MITP Workshop Quantum Vacuum and Gravitation Ruth Durrer (Universit - - PowerPoint PPT Presentation

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MITP Workshop Quantum Vacuum and Gravitation Ruth Durrer (Universit - - PowerPoint PPT Presentation

Aug 21, 2022 38 likes •644 views

The Cosmic Microwave Background and Quantum Physics Ruth Durrer Universit e de Gen` eve D epartment de Physique Th eorique et Center for Astroparticle Physics MITP Workshop Quantum Vacuum and Gravitation Ruth Durrer (Universit e

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SLIDE 1

The Cosmic Microwave Background and Quantum Physics

Ruth Durrer Universit´ e de Gen` eve D´ epartment de Physique Th´ eorique et Center for Astroparticle Physics

MITP Workshop Quantum Vacuum and Gravitation

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 1 / 26

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SLIDE 2

Contenu

1

Introduction

2

Fluctuations in the CMB

3

Why inflation

4

Evidence for Λ

5

Conclusions

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 2 / 26

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SLIDE 3

Introduction

The cosmological initial fluctuations most probably stem from quantum fluctuations generated during inflation.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 3 / 26

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SLIDE 4

Introduction

The cosmological initial fluctuations most probably stem from quantum fluctuations generated during inflation. What are the strongest indications that this is so?

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 3 / 26

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SLIDE 5

Introduction

The cosmological initial fluctuations most probably stem from quantum fluctuations generated during inflation. What are the strongest indications that this is so? CMB parameter estimation favors a composition of the Universe with close to 70% quantum vacuum energy.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 3 / 26

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SLIDE 6

Introduction

The cosmological initial fluctuations most probably stem from quantum fluctuations generated during inflation. What are the strongest indications that this is so? CMB parameter estimation favors a composition of the Universe with close to 70% quantum vacuum energy. How sure are we?

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 3 / 26

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SLIDE 7

Introduction

Accidental discovery of the CMB by Arno Penzias and Robert Wilson 50 years ago (Nobel Prize 1978)

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 4 / 26

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SLIDE 8

Introduction

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 5 / 26

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SLIDE 9

Introduction

Gamov has predicted the existence of the CMB already in 1948. Here with Alpher and Hermann.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 6 / 26

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SLIDE 10

The cosmic microwave background (CMB)

The Universe is expanding. In the past it was much denser and hotter.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 7 / 26

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SLIDE 11

The cosmic microwave background (CMB)

The Universe is expanding. In the past it was much denser and hotter. At T > 3000K hydrogen was ionised and the ’cosmic plasma’ of protons, electrons and photons was strongly coupled by Thomson scattering and in thermal equilibrium.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 7 / 26

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SLIDE 12

The cosmic microwave background (CMB)

The Universe is expanding. In the past it was much denser and hotter. At T > 3000K hydrogen was ionised and the ’cosmic plasma’ of protons, electrons and photons was strongly coupled by Thomson scattering and in thermal equilibrium. At T ≃ 3000K protons and electrons combined to neutral hydrogen. The photons became free and their distribution evolved simply by redshifting of the photon energies to a thermal distribution with T0 = 2.7255 ± 0.0006K today.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 7 / 26

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SLIDE 13

The cosmic microwave background (CMB)

The Universe is expanding. In the past it was much denser and hotter. At T > 3000K hydrogen was ionised and the ’cosmic plasma’ of protons, electrons and photons was strongly coupled by Thomson scattering and in thermal equilibrium. At T ≃ 3000K protons and electrons combined to neutral hydrogen. The photons became free and their distribution evolved simply by redshifting of the photon energies to a thermal distribution with T0 = 2.7255 ± 0.0006K today. This corresponds to about 400 photons per cm3 with typical energy of Eγ = kT0 ≃ 2.3 × 10−4eV ≃ 150GHz (λ ≃ 0.2cm). This is the observed CMB.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 7 / 26

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SLIDE 14

The cosmic microwave background (CMB)

The Universe is expanding. In the past it was much denser and hotter. At T > 3000K hydrogen was ionised and the ’cosmic plasma’ of protons, electrons and photons was strongly coupled by Thomson scattering and in thermal equilibrium. At T ≃ 3000K protons and electrons combined to neutral hydrogen. The photons became free and their distribution evolved simply by redshifting of the photon energies to a thermal distribution with T0 = 2.7255 ± 0.0006K today. This corresponds to about 400 photons per cm3 with typical energy of Eγ = kT0 ≃ 2.3 × 10−4eV ≃ 150GHz (λ ≃ 0.2cm). This is the observed CMB. At T > 9300K≃ 0.8eV the Universe was ’radiation dominated’, i.e. its energy density was dominated by the contribution from these photons (and 3 species of relativistic neutrinos which made up about 35%). Hence initial fluctuations in the energy density of the Universe should be imprinted as fluctuations in the CMB temperature.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 7 / 26

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SLIDE 15

The frequency spectrum of the CMB

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 8 / 26

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SLIDE 16

CMB fluctuations and structure formation

We assume that structures in the Universe (galaxies, clusters, filaments and voids) formed by gravitational instability from small initial fluctuations.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 9 / 26

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SLIDE 17

CMB fluctuations and structure formation

We assume that structures in the Universe (galaxies, clusters, filaments and voids) formed by gravitational instability from small initial fluctuations. Due to the expansion of the Universe the fluctuations grow only very slowly and statistical initial fluctuations are far too small. Initial fluctuations of the order of 10−5 are needed.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 9 / 26

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SLIDE 18

CMB fluctuations and structure formation

We assume that structures in the Universe (galaxies, clusters, filaments and voids) formed by gravitational instability from small initial fluctuations. Due to the expansion of the Universe the fluctuations grow only very slowly and statistical initial fluctuations are far too small. Initial fluctuations of the order of 10−5 are needed. A inflationary phase can generate them. As we have seen in the previous talk, during inflation quantum fluctuations of the metric and of the scalar field are amplified by their coupling to the time dependent background metric.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 9 / 26

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SLIDE 19

CMB fluctuations and structure formation

We assume that structures in the Universe (galaxies, clusters, filaments and voids) formed by gravitational instability from small initial fluctuations. Due to the expansion of the Universe the fluctuations grow only very slowly and statistical initial fluctuations are far too small. Initial fluctuations of the order of 10−5 are needed. A inflationary phase can generate them. As we have seen in the previous talk, during inflation quantum fluctuations of the metric and of the scalar field are amplified by their coupling to the time dependent background metric. These fluctuations get ’squeezed’ and after inflation they become classical fluctuations of the energy density and of the metric. They are also present as coherent fluctuations in the CMB.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 9 / 26

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SLIDE 20

CMB fluctuations and structure formation

We assume that structures in the Universe (galaxies, clusters, filaments and voids) formed by gravitational instability from small initial fluctuations. Due to the expansion of the Universe the fluctuations grow only very slowly and statistical initial fluctuations are far too small. Initial fluctuations of the order of 10−5 are needed. A inflationary phase can generate them. As we have seen in the previous talk, during inflation quantum fluctuations of the metric and of the scalar field are amplified by their coupling to the time dependent background metric. These fluctuations get ’squeezed’ and after inflation they become classical fluctuations of the energy density and of the metric. They are also present as coherent fluctuations in the CMB. Immediately after its discovery, astrophysicists began to search for fluctuations in the CMB. The found them in 1992 with the COBE satellite (Nobel Prize 2006).

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 9 / 26

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SLIDE 21

Fluctuations in the CMB

T0 = 2.7255K ∆T(n) =

ℓm aℓmYℓm(n)

Cℓ = |aℓm|2, Dℓ = ℓ(ℓ + 1)Cℓ/(2π)

1000 2000 3000 4000 5000 6000

DTT

  • [µK2]

30 500 1000 1500 2000 2500

  • 60
  • 30

30 60

∆DTT

  • 2

10

  • 600
  • 300

300 600

From the Planck Collaboration Planck Results XIII (2015) arXiv:1502.01589

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 10 / 26

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SLIDE 22

The cosmic microwave background (CMB)

100 1000 2000 3000 4000 5000 6000 DTT

  • [µK2]

30 500 1000 1500 2000 2500

  • 60
  • 30

30 60

∆DTT

  • 2

10

  • 600
  • 300

300 600

(Hu & Dodelson, 2002) (Planck Collaboration 2015)

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 11 / 26

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SLIDE 23

The physics of CMB fluctuations

The CMB fluctuations into a direction n in the instant decoupling approximation and in linear perturbation theory are given by ∆T T (n) = 1 4Dg + n · V + Ψ + Φ

  • (n, τ∗) +

s0

s∗

∂τ(Ψ + Φ)ds . (RD 1991) In the radiation dominated Universe small density fluctuations perform acoustic

  • scillations at constant amplitude, Dg ≃ − 20

3 Ψ0 cos(k

  • csdτ).

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 12 / 26

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SLIDE 24

The physics of CMB fluctuations

The CMB fluctuations into a direction n in the instant decoupling approximation and in linear perturbation theory are given by ∆T T (n) = 1 4Dg + n · V + Ψ + Φ

  • (n, τ∗) +

s0

s∗

∂τ(Ψ + Φ)ds . (RD 1991) In the radiation dominated Universe small density fluctuations perform acoustic

  • scillations at constant amplitude, Dg ≃ − 20

3 Ψ0 cos(k

  • csdτ).

The wavelength corresponding to the first acoustic peak is λ∗ = 2π/k∗ with k∗ τ∗ csdτ = π. In a matter-radiation Universe this gives (ωx = Ωxh2) H0 h (1 + z∗)λ∗ = 4 √ 3rωm log   √ 1 + z∗ + r +

  • (1+z∗)rωr

ωm

+ r √ 1 + z∗

  • 1 +
  • rωr

ωm

 , r = 3ωb 4ωγ .

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 12 / 26

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SLIDE 25

The physics of CMB fluctuations

The CMB fluctuations into a direction n in the instant decoupling approximation and in linear perturbation theory are given by ∆T T (n) = 1 4Dg + n · V + Ψ + Φ

  • (n, τ∗) +

s0

s∗

∂τ(Ψ + Φ)ds . (RD 1991) In the radiation dominated Universe small density fluctuations perform acoustic

  • scillations at constant amplitude, Dg ≃ − 20

3 Ψ0 cos(k

  • csdτ).

The wavelength corresponding to the first acoustic peak is λ∗ = 2π/k∗ with k∗ τ∗ csdτ = π. In a matter-radiation Universe this gives (ωx = Ωxh2) H0 h (1 + z∗)λ∗ = 4 √ 3rωm log   √ 1 + z∗ + r +

  • (1+z∗)rωr

ωm

+ r √ 1 + z∗

  • 1 +
  • rωr

ωm

 , r = 3ωb 4ωγ . On small scales fluctuations are damped by free streaming (Silk damping). The fluctuations are lensed by foreground structures.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 12 / 26

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SLIDE 26

The distance to the CMB

The angle onto which the scale k∗ is projected depends on the angular diameter distance to the CMB, θ∗ = λ∗/(2dA(z∗) This is the best measured quantity of the CMB, with a relative error of about 3 × 10−4 θ∗ = r∗ dA(z∗) = (1.04077 ± 0.00032) × 10−2 . (Planck Collaboration: Planck results 2015 XIII [arXiv:1502.01589])

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 13 / 26

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SLIDE 27

The distance to the CMB

The angle onto which the scale k∗ is projected depends on the angular diameter distance to the CMB, θ∗ = λ∗/(2dA(z∗) This is the best measured quantity of the CMB, with a relative error of about 3 × 10−4 θ∗ = r∗ dA(z∗) = (1.04077 ± 0.00032) × 10−2 . (Planck Collaboration: Planck results 2015 XIII [arXiv:1502.01589]) The distance to the CMB is given by (1 + z∗)dA(z∗) = z∗ H(z)−1dz = h H0 z∗ 1

  • ωm(1 + z)3 + ωK(1 + z)2 + ωx(z)

dz

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 13 / 26

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SLIDE 28

Coherence

Why do we believe that these fluctuations come from a period of inflation?

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 14 / 26

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SLIDE 29

Coherence

Why do we believe that these fluctuations come from a period of inflation? They have a nearly scale invariant, slightly red spectrum. ns = 0.9653 ± 0.0048

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 14 / 26

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SLIDE 30

Coherence

Why do we believe that these fluctuations come from a period of inflation? They have a nearly scale invariant, slightly red spectrum. ns = 0.9653 ± 0.0048 they are coherent: all fluctuations of a given wave number are in phase.

( + 1)C

(T) (V) (S)

( + 1)C ( + 1)C

RD, Kunz & Melchiorri, 2001

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 14 / 26

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SLIDE 31

Coherence & causality

It is extremely difficult to generate such coherent fluctuations in a causal way without invoking a period of inflation.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 15 / 26

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SLIDE 32

Coherence & causality

It is extremely difficult to generate such coherent fluctuations in a causal way without invoking a period of inflation. Fluctuations on very large scales, ℓ < 150 were super-Hubble at the time of decoupling and therefore, without invoking a period of inflation, there cannot be any structure in the CMB on these scales.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 15 / 26

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SLIDE 33

Coherence & causality

It is extremely difficult to generate such coherent fluctuations in a causal way without invoking a period of inflation. Fluctuations on very large scales, ℓ < 150 were super-Hubble at the time of decoupling and therefore, without invoking a period of inflation, there cannot be any structure in the CMB on these scales. In a ’causally generated’ CMB spectrum the first acoustic peak in the T-E correlation spectrum must be absent. (Spergel & Zaldarriaga 1997)

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 15 / 26

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SLIDE 34

Polarisation

The Thompson scattering cross section depends on polarisation.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 16 / 26

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SLIDE 35

Polarisation

The Thompson scattering cross section depends on polarisation. It is suppressed by a factor cos2ϑ for polarisation in the scattering plane.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 16 / 26

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SLIDE 36

Polarisation

The Thompson scattering cross section depends on polarisation. It is suppressed by a factor cos2ϑ for polarisation in the scattering plane. ⇒ A quadrupole anisotropy in the intensity (temperature) introduces linear polarisation.

e–

Linear Polarization Thomson Scattering Quadrupole x y z

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 16 / 26

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SLIDE 37

Polarisation

  • 140
  • 70

70 140

DT E

`

[µK2]

30 500 1000 1500 2000

`

  • 10

10

∆DT E

`

20 40 60 80 100

CEE

  • [10−5 µK2]

30 500 1000 1500 2000

  • 4

4

∆CEE

  • (The Planck Collaboration 2015)

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 17 / 26

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SLIDE 38

Acausality

We have considered a model with relativistic exploding shells leading to a scale invariant spectrum of fluctuations (Scodeller, Kunz & RD 2009) T-E spectrum E-E spectrum T-E spectrum E-E spectrum causal acausal v1 = 1.65, v2 = 2.4 (From Scodeller, Kunz, RD 2009)

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 18 / 26

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SLIDE 39

Polarisarion B and gravitational waves

Only tensor (and vector) perturbations can generate B polarisation. E B

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 19 / 26

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SLIDE 40

Limits on initial fluctuations

φ2

0.95 0.96 0.97 0.98 0.99 1.00

ns

0.00 0.05 0.10 0.15 0.20 0.25

r0.002

N = 5 N = 6 Convex Concave

φ

Planck TT+lowP Planck TT+lowP+BKP +lensing+ext

Planck Collaboration: Cosmological φ2

0.95 0.96 0.97 0.98 0.99 1.00

ns

0.00 0.05 0.10 0.15 0.20 0.25

r0.002

N = 5 N = 6 C

  • n

v e x C

  • n

c a v e

φ

Planck TT+lowP+lensing (∆Neff = 0.39) ΛCDM Planck TT+lowP +lensing+ext

The tensor to scalar ratio is r < ∼ 0.1. If r = 0 we might be able to test the slow roll consistency relation, r = −8nt.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 20 / 26

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SLIDE 41

The Planck ’base’ model

Curvature K = 0

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

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SLIDE 42

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

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SLIDE 43

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, Neff = 3.046 with temperature Tν = (4/11)1/3 T0

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

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SLIDE 44

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, Neff = 3.046 with temperature Tν = (4/11)1/3 T0 2 neutrino species are massless and the third has m3 = 0.06eV such that

  • i mi = 0.06eV.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

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SLIDE 45

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, Neff = 3.046 with temperature Tν = (4/11)1/3 T0 2 neutrino species are massless and the third has m3 = 0.06eV such that

  • i mi = 0.06eV.

Helium fraction Yp = 4nHe/nb is calculated from Neff and ωb.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

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SLIDE 46

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, Neff = 3.046 with temperature Tν = (4/11)1/3 T0 2 neutrino species are massless and the third has m3 = 0.06eV such that

  • i mi = 0.06eV.

Helium fraction Yp = 4nHe/nb is calculated from Neff and ωb. Parameters Amplitude uf curvature perturbations, As

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

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SLIDE 47

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, Neff = 3.046 with temperature Tν = (4/11)1/3 T0 2 neutrino species are massless and the third has m3 = 0.06eV such that

  • i mi = 0.06eV.

Helium fraction Yp = 4nHe/nb is calculated from Neff and ωb. Parameters Amplitude uf curvature perturbations, As Scalar spectral index, ns

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

slide-48
SLIDE 48

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, Neff = 3.046 with temperature Tν = (4/11)1/3 T0 2 neutrino species are massless and the third has m3 = 0.06eV such that

  • i mi = 0.06eV.

Helium fraction Yp = 4nHe/nb is calculated from Neff and ωb. Parameters Amplitude uf curvature perturbations, As Scalar spectral index, ns Baryon density ωb = Ωbh2

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

slide-49
SLIDE 49

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, Neff = 3.046 with temperature Tν = (4/11)1/3 T0 2 neutrino species are massless and the third has m3 = 0.06eV such that

  • i mi = 0.06eV.

Helium fraction Yp = 4nHe/nb is calculated from Neff and ωb. Parameters Amplitude uf curvature perturbations, As Scalar spectral index, ns Baryon density ωb = Ωbh2 Cold dark matter density ωc = Ωch2

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

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SLIDE 50

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, Neff = 3.046 with temperature Tν = (4/11)1/3 T0 2 neutrino species are massless and the third has m3 = 0.06eV such that

  • i mi = 0.06eV.

Helium fraction Yp = 4nHe/nb is calculated from Neff and ωb. Parameters Amplitude uf curvature perturbations, As Scalar spectral index, ns Baryon density ωb = Ωbh2 Cold dark matter density ωc = Ωch2 Present value of Hubble parameter H0 = 100hkm/sec/Mpc ΩΛ = 1 − (ωb + ωc)/h2.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

slide-51
SLIDE 51

The Planck ’base’ model

Curvature K = 0 No tensor perturbations, r = 0 Three species of thermal neutrinos, Neff = 3.046 with temperature Tν = (4/11)1/3 T0 2 neutrino species are massless and the third has m3 = 0.06eV such that

  • i mi = 0.06eV.

Helium fraction Yp = 4nHe/nb is calculated from Neff and ωb. Parameters Amplitude uf curvature perturbations, As Scalar spectral index, ns Baryon density ωb = Ωbh2 Cold dark matter density ωc = Ωch2 Present value of Hubble parameter H0 = 100hkm/sec/Mpc ΩΛ = 1 − (ωb + ωc)/h2.

  • ptical depth to reionization τ

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 21 / 26

slide-52
SLIDE 52

Cosmological parameters from Planck 2015 arXiv:1502.01589

0.04 0.08 0.12 0.16 τ 0.0200 0.0225 0.0250 0.0275 Ωbh2 0.10 0.11 0.12 0.13 Ωch2 2.96 3.04 3.12 3.20 ln(1010As) 0.93 0.96 0.99 1.02 ns 1.038 1.040 1.042 100θMC 0.04 0.08 0.12 0.16 τ 0.0200 0.0225 0.0250 0.0275 Ωbh2 0.10 0.11 0.12 0.13 Ωch2 2.96 3.04 3.12 3.20 ln(1010As) 0.93 0.96 0.99 1.02 ns

Planck EE+lowP Planck TE+lowP Planck TT+lowP Planck TT,TE,EE+lowP

ns = 0.9653 ± 0.0048 Ωch2 = 0.1188 ± 0.0010 Ωbh2 = 0.0223 ± 0.00011 ln(1010As) = 3.064 ± 0.023 H0 = (67.74 ± 0.46)km/sec/Mpc ΩΛ = 0.6911 ± 0.0062 τ = 0.066 ± 0.012

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 22 / 26

slide-53
SLIDE 53

The lensing potential (Planck 2015 arXiv:1502.01591)

φ(n) = − r∗ dr (r∗ − r) r∗r (Φ + Ψ)(rn, τ0 − r)

ˆ φWF (Data) −0.5 0.5 1 1.5 2 1 10 100 500 1000 2000

[L(L + 1)]2Cφφ

L /2π [×107]

L Planck (2015) Planck (2013) SPT ACT Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 23 / 26

slide-54
SLIDE 54

Lensing breaks degeneracies

0.30 0.45 0.60 0.75

Ωm

0.30 0.45 0.60 0.75

ΩΛ

+TE+EE +lensing +lensing+BAO

40 44 48 52 56 60 64 68

H0

(Planck 1502.01589) ΩK = −0.040 ± 0.04 (TT,EE,TE) −0.005 ± 0.016 add lensing −0.000 ± 0.005 add BAO’s 95%

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 24 / 26

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SLIDE 55

Dark energy models

A simple Taylor expansion, PDE ρDE = w = w0 + (1 − a)wa

−1.2 −1.0 −0.8 −0.6

w0

−1.6 −0.8 0.0 0.8

wa

65.6 66.4 67.2 68.0 68.8 69.6 70.4 71.2

H0

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 25 / 26

slide-56
SLIDE 56

Conclusions

  • R. Durrer, ”The Cosmic Microwave Background” ( Cambridge University Press 2008)

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 26 / 26

slide-57
SLIDE 57

Conclusions

  • R. Durrer, ”The Cosmic Microwave Background” ( Cambridge University Press 2008)

A flat Λ dominated Universe with a nearly scale invariant spectrum of scalar initial fluctuations from inflation is a good fit to the CMB data.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 26 / 26

slide-58
SLIDE 58

Conclusions

  • R. Durrer, ”The Cosmic Microwave Background” ( Cambridge University Press 2008)

A flat Λ dominated Universe with a nearly scale invariant spectrum of scalar initial fluctuations from inflation is a good fit to the CMB data. In this picture The biggest structures in the Universe have been generated by small quantum fluctuations.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 26 / 26

slide-59
SLIDE 59

Conclusions

  • R. Durrer, ”The Cosmic Microwave Background” ( Cambridge University Press 2008)

A flat Λ dominated Universe with a nearly scale invariant spectrum of scalar initial fluctuations from inflation is a good fit to the CMB data. In this picture The biggest structures in the Universe have been generated by small quantum fluctuations. If we ever find B polarisation it probably originates from quantum fluctuations of the gravitational field.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 26 / 26

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SLIDE 60

Conclusions

  • R. Durrer, ”The Cosmic Microwave Background” ( Cambridge University Press 2008)

A flat Λ dominated Universe with a nearly scale invariant spectrum of scalar initial fluctuations from inflation is a good fit to the CMB data. In this picture The biggest structures in the Universe have been generated by small quantum fluctuations. If we ever find B polarisation it probably originates from quantum fluctuations of the gravitational field. The energy density in the Universe is at present and for all future times dominated by vacuum energy.

Ruth Durrer (Universit´ e de Gen` eve, DPT & CAP) CMB Mainz, June 2015 26 / 26