ΛCDM Model and Hubble Tension Jaeok Yi KAIST November 23, 2019 Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 1 / 43
Introduction Outline Introduction 1 ΛCDM Model 2 Λ, Cosmological Constant Cold Dark Matter ΛCDM model Hubble Tension 3 Hubble Constant Measurement from Planck and HST Hubble Tension Summary 4 Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 2 / 43
Introduction The Famous Figure Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 3 / 43
Introduction Question How our universe looks like? (assuming dark matter and dark energy) Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 4 / 43
Introduction Occam’s Razor Entities are not to be multiplied beyond necessity. If there are many ways to explain the phenomena, then the simplest one is likely to correct. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 5 / 43
Introduction Slight Different Question and Answer What is the simplest model for our universe? (assuming dark matter and dark energy) Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 6 / 43
Introduction Slight Different Question and Answer What is the simplest model for our universe? (assuming dark matter and dark energy) Answer : ΛCDM Model Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 7 / 43
ΛCDM Model Λ, Cosmological Constant Outline Introduction 1 ΛCDM Model 2 Λ, Cosmological Constant Cold Dark Matter ΛCDM model Hubble Tension 3 Hubble Constant Measurement from Planck and HST Hubble Tension Summary 4 Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 8 / 43
ΛCDM Model Λ, Cosmological Constant Suggest of Λ When Einstein developed his field equation, he wanted a static universe. But His equation seems to reject static universe. So he introduced a cosmological constant, Λ to make our universe static. R µν − 1 2 Rg µν + Λ g µν = 8 π G c 4 T µν Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 9 / 43
ΛCDM Model Λ, Cosmological Constant “Biggest Blunder” Later, Hubble discovered that our universe is expanding. v = H 0 d (Hubble-Lemaˆ ıtre law) So the hypothesis of static universe is rejected. Einstein withdrew his cosmological constant and he called it as his “biggest blunder.” Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 10 / 43
ΛCDM Model Λ, Cosmological Constant Accelerating Expansion However, the accelerating expansion of universe is discovered. To explain this, the notion of dark energy is suggested. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 11 / 43
ΛCDM Model Λ, Cosmological Constant Λ Revive Cosmological constant Λ acts as a repulsive force. By using Λ, the accelerating expansion can be explained. Also, quantum field theory suggests the vacuum energy which can be interpreted as a source of cosmological constant. Due to its simplicity, Λ is used to denoting dark energy. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 12 / 43
ΛCDM Model Cold Dark Matter Outline Introduction 1 ΛCDM Model 2 Λ, Cosmological Constant Cold Dark Matter ΛCDM model Hubble Tension 3 Hubble Constant Measurement from Planck and HST Hubble Tension Summary 4 Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 13 / 43
ΛCDM Model Cold Dark Matter Galaxy Rotation Curve Galaxy rotation curve suggests the existence of unknown mass. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 14 / 43
ΛCDM Model Cold Dark Matter Properties of Dark Matter Dark matter should have these properties. Non-baryonic It consists of matter other than baryons (and electrons). Dissipationless It cannot cool by radiating process. Collisionless It interact with each other and other particles only through gravity and possibly the weak force. If not, it can interact through electromagnetic process. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 15 / 43
ΛCDM Model Cold Dark Matter Galaxy and Dark Matter Galaxies are surrounded by dark matter halo. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 16 / 43
ΛCDM Model Cold Dark Matter Coldness of Dark Matter To explain the structure of galaxies, the coldness of dark matter is usually assumed. It means that the velocity of dark matter is far less than the speed of light. In this case, the small objects merge into larger objects by gravitational interaction. To make dark matter halo, we need to assume cold dark matter. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 17 / 43
ΛCDM Model ΛCDM model Outline Introduction 1 ΛCDM Model 2 Λ, Cosmological Constant Cold Dark Matter ΛCDM model Hubble Tension 3 Hubble Constant Measurement from Planck and HST Hubble Tension Summary 4 Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 18 / 43
ΛCDM Model ΛCDM model Constituents of ΛCDM Model ΛCDM model is abbreviation of “Λ Cold Dark Matter model”. It has 3 constituents listed below. Dark energy It behaves just like the energy density of the vacuum and is denoted by Λ. Cold dark matter It interacts with ordinary matter gravitationally and its velocity is much less than that of light. Ordinary matter Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 19 / 43
ΛCDM Model ΛCDM model Assumptions of ΛCDM Model ΛCDM model has a few assumptions. Physics is the same throughout the observable universe. General Relativity is an adequate description of gravity. On large scales the Universe is statistically the same everywhere. The Universe was once much hotter and denser and has been expanding since early times. The curvature of space is very small. Variations in density were laid down everywhere at early times, and are Gaussian, adiabatic, and nearly scale invariant as predicted by inflation. The observable Universe has “trivial” topology. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 20 / 43
ΛCDM Model ΛCDM model 6 Parameters of ΛCDM Model Density of baryons Ω b Density of cold dark matter Ω c Amplitude of a power-law spectrum of adiabatic perturbations A s Scalar spectral index of a power-law spectrum of adiabatic perturbations n s Angular scale of acoustic oscillations θ ∗ Optical depth to Thomson scattering from reionization τ Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 21 / 43
ΛCDM Model ΛCDM model 6 Parameters of ΛCDM Model Ω b Ω c A s n s θ ∗ τ Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 22 / 43
ΛCDM Model ΛCDM model Success of ΛCDM Model Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 23 / 43
ΛCDM Model ΛCDM model It’s That Easy Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 24 / 43
ΛCDM Model ΛCDM model It’s That Easy No, it’s not that easy. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 24 / 43
ΛCDM Model ΛCDM model Unsolved Problem of ΛCDM Model Cosmological Constnant Problem Small Scale Crisis Warm Dark Matter Hubble Tension Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 25 / 43
Hubble Tension Hubble Constant Outline Introduction 1 ΛCDM Model 2 Λ, Cosmological Constant Cold Dark Matter ΛCDM model Hubble Tension 3 Hubble Constant Measurement from Planck and HST Hubble Tension Summary 4 Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 26 / 43
Hubble Tension Hubble Constant Hubble Lemaˆ ıtre Law Hubble Lemaˆ ıtre Law says v = H 0 d v is recession velocity, d is proper distance, and H 0 is Hubble constant. According to Friedmann equation, Hubble parameter H varies with time. ρ − kc 2 a 2 + Λ c 2 H 2 = 8 π G 3 3 When we use the word Hubble constant H 0 , it points out the value of Hubble parameter in this time. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 27 / 43
Hubble Tension Measurement from Planck and HST Outline Introduction 1 ΛCDM Model 2 Λ, Cosmological Constant Cold Dark Matter ΛCDM model Hubble Tension 3 Hubble Constant Measurement from Planck and HST Hubble Tension Summary 4 Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 28 / 43
Hubble Tension Measurement from Planck and HST Planck Mission Planck was ESA’s mission to observe the cosmic microwave background. It was designed to image the temperature and polarization anisotropies of the Cosmic Background Radiation Field. Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 29 / 43
Hubble Tension Measurement from Planck and HST Hubble Constant from Planck Data from Planck constrain 6 parameters governing ΛCDM model. Using these, other cosmological quantities including Hubble constant can be calculated. In 2018, Planck releases final results and it gives H 0 = 67 . 66 ± 0 . 42 km/s/Mpc Jaeok Yi (KAIST) ΛCDM Model and Hubble Tension November 23, 2019 30 / 43
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