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

1 Introduction

2 ΛCDM ModelΛ, Cosmological ConstantCold Dark MatterΛCDM model

3 Hubble TensionHubble ConstantMeasurement from Planck and HSTHubble Tension

4 Summary

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Introduction

The Famous Figure

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Introduction

Question

How our universe looks like?

(assuming dark matter and dark energy)

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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.

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Introduction

Slight Different Question and Answer

What is the simplest modelfor our universe?

(assuming dark matter and dark energy)

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Introduction

Slight Different Question and Answer

What is the simplest modelfor our universe?

(assuming dark matter and dark energy)

Answer : ΛCDM Model

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ΛCDM Model Λ, Cosmological Constant

Outline

1 Introduction

2 ΛCDM ModelΛ, Cosmological ConstantCold Dark MatterΛCDM model

3 Hubble TensionHubble ConstantMeasurement from Planck and HSTHubble Tension

4 Summary

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ΛCDM Model Λ, Cosmological Constant

Suggest of Λ

When Einstein developed his fieldequation, he wanted a static universe.

But His equation seems to reject staticuniverse.

So he introduced a cosmologicalconstant, Λ to make our universe static.

Rµν −1

2Rgµν + Λgµν =

8πG

c4Tµν

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ΛCDM Model Λ, Cosmological Constant

“Biggest Blunder”

Later, Hubble discovered that ouruniverse is expanding.

v = H0d (Hubble-Lemaıtre law)

So the hypothesis of static universe isrejected.

Einstein withdrew his cosmologicalconstant and he called it as his“biggest blunder.”

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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.

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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 beinterpreted as a source of cosmological constant.

Due to its simplicity, Λ is used to denoting dark energy.

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ΛCDM Model Cold Dark Matter

Outline

1 Introduction

2 ΛCDM ModelΛ, Cosmological ConstantCold Dark MatterΛCDM model

3 Hubble TensionHubble ConstantMeasurement from Planck and HSTHubble Tension

4 Summary

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ΛCDM Model Cold Dark Matter

Galaxy Rotation Curve

Galaxy rotation curve suggests the existence of unknown mass.

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ΛCDM Model Cold Dark Matter

Properties of Dark Matter

Dark matter should have these properties.

Non-baryonicIt consists of matter other than baryons (and electrons).

DissipationlessIt cannot cool by radiating process.

CollisionlessIt interact with each other and other particles only through gravityand possibly the weak force.

If not, it can interact through electromagnetic process.

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ΛCDM Model Cold Dark Matter

Galaxy and Dark Matter

Galaxies are surrounded by dark matter halo.

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ΛCDM Model Cold Dark Matter

Coldness of Dark Matter

To explain the structure of galaxies, the coldness of dark matter isusually assumed.

It means that the velocity of dark matter is far less than the speed oflight.

In this case, the small objects merge into larger objects by gravitationalinteraction.

To make dark matter halo, we need to assume cold dark matter.

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ΛCDM Model ΛCDM model

Outline

1 Introduction

2 ΛCDM ModelΛ, Cosmological ConstantCold Dark MatterΛCDM model

3 Hubble TensionHubble ConstantMeasurement from Planck and HSTHubble Tension

4 Summary

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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 energyIt behaves just like the energy density of the vacuum and isdenoted by Λ.

Cold dark matterIt interacts with ordinary matter gravitationally and its velocity ismuch less than that of light.

Ordinary matter

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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 beenexpanding since early times.

The curvature of space is very small.

Variations in density were laid down everywhere at early times, andare Gaussian, adiabatic, and nearly scale invariant as predicted byinflation.

The observable Universe has “trivial” topology.

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ΛCDM Model ΛCDM model

6 Parameters of ΛCDM Model

Density of baryons Ωb

Density of cold dark matter Ωc

Amplitude of a power-law spectrum of adiabatic perturbations As

Scalar spectral index of a power-law spectrum of adiabaticperturbations ns

Angular scale of acoustic oscillations θ∗

Optical depth to Thomson scattering from reionization τ

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ΛCDM Model ΛCDM model

6 Parameters of ΛCDM Model

Ωb Ωc As ns θ∗ τ

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ΛCDM Model ΛCDM model

Success of ΛCDM Model

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ΛCDM Model ΛCDM model

It’s That Easy

No, it’s not that easy.

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ΛCDM Model ΛCDM model

It’s That Easy

No, it’s not that easy.

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ΛCDM Model ΛCDM model

Unsolved Problem of ΛCDM Model

Cosmological Constnant Problem

Small Scale Crisis

Warm Dark Matter

Hubble Tension

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Hubble Tension Hubble Constant

Outline

1 Introduction

2 ΛCDM ModelΛ, Cosmological ConstantCold Dark MatterΛCDM model

3 Hubble TensionHubble ConstantMeasurement from Planck and HSTHubble Tension

4 Summary

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Hubble Tension Hubble Constant

Hubble Lemaıtre Law

Hubble Lemaıtre Law saysv = H0d

v is recession velocity, d is proper distance, and H0 is Hubble constant.

According to Friedmann equation, Hubble parameter H varies with time.

H2 =8πG

3ρ− kc2

a2+

Λc2

3

When we use the word Hubble constant H0, it points out the value ofHubble parameter in this time.

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Hubble Tension Measurement from Planck and HST

Outline

1 Introduction

2 ΛCDM ModelΛ, Cosmological ConstantCold Dark MatterΛCDM model

3 Hubble TensionHubble ConstantMeasurement from Planck and HSTHubble Tension

4 Summary

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Hubble Tension Measurement from Planck and HST

Planck Mission

Planck was ESA’s mission to observethe cosmic microwave background.

It was designed to image thetemperature and polarizationanisotropies of the Cosmic BackgroundRadiation Field.

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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 constantcan be calculated.

In 2018, Planck releases final results and it gives

H0 = 67.66 ± 0.42 km/s/Mpc

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Hubble Tension Measurement from Planck and HST

Intuitive Way to Measure Hubble Constant

Hubble constant is the ration between recession velocity and distance.

Although Planck gives the value of H0, the way of measurement is notintuitive.

The direct way to measure H0 is measuring v and d for cosmologicalobjects and calculating H0 = v/d .

v can be measured by measuring red shift but measuring d is difficult.

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Hubble Tension Measurement from Planck and HST

Tools for Distance Measurement

Type Ia Supernovae

Characteristic Light Curve

Cepheid Variables

Period Luminosity Relation

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Hubble Tension Measurement from Planck and HST

Hubble Constant from HST

Hubble Space Telescope can measurethe luminosity of Type Ia supernovaeand Cepheid variables.

So it can measure the distance ofgalaxy including them.

HST release its result for H0.

H0 = 74.03 ± 1.42 km/s/Mpc

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Hubble Tension Hubble Tension

Outline

1 Introduction

2 ΛCDM ModelΛ, Cosmological ConstantCold Dark MatterΛCDM model

3 Hubble TensionHubble ConstantMeasurement from Planck and HSTHubble Tension

4 Summary

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Hubble Tension Hubble Tension

Hubble Tension

Now we have two result for H0.

H0 = 67.66 ± 0.42 km/s/Mpc (Planck)

H0 = 74.03 ± 1.42 km/s/Mpc (HST)

There exists the 4.4σ difference between local measurements of H0 byHST and the value predicted from Planck + ΛCDM.

This difference is called Hubble Tension.

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Hubble Tension Hubble Tension

Hubble Tension

Now we have two result for H0.

H0 = 67.66 ± 0.42 km/s/Mpc (Planck)

H0 = 74.03 ± 1.42 km/s/Mpc (HST)

There exists the 4.4σ difference between local measurements of H0 byHST and the value predicted from Planck + ΛCDM.

This difference is called Hubble Tension.

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Hubble Tension Hubble Tension

Hubble Tension

Now we have two result for H0.

H0 = 67.66 ± 0.42 km/s/Mpc (Planck)

H0 = 74.03 ± 1.42 km/s/Mpc (HST)

There exists the 4.4σ difference between local measurements of H0 byHST and the value predicted from Planck + ΛCDM.

This difference is called Hubble Tension.

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Hubble Tension Hubble Tension

Plot for Hubble Tension

ΛCDM model is not sufficient to explain whole history of universe.

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Hubble Tension Hubble Tension

Moreover

Also, H0 = 54.4 ± 4.0 km/s/Mpc is proposed. (Nature Astronomy (2019)).

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Summary

Outline

1 Introduction

2 ΛCDM ModelΛ, Cosmological ConstantCold Dark MatterΛCDM model

3 Hubble TensionHubble ConstantMeasurement from Planck and HSTHubble Tension

4 Summary

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Summary

Summary

ΛCDM model is the simplest model for our universe. It can explainmany cosmological phenomena.

Hubble constant from Planck and HST shows significant difference.It indicates that ΛCDM model is not perfect.

Our universe is not simple as we expected.

It is more interesting than we expected.

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Summary

Thank You for Your Listening

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Summary

References

Vennin, Vincent. (2014). Cosmological Inflation: Theoretical Aspects and Observational Constraints.

arXiv:1807.06205

http://www.esa.int/ESA_Multimedia/Images/2007/01/Front_view_of_the_Planck_satellite

https://catalog.archives.gov/OpaAPI/media/23486741/content/stillpix/255-sts/STS125/STS125_ESC_

JPG/255-STS-s125e011848.jpg

arXiv:astro-ph/0604069

http://pla.esac.esa.int/pla/#home

arXiv:1807.06209

A. G. Riess, L. M. Macri, S. L. Hoffmann, D. Scolnic, S. Casertano, A. V. Filippenko, B. E. Tucker, M. J. Reid, D.O. Jones, J. M. Silverman, R. Chornock, P. Challis, W. Yuan, P. J. Brown, and R. J. Foley, The AstrophysicalJournal 826, 56 (2016).

http://www.outerspacecentral.com/supernova_page.html

I. Meschin, C. Gallart, A. Aparicio, S. Cassisi, and A. Rosenberg, The Astronomical Journal 137, 3619 (2009).

A. G. Riess, S. Casertano, W. Yuan, L. M. Macri, and D. Scolnic, The Astrophysical Journal 876, 85 (2019).

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