School Observational Cosmology Angra Terceira Açores 3 rd June Juan García-Bellido Física Teórica UAM Madrid, Spain

Transcription

1 School Observational Cosmology Angra Terceira Açores 3 rd June 2014 Juan García-Bellido Física Teórica UAM Madrid, Spain

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3 Outline Lecture 1 Shortcomings of the Hot Big Bang The Inflationary Paradigm Homogeneous Scalar Field Dynamics Slow roll approximation Quantum Fluctuations in de Sitter

4 Shortcomings of the Hot Big Bang The space-time structure of the observable Universe - Why is the Universe so close to spatial flatness? - Why is matter so homogeneously distributed on large scales? The origin of structures in the Universe - How did primordial spectrum of density perturbations originate? The origin of matter and radiation - Where does all the energy in the Universe come from? - How did the matter-antimatter asymmetry arise? The initial singularity - Did the Universe have a beginning? - What is the global structure of the Universe beyond our observable patch?

5 Einstein-Friedmann equations Energy density conservation: p(t) = w ρ(t) barotropic fluid

6 Time evolution of density params x Ω M (a) = 8πG ρ M (a) y Ω Λ (a) = 3H 2 (a) = Ω M Ω M + Ω K a + Ω Λ a 3 Λ 3H 2 (a) = Ω a 3 Λ Ω + Ω a + Ω a 3 M K Λ Homogeneous system of eqs. x' dx dn y' dy dn = x(1 x + 2y) = +y(x + 2(1 y)) N = lna critical points (x = 0, y = 0) (x = 1, y = 0) (x = 0, y = 1)

7 Flatness is unstable critical points (x = 0, y = 0) (x = 1,y = 0) (x = 0, y = 1) Ω K = 0, Ω M + Ω Λ = 1

8 Flatness H 2 = 8πG 3 ρ K a 2, Ω = 8πG 3H 2 ρ, d lnρ d lna = x Ω 1 Ω ρ' = 3(1 + w) x' = (1 + 3w)x ρ = 3K /8πG ρa 2 Matter & Radiation Vacuum energy x = 0 unstable x a 2, a x = 0 stable x a 2 x 0 = x in T in T eq 2 (1 + z eq ) < 10 3 e.g. x BBN < 10 18

9 Causality

10 Homogeneity Scale Factor Particle Horizon Causally Disconnected

11 Homogeneity Size Universe Horizon Causally Disconnected Regions Big Bang Radiation Matter

12 A very elegant solution: INFLATION

13 1fmΔx Δx 200 Δpc MeV c 1

14 Vacuum fluctuations e e + e e +

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16 Inflation Our Universe could be the result of a quantum fluctuation Alan Guth Andrei Linde A small bubble of quantum vacuum expands very rapidly until it encompasses all our Universe

17 Effective description (scalar field) Constant density GR Exponential Growth Flat spatial homogeneous sections

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19 SCALAR FIELD DYNAMICS

20 HAMILTON-JACOBI EQUATION Constraint equations Then

21 SLOW-ROLL PARAMETERS The scalar field φ acts as a new time The number of e -folds N e to the end inflation

22 Then SLOW-ROLL ATTRACTOR exact particular solution linear perturbation with solution: end inflation single trajectory

23 SLOW-ROLL APPROXIMATION just dynamics

24 INFLATIONARY SOLUTIONS OF HBBP curvature matter

25 LINEAR METRIC PERTURBATIONS linear pert. eqs. Mukhanov variables

26 QUANTUM FLUCTUATIONS IN ds

27 QUANTUM FLUCTUATIONS IN ds

28 SOLUTIONS OF MODE EQUATIONS approx. constant

29 EXACT SOLUTIONS OF MODE EQS.

30 EXACT SOLUTIONS OF MODE EQS.

31 SCALAR CURVATURE PERTURBATIONS

32 λ inside inside k 2 1 st HC 2 nd HC outside inflation matter η

33 SCALAR CURVATURE PERTURBATIONS

34 Classical Metric perturbations Quantum Fluctuations within the horizon

35 Metric Perturbation Enters horizon Horizon Exits horizon Inflation Radiation Matter

36 Scale Invariant Spectrum

37 Gaussian Random Field

38 Horizon Crossing perturbation horizon causal region Inflation Radiation Matter

39 During Inflation

40 After Inflation

41 Ripples in Space A y x Stretched to cosmological distances

42 GRAVITATIONAL WAVE PERTURBATIONS

43 TENSOR MODE EQUATION

44 EXACT SOLUTIONS

45 Predictions of Inflation Quantum fluctuations Inflation Radiation background anisotropies years after the Big Bang photons gravitational waves Million years after the Big Bang Structure formation

46 Basic Inflationary Predictions Geometry and matter: Homogeneity (acausal origin) Flat spatial sections (exp. growth) No appreciable topology (exp.growth) Origin matter & radiation (reheating) Metric Perturbations: Gaussian spectrum (ground state) Aprox. scale invariant (slow roll cond.) Adiabatic density fluctuations (single fluid) Gravitational waves (tensor metric pert.) No vector perturbations (no defects)

47 Cosmological Observations Cosmic Microwave Background: Temperature Anisotropies (WMAP9+Planck) Polarization Anisotropies (BICEP2+Planck) Large Scale Structure: Matter Power Spectrum (2dFGRS+SDSS) Baryon Acoustic Oscillations (BOSS+DES) Weak Lensing (KIDS, DES, LSST, Euclid)

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