Symmetries of String Theory and Early Introduction Universe - PowerPoint PPT Presentation

String Cosmology R. Branden- berger Symmetries of String Theory and Early Introduction Universe Cosmology T-Duality: Key Symmetry of String Theory String Gas Cosmology Robert Brandenberger Structure Physics Department, McGill University Perturbations Overview Analysis DFT Conclusions Yukawa Institute, Kyoto University, Feb. 26, 2018 1 / 61

Outline String Cosmology Introduction 1 R. Branden- berger T-Duality: Key Symmetry of String Theory 2 Introduction String Gas Cosmology 3 T-Duality: Key Symmetry of String Theory String Gas Cosmology and Structure Formation 4 String Gas Cosmology Review of the Theory of Cosmological Perturbations Structure Overview Perturbations Overview Analysis Analysis DFT 5 Double Field Theory as a Background for String Gas Conclusions Cosmology Conclusions 6 2 / 61

Plan String Cosmology Introduction 1 R. Branden- berger T-Duality: Key Symmetry of String Theory 2 Introduction String Gas Cosmology 3 T-Duality: Key Symmetry of String Theory String Gas Cosmology and Structure Formation 4 String Gas Cosmology Review of the Theory of Cosmological Perturbations Structure Overview Perturbations Overview Analysis Analysis DFT 5 Double Field Theory as a Background for String Gas Conclusions Cosmology Conclusions 6 3 / 61

Inflation: the Standard Model of Early Universe Cosmology String Cosmology R. Branden- berger Inflation is the standard paradigm of early universe Introduction cosmology. T-Duality: Key Symmetry of Inflation solves conceptual problems of Standard Big String Theory Bang Cosmology. String Gas Cosmology Inflation predicts an almost scale-invariant spectrum of Structure primordial cosmological perturbations with a small red Perturbations Overview tilt (Chibisov & Mukhanov, 1981). Analysis DFT Fluctuations are nearly Gaussian and nearly adiabatic. Conclusions 4 / 61

Map of the Cosmic Microwave Background (CMB) String Cosmology R. Branden- berger Introduction T-Duality: Key Symmetry of String Theory String Gas Cosmology Structure Perturbations Overview Analysis DFT Conclusions Credit: NASA/WMAP Science Team 5 / 61

Angular Power Spectrum of CMB Anisotropies String Cosmology R. Branden- berger Introduction T-Duality: Key Symmetry of String Theory String Gas Cosmology Structure Perturbations Overview Analysis DFT Conclusions Credit: NASA/WMAP Science Team 6 / 61

Motivation String Cosmology R. Branden- berger No convincing embedding of inflation in string theory Introduction exists. T-Duality: Key Symmetry of String Theory Alternatives to cosmological inflation for producing the String Gas structure we observe exist. Cosmology Structure Question: what early universe scenario emerges from Perturbations string theory? Overview Analysis Key tool: symmetries of string theory. DFT Conclusions 7 / 61

Motivation String Cosmology R. Branden- berger No convincing embedding of inflation in string theory Introduction exists. T-Duality: Key Symmetry of String Theory Alternatives to cosmological inflation for producing the String Gas structure we observe exist. Cosmology Structure Question: what early universe scenario emerges from Perturbations string theory? Overview Analysis Key tool: symmetries of string theory. DFT Conclusions 7 / 61

Motivation String Cosmology R. Branden- berger No convincing embedding of inflation in string theory Introduction exists. T-Duality: Key Symmetry of String Theory Alternatives to cosmological inflation for producing the String Gas structure we observe exist. Cosmology Structure Question: what early universe scenario emerges from Perturbations string theory? Overview Analysis Key tool: symmetries of string theory. DFT Conclusions 7 / 61

Motivation String Cosmology R. Branden- berger No convincing embedding of inflation in string theory Introduction exists. T-Duality: Key Symmetry of String Theory Alternatives to cosmological inflation for producing the String Gas structure we observe exist. Cosmology Structure Question: what early universe scenario emerges from Perturbations string theory? Overview Analysis Key tool: symmetries of string theory. DFT Conclusions 7 / 61

Criteria String Cosmology R. Branden- berger Introduction T-Duality: Key Symmetry of String Theory String Gas Cosmology Structure Perturbations Overview Analysis DFT Conclusions 8 / 61

Key Realization R. Sunyaev and Y. Zel’dovich, Astrophys. and Space Science 7 , 3 (1970); P . Peebles and J. Yu, Ap. J. 162 , 815 (1970). String Cosmology R. Branden- berger Introduction Given a scale-invariant power spectrum of adiabatic T-Duality: Key fluctuations on "super-horizon" scales before t eq , i.e. Symmetry of String Theory standing waves. String Gas Cosmology → "correct" power spectrum of galaxies. Structure → acoustic oscillations in CMB angular power Perturbations Overview spectrum. Analysis DFT Conclusions 9 / 61

Angular Power Spectrum of CMB Anisotropies String Cosmology R. Branden- berger Introduction T-Duality: Key Symmetry of String Theory String Gas Cosmology Structure Perturbations Overview Analysis DFT Conclusions Credit: NASA/WMAP Science Team 10 / 61

Early Work String Cosmology R. Branden- berger Introduction T-Duality: Key Symmetry of String Theory String Gas Cosmology Structure Perturbations Overview Analysis DFT Conclusions 11 / 61

Predictions from 1970 R. Sunyaev and Y. Zel’dovich, Astrophys. and Space Science 7 , 3 (1970); P . Peebles and J. Yu, Ap. J. 162 , 815 (1970). String Cosmology R. Branden- berger Given a scale-invariant power spectrum of adiabatic Introduction fluctuations on "super-horizon" scales before t eq , i.e. T-Duality: Key Symmetry of standing waves. String Theory → "correct" power spectrum of galaxies. String Gas Cosmology → acoustic oscillations in CMB angular power Structure spectrum. Perturbations Overview Analysis → baryon acoustic oscillations in matter power DFT spectrum. Conclusions 12 / 61

Key Challenge String Cosmology R. Branden- berger Introduction How does one obtain such a spectrum? T-Duality: Key Symmetry of String Theory Inflationary Cosmology is the first scenario based on String Gas causal physics which yields such a spectrum. Cosmology Structure But it is not the only one. Perturbations Overview Analysis DFT Conclusions 13 / 61

Key Challenge String Cosmology R. Branden- berger Introduction How does one obtain such a spectrum? T-Duality: Key Symmetry of String Theory Inflationary Cosmology is the first scenario based on String Gas causal physics which yields such a spectrum. Cosmology Structure But it is not the only one. Perturbations Overview Analysis DFT Conclusions 13 / 61

Key Challenge String Cosmology R. Branden- berger Introduction How does one obtain such a spectrum? T-Duality: Key Symmetry of String Theory Inflationary Cosmology is the first scenario based on String Gas causal physics which yields such a spectrum. Cosmology Structure But it is not the only one. Perturbations Overview Analysis DFT Conclusions 13 / 61

Hubble Radius vs. Horizon String Cosmology R. Branden- Horizon: Forward light cone of a point on the initial berger Cauchy surface. Introduction Horizon: region of causal contact. T-Duality: Key Symmetry of Hubble radius: l H ( t ) = H − 1 ( t ) inverse expansion rate. String Theory String Gas Hubble radius: local concept, relevant for dynamics of Cosmology cosmological fluctuations. Structure Perturbations In Standard Big Bang Cosmology: Hubble radius = Overview Analysis horizon. DFT In any theory which can provide a mechanism for the Conclusions origin of structure: Hubble radius � = horizon. 14 / 61

Criteria for a Successful Early Universe Scenario String Cosmology R. Branden- Horizon ≫ Hubble radius in order for the scenario to berger solve the “horizon problem” of Standard Big Bang Introduction Cosmology. T-Duality: Key Symmetry of Scales of cosmological interest today originate inside String Theory the Hubble radius at early times in order for a causal String Gas Cosmology generation mechanism of fluctuations to be possible. Structure Squeezing of fluctuations on super-Hubble scales in Perturbations Overview order to obtain the acoustic oscillations in the CMB Analysis DFT angular power spectrum. Conclusions Mechanism for producing a scale-invariant spectrum of curvature fluctuations on super-Hubble scales. 15 / 61

Criteria for a Successful Early Universe Scenario String Cosmology R. Branden- Horizon ≫ Hubble radius in order for the scenario to berger solve the “horizon problem” of Standard Big Bang Introduction Cosmology. T-Duality: Key Symmetry of Scales of cosmological interest today originate inside String Theory the Hubble radius at early times in order for a causal String Gas Cosmology generation mechanism of fluctuations to be possible. Structure Squeezing of fluctuations on super-Hubble scales in Perturbations Overview order to obtain the acoustic oscillations in the CMB Analysis DFT angular power spectrum. Conclusions Mechanism for producing a scale-invariant spectrum of curvature fluctuations on super-Hubble scales. 15 / 61