Summary of part II: the homogeneous Universe

(1)

Copyleft Martín Makler

Friedmann’s Equation

Energy Conservation

Two paths: Newtonian General Relativity

Energy conservation (of test

particle) in spherical gravitational potential

First law of

thermodynamics

(+ special relativity)

(2)

Friedmann’s Equation

Energy Conservation

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

Energy conservation (of test

particle) in spherical gravitational potential

First law of

thermodynamics (+ special relativity)

G _µ⌫ = 8⇡ GT _µ⌫

Homogeneous and isotropic line element

+ Einstein’s equation

(3)

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

Homogeneous and isotropic line element

+ Null geodesic:

(4)

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

a(t)dr = dt

Light propagation in co-moving coordinates ( ^{c =1} )

Homogeneous and isotropic line element

+ Null geodesic:

(5)

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

a(t)dr = dt

Light propagation in co-moving coordinates ( ^{c =1} )

Homogeneous and isotropic line element

+ Null geodesic:

Flux:

(6)

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

a(t)dr = dt

Light propagation in co-moving coordinates ( ^{c =1} )

Homogeneous and isotropic line element

+ Null geodesic:

Flux:

For ^{K = 0}

(7)

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

a(t)dr = dt

Light propagation in co-moving coordinates ( ^{c =1} )

Homogeneous and isotropic line element

+ Null geodesic:

Flux:

For ^{K = 0}

(8)

The Dark Side of the Universe

Episode II

The Accelerating

Universe

(9)

Type Ia Supernovae and Cosmology

Advantages:

Extreme Luminosities (10 ⁹ - 10 ¹⁰ L _ )

 May be detected at

large distances

(10)

Very homogeneous

 Standardizable candles

Type Ia Supernovae Light Curves

(11)

Type Ia Supernovae and Cosmology

Advantages:

Extreme Luminosities (10 ⁹ - 10 ¹⁰ L _ )

Very homogeneous

 Standardizable candles

Disadvantages:

• Rare and random events

~ 1/500 yr/galaxy

• Short duration

Solution:

• Automated search

• SCP, High-z team

(12)

The Accelerating Universe

Dark Energy or Cosmological Constant

• Hubble diagram for large distances

 The expansion is accelerating

But

(13)

The Decelerated Universe!

(14)

Current Results

14 Betoule, et al. ApJ, 2014, 568, A22;

arXiv:1401.4064

Joint light-curve analysis (JLA)

p = w ⇢

Combined with CMB (+flat):

Combined with BAO (+flat):

(15)

Scale factor

Evolution of the Universe (Λ = 0)

Age x H ₀ ^-1 a

Figure: Kepler Oliveira, Maria de Fátima Saraiva Astronomia e Astrofísica, http://astro.if.ufrgs.br /

Age of the Universe

(16)

Age of the Universe

 Acceleration

solves the age problem

Figure: Kepler Oliveira, Maria de Fátima Saraiva, Astronomia e Astrofísica, http://astro.if.ufrgs.br /

(17)

Dark Energy

2/3 of the energy density of the Universe are in the form of Dark Energy! (or Λ = 0)

Evidences:

 Accelerated expansion of distant galaxies

 Age of the Universe

 Small curvature

 Integrated Sachs-Wolfe effect

 Combined analyses of cosmological observables (cosmic concordance)

Candidates (Taxonomy of Dark Energy):

 Cosmological constant

 Scalar field:

– Quintessence

– Quartessence, k-essence, spintessencia, snot...

Modified gravity

(18)

Part III

The Homogeneous Universe II:

A Brief Thermal History of the Universe

(19)

Nucleosynthesis:

Alchemy in the primordial Universe

Production of ⁷ Li, ³ He, D, ⁴ He

z ~ 10 ⁴ , 3MeV,T ~ 10 ¹⁰ K - 10 ⁹ K, 1s a 3min “after BB”

Cartoon from http://blueox.uoregon.edu/~karen/astro123/lectures/lec20.html

(20)

(

Light Element Production

Figure: Kepler Oliveira, Maria de Fátima Saraiva Astronomia e Astrofísica, http://astro.if.ufrgs.br /

Radiation dominated

Universe: )

Radiation dominated Universe:

• H = H(T)

• interaction rate f(T) depends only on

η = n _b /n _γ

(21)

Light Element Abundance

Production of ⁷ Li, ³ He, D, ⁴ He with the same η !

D is the best “baryometer”

Independent of

Dark Matter

(22)

Recombination

Happens at 0.26eV instead of 13.6eV!

plasma

neutral matter

Figure from http://blueox.uoregon.edu/~karen/astro123/lectures/lec20.html

(23)

When the temperature drops below 3.000K the electrons get bounded to the nuclei

 The Universe becomes transparent

 Light propagates freely

Figure from http://blueox.uoregon.edu/~karen/astro123/lectures/lec21.html

Recombination

(24)

The Cosmic Microwave Background

“Photosphere”

seen from our galaxy

Expect to see:

Black body with redshift

z ~ 1000

(25)

Spectrum of the CMB

Wavelenght [cm ^-1 ]

100σ error bars

thermal spectrum with

T = 2.725 ± 0.002 K

(26)

Cosmic Microwave Background I

Cosmic Microwave Background Radiation Map

 Epoch of matter and radiation decoupling (about 380.000 years after the “Big-Bang”).

 T ₀ = 2.725 ± 0.002. Redshift, z = 1089.

 Highly homogeneous primordial Unverse

 Dipole: ΔT = 3.346 ± 0.017 mK  v _gal = 360 Km/s

Contrast: 1x 400x

(27)

Cosmic Microwave Background I

Cosmic Microwave Background Radiation Map

 Epoch of matter and radiation decoupling (about 380.000 years after the “Big-Bang”).

 T ₀ = 2.725 ± 0.002. Redshift, z = 1089.

 Highly homogeneous primordial Unverse

 Dipole: ΔT = 3.346 ± 0.017 mK  v _gal = 360 Km/s

Contrast: 1x 400x

(28)

Some Milestones in the History of the Universe

kT (radiation) Event 2 x 10 ^-4 eV Today

10 ^-3 eV Galaxy formation

0.26 eV H recombination ⁽ matter-radiation decoupling )

10 eV Matter domination

300 keV Formation of light elements (He ⁴ , He ³ , D e Li)

(primordial nucleosynthesis)

0.5 MeV End of leptonic era ⁽ ^e

⁺

^e

^-

annihilation )

100 MeV End of hadronic era and beginning of leptonic era

( hadronization, annihilation hadron anti-hadron )

1000 GeV Electroweak phase transition

10 ¹⁵ GeV Bariosynthesis? Great Unification?

10 ¹⁹ GeV End of quantum era? Inflation?

(29)

The Perturbed Universe CMB anisotropies and

Large-scale Structure

(30)

Anisotropies in the Cosmic Background

 T ₀ = 2.725 ± 0.002.

redshift, z = 1089

 The primordial Universe was highly homogeneous

 Dipole:

Δ T = 3.346 ± 0.017 mK

⇒ v _gal = 360 Km/s

 Temperature fluctuations:

Nobel prizes: 1978, 2006

(31)

WMAP2008

Cosmic Microwave Background

Power Spectrum

(32)

Planck 2015 Anisotropy Map

32

(33)

Relativistic perturbation theory

 The starting point is the perturbed Robertson-Walker metric

 At the linear level modes decouple

 Scalar perturbations:

(for a perfect fluid Φ = Ψ)

(34)

Results from the linear analysis

Need for Dark Matter

 Baryonic matter: can only cluster after decoupling t _dec ~ 380.000 years

and for r > λ _J (Jeans length)

 Cold Dark Matter starts clustering at t _eq ~ 56.000 years (matter-radiation equality)

 Baryons follow the Dark Matter potential wells

 Silk damping decreases the amplitude of baryon

perturbations

(35)

CMB Anisotropies

 Primary Anisotropies

Doppler effect

Intrinsic temperature fluctuation

Sachs-Wolfe effect

 On large scales

 Sachs-Wolfe plateau

 On small scales:

baryon acoustic oscillations

(36)

Integrated Sachs-Wolfe Effect

 Cumulative effect of gravitational shifts

 Linear evolution, Ω _M = 1  φ = const.

 Late effect:

 Correlation between the cosmic microwave background and large-scale structure!

Dark Energy

http://physicsworld.com/cws/article/print/19419

(37)

Combining the Contributions

 Damping:

 Photon diffusion in hot regions (Silk damping)

 Finite thickness of last scattering surface

ht tp: // ba ckground.uc hi ca go.e du/ ~w hu/ phys ic s/ tour .ht m l

(38)

Angular Power Spectrum

+polarização…

• As predicted

• Concordance model

• Only 6

parameters fit the data!

l

l ≈ 180°/θ

WMAP5

(39)

d _A ⌘ D

✓

(for ✓ ⌧ 1)

Angular Diameter Distance

39 Standard ruler

d A may decrease with z!

D = a (t ₁ ) r ₁ ✓

thus such that ^d A = a (t ₁ ) r ₁

(40)

d _A ⌘ D

✓

(for ✓ ⌧ 1)

d _A = (1 + z ) ² d _L

Angular Diameter Distance

40 Standard ruler

D = a (t ₁ ) r ₁ ✓

thus such that ^d A = a (t ₁ ) r ₁

Valid for any space-time!

(41)

Angular scale of acoustic horizon at decoupling:

Acoustic horizon

Angular diameter distance

At z ~ 1000 is mostly sensitive on For a flat Universe,

Peaks in the Cosmic Microwave Background

where Sta nda rd rule r

✓ _A ⌦ _K = 1 ⌦ ₀

✓ _A ' 1

(42)

The Universe is flat!

Dark Matter Dark Energy

Power spectrum according to WMAP5

l

(43)

The wholly grail of Cosmology

Dark Matter and Dark Energy

ordinary matter: 4%

Dark

matter:

~ 22%

The Universe is (almost) flat remaining ∼ 74%:

dark energy

l

(44)

Planck 2015 power spectrum

44 Planck collaboration, 2016, A&A 594, A11 (2016)

(45)

Secondary Anisotropies

 Integrated Sachs-Wolfe effect

 Gravitational Lensing

 Rees-Sciama effect

 Gravitational waves

 Scattering: reionization

and Sunyaev Zel’dovich

(46)

Sunyaev Zel’dovich Effect

 Efeito Compton inverso

 Distorção da RCF em escalas de arcmin

 Independente de z

(47)

Advantage of Sunyaev Zel’dovich Effect

 X-ray flux drops as (1 + z ) ^-4

 Decrement is independent from z

X-ray emission

SZ effect

(48)

CMB Polarization

(49)

Polarization Spectrum

 TE and EE components

 BB component

 Gravitational

waves

(50)

Planck Polarization Map

50

(51)

Polarization Power Spectra

51 Planck 2015

Summary of part II: the homogeneous Universe - MESONPI

Friedmann’s Equation

Energy Conservation

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

Energy conservation (of test

particle) in spherical gravitational potential

First law of

thermodynamics

(+ special relativity)

Friedmann’s Equation

Energy Conservation

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

Energy conservation (of test

particle) in spherical gravitational potential

First law of

thermodynamics (+ special relativity)

G µ⌫ = 8⇡ GT µ⌫

Homogeneous and isotropic line element

+ Einstein’s equation

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

Homogeneous and isotropic line element

+ Null geodesic:

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

a(t)dr = dt

Light propagation in co-moving coordinates ( c =1 )

Homogeneous and isotropic line element

+ Null geodesic:

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

a(t)dr = dt

Light propagation in co-moving coordinates ( c =1 )

Homogeneous and isotropic line element

+ Null geodesic:

Flux:

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

a(t)dr = dt

Light propagation in co-moving coordinates ( c =1 )

Homogeneous and isotropic line element

+ Null geodesic:

Flux:

For K = 0

Summary of part II: the homogeneous Universe

Two paths: Newtonian General Relativity

a(t)dr = dt

Light propagation in co-moving coordinates ( c =1 )

Homogeneous and isotropic line element

+ Null geodesic:

Flux:

For K = 0

The Dark Side of the Universe

Episode II

The Accelerating

Universe

Type Ia Supernovae and Cosmology

Advantages:

Extreme Luminosities (10 9 - 10 10 L  )

 May be detected at

large distances

Very homogeneous

 Standardizable candles

Type Ia Supernovae Light Curves

Type Ia Supernovae and Cosmology

Advantages:

Extreme Luminosities (10 9 - 10 10 L  )

Very homogeneous

 Standardizable candles

Disadvantages:

• Rare and random events

~ 1/500 yr/galaxy

• Short duration

Solution:

• Automated search

• SCP, High-z team

The Accelerating Universe

Dark Energy or Cosmological Constant

G _µ⌫ = 8⇡ GT _µ⌫

Light propagation in co-moving coordinates ( ^{c =1} )

Light propagation in co-moving coordinates ( ^{c =1} )

Light propagation in co-moving coordinates ( ^{c =1} )

For ^{K = 0}

Light propagation in co-moving coordinates ( ^{c =1} )

For ^{K = 0}

Extreme Luminosities (10 ⁹ - 10 ¹⁰ L _ )

Extreme Luminosities (10 ⁹ - 10 ¹⁰ L _ )

Age x H ₀ ^-1 a

Production of ⁷ Li, ³ He, D, ⁴ He

z ~ 10 ⁴ , 3MeV,T ~ 10 ¹⁰ K - 10 ⁹ K, 1s a 3min “after BB”

η = n _b /n _γ

Production of ⁷ Li, ³ He, D, ⁴ He with the same η !