MODERN COSMOLOGY LECTURE FYTN08 - Lunds...

ModernCosmologyFYTN08

Johan Bijnens

Overview

Problems

Inflation

Epochs

Distanceladder,expansion

CMB

Acousticpeaks

Dark matter

Hubbleconstant

1/37

MODERN COSMOLOGY LECTURE FYTN08

Johan Bijnens

Lund University

[email protected]

http://www.thep.lu.se/∼bijnens

Cosmology Lecture — FYTN08 —Updated 2020

http://www.thep.lu.se/~bijnens/


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

2/37

Overview


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

3/37

Overview

1 Overview

2 Some problems with a simple expanding universe

3 Inflation

4 Epochs

5 Distance ladder, expansion

6 CMB

7 Acoustic peaks

8 Dark matter

9 Hubble constant

Credit many pictures: ESA, NASA, WMAP, Planck, Scientific American


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

4/37

Problems I: Flatness problem

Rewrite Friedman-Lemaıtre equation as

3H2

8π= − 3k2

8πR2+ ρ H =

R

R

k = 0 or flat defines critical density ρc ≡ 3H2

8π

measure all components of ρ in units of ρc : Ωi = ρiρc

Time evolution

k

R(t)2= H(t)2 (Ω(t)− 1)

e.g. Matterdominated (Ω(t)− 1) ∝ kt2/3

Ω ≈ 1 does not stay there

Flatness problem: close to 1 now, really close to 1 in earlyuniverse

For cosmological constant dominated:R(t) ∝ eαt =⇒ (Ω(t)− 1) ∝ e−2αt


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

5/37

Problems II

We see the universe as the same from all directions

Not all these spots have had time to talk to each other

Homogeneity problem

Many phase transitions possible

Create defects: vortices (cosmic strings), domain walls,. . .

All of these contain large amounts of energy

None seen, so either no phase transitions or they have hadtime to align

Monopole problem


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

6/37

Problems III

The early universe was very smooth

Where does the observed structure come from?

Much structure seen: galaxies, voids, sheets, the greatwall,. . .

How are these formed?

Structure formation problem


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

7/37

Inflation

At some point very early in the universe we had a perioddominated by Λ

This is not the present Λ or dark energy

Blow up a small region that had fully homogeneized toenormous size

Solves homogeneity problemSolves monopole problem (for earlier first order phasetransitions)

That bit also gets really flat

Solves flatness problem

During the blowup: quantum fluctuations get very big,become real

Possible seeds of structure

Can solve structure problem


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

8/37

Inflation

credit NASA/IPAC


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

9/37

Epochs

Matter ρM ∝ R−3, radiation ρR ∝ R−4

In addition all momenta were bigger earlier sinceλ ∝ 1

p ∝ R(t)

Early universe dominated by radiation

Present: Matter+cosmological constant (dark energy)

t ≈ 300000 years or T ≈ 1eV : decoupling/recombination

Accident: becomes radiation dominated at about the sametime

t ≈ a few minutes or T ≈ 1 MeV: Primordialnucleosynthesis (BBN)

Much earlier T >> 100 GeV: Inflation


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

10/37

Distance ladder

Main problem in cosmology: Measuring distances

Distance ladder:

Parallax: triangulation

easy in principletake base: Earth orbitmain problem: how accurate to measure the anglesNote old debate: if earth moves around sun,why don’t the stars move?Now dominated by satellite: Hipparchos, Hubble, Gaia

Redshift distance: simply take the redshift as a measure ofdistance

Luminosity distance


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

11/37

Distance ladder

Luminosity distance

Flux (in flat space) goes like 1/d2

Know Luminosity at source, measure luminosity at earth⇒ know the distanceSmall correction: if curvature take into account (exampleall the light emitted in a sphere surface from Southpolearrives at Northpole)

Essentially start close by and then work further out

Cepheid variables: period ⇒ Luminosity

. . .

Supernovae Ia: Luminosity decay period ⇒ Luminosity


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

12/37

Expansion

Nobel Prize 2011


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

13/37

Three main satellites

COBE: up 1989-1992 Final data 1996

WMAP : up 2001-2010 Final data 2012

Planck: up 2009-2013: Final data released: 2018

Also many ground based measurements, galaxy surveys,. . .


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

14/37

Perfect black body radiation


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

15/37

Perfect black body radiation


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

16/37

CMB: homogeneity/isotropy

This is data, not a uniform pictureNote: CMB discovered 1960s, Nobel Prize 1978 Penzias Wilson


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

17/37


So v ≈ 600 km/sOriginally discovered in 1970s


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

18/37


Nobel Prize 2006 Mather Smoot


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

19/37



Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

20/37

WMAP/Planck

More frequencies (COBE 3, WMAP 5, Planck 9)

Much better angular resolution

Much better sensitivity

Polarization

Note: all-sky pictures have a fit of the foreground removedand a simualated spectrum across the galaxy


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

21/37

WMAP 5 year


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

22/37

Planck Nine months


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

23/37

Planck 2 years


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

24/37

Angular spectrum of fluctuations


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

25/37

WMAP 5 year

Plot temperature or intensity as a function of I (θ, φ)

I (θ, φ) =∑lm

ClmYml (θ, φ)

For each l average the power over m: Cl

So we have an angular measure and fluctuations

Ground based ones add at high l


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

26/37

Planck Two years

Note: SEVEN peaks now visible


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

27/37

Everyone

2 100 500 1000 1500 2000 2500 3000

ℓ

102

103

104

D ℓ[µK2 ]

Planck

WMAP9

ACT

SPT

Can fit to nine peaks


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

28/37

The source of the fluctuations

Small quantum fluctuations do exist

Inflation blows them up so they cannot disappear again

Expected power spectrum Ps = As

(k

k0

)ns

Tensor spectrum can come from priomordial gravitational

waves Pt = At

(k

k0

)nt

Inflation predics ns ≈ 1 (scale invariant) and usually alittle below 1.

So then inflation stops, what now?


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

29/37

Growing and oscillating

Very long wavelength: frozen in, no time to interact

As soon as within horizon (i.e. time to interact)Fluctuations grow: denser spots grow denser, rarer spotsgrow rarer (gravity is attractive)

Then however: universe is dominated by radiation: weknow the photon gas

If too dense, pressure counteracts the compression bygravity, like sound waves (hence acoustic oscillations)

Matter reacts much slower and in first hand only normalmatter reacts with the photons

So height first peak depends on photon density, we knowthat one, so get information on total matter and from thedifferent sizes first second peak also on baryonic matter


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

30/37

How big is the first peak

We know the real size of the first peak plus the age, so theangle of view tells us flat, open (hyperbolical) or closed(spherical) from the shape of the triangles

If neutrinos had mass: streaming kills of those peaks soupper limit on neutrino mass.

CMB fluctuations should hook on to those measured fromgalaxy distributions (surveys)

Number of neutrinos: how many radiation species: affectsrate of expansion also visible


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

31/37

Parameters

1− Ω −0.0008± 0.0040ΩΛ 0.6911±0.0062

Ωbh2 0.02230± 0.00014

Ωch2 0.1188± 0.0010

H0 67.74± 0.46 km/s/Mpch 0.6774± 0.0046

Age 13.799± 0.021 Gyrns 0.9667± 0.0040∑ν mν < 0.194 eVw −1.006± 0.045


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

32/37

Universe content (WMAP)

No Big Bang

1 20 1 2 3

expands forever

−1

0

1

2

3

2

3

closed

Supernovae

CMB

Clusters

SNe: Knop et al. (2003)CMB: Spergel et al. (2003)Clusters: Allen et al. (2002)

ΩΛ

ΩM

open

flat

recollapses eventually


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

33/37

Universe content (WMAP)


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

34/37

Dark matter

Galaxy rotation curves: flat???


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

35/37

Dark matter

Globular clusters: also more matter needed than visible tobound them

Seen in essentially all galaxies

Clusters of galaxies

Dark matter needed for galaxy formation

Weigh galaxies by gravitational lensing: see directly darkmatter

Colliding galaxies: dust interacts strongly, starsless, darkmatter even less


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

36/37

Dark matter

Credit: X-ray: NASA/CXC/M.Markevitch et al. Optical: NASA/STScI; Magellan/U.Arizona/D.Clowe et al.

Lensing Map: NASA/STScI; ESO WFI; Magellan/U.Arizona/D.Clowe et al.


Johan Bijnens

Overview

Problems

Inflation

Epochs


CMB

Acousticpeaks

Dark matter

Hubbleconstant

37/37

Hubble constant

Lensed quasars: 73.3+1.7−1.8 km/s/Mpc

Cepheid/supernova Ia: 74.0± 1.4 km/s/Mpc

CMB (dominated by Planck): 67.4± 0.5 km/s/Mpc

CMB is at z ≈ 1000

Others are at z ∼ a few

Systematic errors, Λ varies with time,. . .

MODERN COSMOLOGY LECTURE FYTN08 - Lunds...

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