corner 39 4.1 Model and main equations ........................... 43 4.2 Conformal transformations, gauges and acoustic geometry ......... 49 v 4.3 Inverse method: reconstructing the theory from its solutions . 51 4.4 Phase space.................................... 54 4.5 Discussion..................................... 55 II Modifying GR via variable deformations, action corrections and semiclassical effects 58 5 Hamiltonian consistency of the gravitational constraint algebra under deformations 59 5.1 Transforming the action from its canonical variables ............. 62 5.1.1 Transformations into theories with second-order equations of motion 62 5.1.2 Transformations into higher-order theories............... 64 5.2 Review of Hamiltonian general relativity and the gauge algebra . 67 5.3 Deforming canonical general relativity..................... 74 5.3.1 Lovelock’s theorem............................ 74 5.3.2 Deforming GR by introducing extra degrees of freedom . 76 5.3.3 Further constraints in the deformations ................ 83 5.4 Deforming general relativity in tetrad theory and Ashtekar variables . 84 5.5 Discussion..................................... 92 6 Unscreening scalarons with a black hole 94 6.1 Matter distribution for spherically symmetric black holes........... 95 6.2 Scalar accretion in f(R) theories ........................ 97 6.2.1 Chameleons in Starobinsky and Hu-Sawicki model.......... 98 6.2.2 Accreting chameleons in Hu-Sawicki and Starobinsky models . 100 6.3 Resolving curvature singularities in f(R) theories . 107 6.4 Scalar accretion for the symmetron model................... 109 6.4.1 Action and equations of motion..................... 109 6.4.2 Accreting symmetrons.......................... 111 6.5 Accretion of the Ratra-Peebles chameleons................... 112 6.5.1 Equations of motion and setup ..................... 112 6.5.2 Accreting chameleons .......................... 115 6.6 Discussion..................................... 118 7 Echoes from the scattering of wavepackets on wormholes 119 7.1 Scattering of scalar wavepackets......................... 121 7.1.1 Scattering by a Schwarzschild black hole . 121 7.1.2 Scattering by a traversable wormhole.................. 125 7.2 Scattering of tensor wavepackets ........................ 131 vi 7.3 Echoes and gravitational wave polarimetry................... 138 7.4 Discussion..................................... 139 8 Concluding remarks 140 Bibliography 145 Appendix A Deviations of ns and r from the slow-roll expressions 160 Appendix B Decomposition scheme in a curved field space 162 Appendix C Plotting two-point correlation functions 164 Appendix D Power spectra in the Ijjas-Steinhardt bounce 166 D.1 Setting up the equations of motion and initial conditions . 166 D.2 Evolution of the mode amplitudes and length scales . 169 Appendix E Numerical setup for scalar accretion and scattering 174 E.1 Scalar field equations of motion......................... 174 E.2 Absorbing boundary conditions......................... 175 E.3 Spectral basis................................... 176 E.4 Gauss-Legendre integrator............................ 177 E.5 Static solver.................................... 178 E.6 Inverting tortoise coordinate........................... 178 vii List of Tables Table 5.1 The various ways to decompose the tensorial structure of the new degree of freedom Jab. ................................. 81 viii List of Figures Figure 1.1 Cosmic Microwave Background (CMB) obtained by the Planck Mis- sion. ................................... 3 Figure 1.2 Features of the gravitational wave profile............... 7 Figure 2.1 Constant-Roll potential and phase space for the background. 12 Figure 2.2 Evolution of scalar and tensor fluctuations in Constant-Roll Inflation 13 Figure 2.3 Power spectrum of scalar curvature and tensor fluctuations in Constant- Roll Inflation............................... 15 Figure 2.4 Injection scheme for the scalar and tensor modes for Constant-Roll Inflation.................................. 17 Figure 2.5 Scanning the model parameters in the potential at N∗ = 0, 30, 60, 80. 18 Figure 2.6 Different projections of the joint probability distribution from Planck 2015 posterior for Constant-Roll Inflation............... 19 Figure 2.7 Constraints for the Constant-Roll model parameters from joint Planck 2015/BKP likelihood on ns and r.................... 21 Figure 3.1 Schematic representation of the Cholesky gauge separation. 27 Figure 3.2 Phase space projections for the double λφ4 model........... 29 Figure 3.3 Projected surface of initial conditions.................. 30 Figure 3.4 Mode injection scheme for the double λφ4 model........... 32 Figure 3.5 Gauge condition hχˆA, χˆBi = δAB at all times. ............ 33 Figure 3.6 Verifying the final gauge condition in (3.14).............. 33 10 Figure 3.7
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