String Cosmology R. Branden- berger Introduction Symmetries of String Theory and Early T-Duality: Key Symmetry of Universe Cosmology String Theory String Gas Cosmology Structure Robert Brandenberger Perturbations Overview Physics Department, McGill University Analysis DFT Conclusions Yukawa Institute, Kyoto University, Feb. 26, 2018 1 / 61 Outline String Cosmology 1 Introduction R. Branden- berger 2 T-Duality: Key Symmetry of String Theory Introduction T-Duality: Key 3 String Gas Cosmology Symmetry of String Theory String Gas 4 String Gas Cosmology and Structure Formation Cosmology Review of the Theory of Cosmological Perturbations Structure Perturbations Overview Overview Analysis Analysis DFT 5 Double Field Theory as a Background for String Gas Conclusions Cosmology 6 Conclusions 2 / 61 Plan String Cosmology 1 Introduction R. Branden- berger 2 T-Duality: Key Symmetry of String Theory Introduction T-Duality: Key 3 String Gas Cosmology Symmetry of String Theory String Gas 4 String Gas Cosmology and Structure Formation Cosmology Review of the Theory of Cosmological Perturbations Structure Perturbations Overview Overview Analysis Analysis DFT 5 Double Field Theory as a Background for String Gas Conclusions Cosmology 6 Conclusions 3 / 61 Inflation: the Standard Model of Early Universe Cosmology String Cosmology R. Branden- berger Introduction Inflation is the standard paradigm of early universe T-Duality: Key cosmology. Symmetry of String Theory Inflation solves conceptual problems of Standard Big String Gas Bang Cosmology. Cosmology Structure Inflation predicts an almost scale-invariant spectrum of Perturbations Overview primordial cosmological perturbations with a small red Analysis tilt (Chibisov & Mukhanov, 1981). DFT Conclusions Fluctuations are nearly Gaussian and nearly adiabatic. 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 Introduction No convincing embedding of inflation in string theory T-Duality: Key exists. Symmetry of String Theory Alternatives to cosmological inflation for producing the String Gas Cosmology structure we observe exist. Structure Question: what early universe scenario emerges from Perturbations Overview string theory? Analysis DFT Key tool: symmetries of string theory. Conclusions 7 / 61 Motivation String Cosmology R. Branden- berger Introduction No convincing embedding of inflation in string theory T-Duality: Key exists. Symmetry of String Theory Alternatives to cosmological inflation for producing the String Gas Cosmology structure we observe exist. Structure Question: what early universe scenario emerges from Perturbations Overview string theory? Analysis DFT Key tool: symmetries of string theory. Conclusions 7 / 61 Motivation String Cosmology R. Branden- berger Introduction No convincing embedding of inflation in string theory T-Duality: Key exists. Symmetry of String Theory Alternatives to cosmological inflation for producing the String Gas Cosmology structure we observe exist. Structure Question: what early universe scenario emerges from Perturbations Overview string theory? Analysis DFT Key tool: symmetries of string theory. Conclusions 7 / 61 Motivation String Cosmology R. Branden- berger Introduction No convincing embedding of inflation in string theory T-Duality: Key exists. Symmetry of String Theory Alternatives to cosmological inflation for producing the String Gas Cosmology structure we observe exist. Structure Question: what early universe scenario emerges from Perturbations Overview string theory? Analysis DFT Key tool: symmetries of string theory. 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 Symmetry of fluctuations on "super-horizon" scales before t , i.e. String Theory eq String Gas standing waves. Cosmology ! "correct" power spectrum of galaxies. Structure Perturbations ! acoustic oscillations in CMB angular power Overview Analysis spectrum. 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 Introduction Given a scale-invariant power spectrum of adiabatic T-Duality: Key fluctuations on "super-horizon" scales before teq, i.e. Symmetry of String Theory standing waves. String Gas ! "correct" power spectrum of galaxies. Cosmology Structure ! acoustic oscillations in CMB angular power Perturbations Overview spectrum. Analysis ! baryon acoustic oscillations in matter power DFT Conclusions spectrum. 12 / 61 Key Challenge String Cosmology R. Branden- berger Introduction T-Duality: Key How does one obtain such a spectrum? Symmetry of String Theory Inflationary Cosmology is the first scenario based on String Gas Cosmology causal physics which yields such a spectrum. Structure Perturbations But it is not the only one. Overview Analysis DFT Conclusions 13 / 61 Key Challenge String Cosmology R. Branden- berger Introduction T-Duality: Key How does one obtain such a spectrum? Symmetry of String Theory Inflationary Cosmology is the first scenario based on String Gas Cosmology causal physics which yields such a spectrum. Structure Perturbations But it is not the only one. Overview Analysis DFT Conclusions 13 / 61 Key Challenge String Cosmology R. Branden- berger Introduction T-Duality: Key How does one obtain such a spectrum? Symmetry of String Theory Inflationary Cosmology is the first scenario based on String Gas Cosmology causal physics which yields such a spectrum. Structure Perturbations But it is not the only one. Overview Analysis DFT Conclusions 13 / 61 Hubble Radius vs. Horizon String Cosmology R. Branden- berger Horizon: Forward light cone of a point on the initial Introduction Cauchy surface. T-Duality: Key Horizon: region of causal contact. Symmetry of String Theory −1 Hubble radius: lH (t) = H (t) inverse expansion rate. String Gas Cosmology Hubble radius: local concept, relevant for dynamics of Structure cosmological fluctuations. Perturbations Overview Analysis In Standard Big Bang Cosmology: Hubble radius = DFT horizon. Conclusions In any theory which can provide a mechanism for the origin of structure: Hubble radius 6= horizon. 14 / 61 Criteria for a Successful Early Universe Scenario String Cosmology R. Branden- berger Horizon Hubble radius in order for the scenario to solve the “horizon problem” of Standard Big Bang Introduction Cosmology. T-Duality: Key Symmetry of String Theory Scales of cosmological interest today originate inside String Gas the Hubble radius at early times in order for a causal Cosmology generation mechanism of fluctuations to be possible. Structure Perturbations Squeezing of fluctuations on super-Hubble scales in Overview Analysis order to obtain the acoustic oscillations in the CMB 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- berger Horizon Hubble radius in order for the scenario to solve the “horizon problem” of Standard Big Bang Introduction Cosmology. T-Duality: Key Symmetry of String Theory Scales of cosmological interest today originate inside String Gas the Hubble radius at early times in order for a causal Cosmology generation mechanism of fluctuations to be possible. Structure Perturbations Squeezing of fluctuations on super-Hubble scales in Overview Analysis order to obtain the acoustic oscillations in the CMB 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- berger Horizon Hubble radius in order for the scenario to solve the “horizon problem” of Standard Big Bang Introduction Cosmology. T-Duality: Key Symmetry of String Theory Scales of cosmological interest today originate inside String Gas the Hubble radius at early times in order for a causal Cosmology generation mechanism of fluctuations to be possible. Structure Perturbations Squeezing of fluctuations on super-Hubble scales in Overview Analysis order to obtain the acoustic oscillations in the CMB DFT angular power spectrum. Conclusions Mechanism for producing a scale-invariant