cosmologie primordiale patrick petercosmologie primordiale paris-sud 1er décembre 2009 patrick...

Orsay - 1er décembre 2009

Cosmologie Primordiale

Paris-Sud1er décembre 2009

Patrick Peter

Institut d’Astrophysique de Paris

Orsay - 1er décembre 2009 2

Isotrope !

Carte du ciel à haute résolution


P

PQ

Q


Homogène !


Homogénéité

+

Isotropie

+

Relativité générale d’Einstein

=

Expansion de l’Univers


Techniquement ...

Métrique homogène & isotrope (FLRW):

LastScatteringsurface

ds2 = −dt2 + a2 (t)[

dr2

1 −Kr2+ r2

(

dθ2 + sin2 θdφ2)

]

,

dη =dt

a(t)=⇒

ds2 = a2(η)(

−dη2 + γijdxidxj)

S =∫ √

−g(

−R

6%2P

+ p

)

d4x

p = ωρ

nT = nS − 1 =12ω

1 + 3ω

T

S$ 4 × 10−2

√

nS − 1

1

Matière = fluide parfait


Tµν = pgµν + (ρ + p)uµuν

ds2 = −dt2 + a2 (t)[

dr2

1 −Kr2+ r2

(

dθ2 + sin2 θdφ2)

]

,

dη =dt

a(t)=⇒

ds2 = a2(η)(


S =∫ √

−g(

−R

6&2P

+ p

)

d4x

p = ωρ

nT = nS − 1 =12ω

1 + 3ω

1


p = ωρ


ds2 = −dt2 + a2 (t)[

dr2

1 −Kr2+ r2

(

dθ2 + sin2 θdφ2)

]

,

dη =dt

a(t)=⇒

ds2 = a2(η)(


S =∫ √

−g(

−R

6'2P

+ p

)

d4x

p = ωρ

1

poussière{


ω = 0

p = ωρ


ds2 = −dt2 + a2 (t)[

dr2

1 −Kr2+ r2

(

dθ2 + sin2 θdφ2)

]

,

dη =dt

a(t)=⇒

ds2 = a2(η)(


S =∫ √

−g(

−R

6'2P

+ p

)

d4x

p = ωρ

1


ω =1

3

p = ωρ


ds2 = −dt2 + a2 (t)[

dr2

1 −Kr2+ r2

(

dθ2 + sin2 θdφ2)

]

,

dη =dt

a(t)=⇒

ds2 = a2(η)(


S =∫ √

−g(

−R

6'2P

+ p

)

d4x

1

radiation


H2 +Ka2

=1

3(8πGNρ + Λ)

ω =1

3

p = ωρ


ds2 = −dt2 + a2 (t)[

dr2

1 −Kr2+ r2

(

dθ2 + sin2 θdφ2)

]

,

dη =dt

a(t)=⇒

ds2 = a2(η)(


1

+ cosmological constant = équations d’EinsteinLastScatteringsurface

ä

a=

1

3[Λ − 4πGN (ρ + p)]

H2 +Ka2

=1

3(8πGNρ + Λ)

ω =1

3

p = ωρ


ds2 = −dt2 + a2 (t)[

dr2

1 −Kr2+ r2

(

dθ2 + sin2 θdφ2)

]

,

dη =dt

a(t)=⇒

1


Hubble 1929Hubble 1929

Vitesse = = H H x x Distance

Orsay - 1er décembre 2009

Riess, Press et Kirshner (1996)Riess, Press et Kirshner (1996)

9


Le rougissement gravitationnel de l’expansion


temps

dis

tan

ce


Bien connu compris


Simulation numérique de la formation des grandes structures

Comparaison avecles données

observationnelles


Fluctuations attendues du rayonnement de corps noirMoment multipolaire

Échelle angulaire


Bien connu compris

Mal connu incompris

!!!!!!!

Bielefeld - 23rd september 2009 22

Singularité

Horizon

Platitude

Homogeneité

Perturbations

Matière noire

Énergie noire / constante cosmologique

Baryogénèse

...

Défauts topologiques (monopôles)

1

also available fromOXFORD UNIVERSITY PRESS

Cosmology Steven Weinberg

Particle Astrophysics: Second EditionDonald H. Perkins

Cosmic Anger—Abdus Salam: The First Muslim Nobel Scientist Gordon Fraser

Revolutionaries of the Cosmos—The Astro-Physicists Ian S. Glass

Cover image: ‘Le vent’ by Madeleine Attal (1997).

This book provides an extensive survey of all the physics necessary to understand the current developments in the field of fundamental cosmology, as well as an overview ofthe observational data and methods. It will help students to get into research by providingdefinitions and main techniques and ideas discussed today. The book is divided into threeparts. Part 1 summarises the fundamentals in theoretical physics needed in cosmology(general relativity, field theory, particle physics). Part 2 describes the standard model ofcosmology and includes cosmological solutions of Einstein equations, the hot big bangmodel, cosmological perturbation theory, cosmic microwave background anisotropies,lensing and evidence for dark matter, and inflation. Part 3 describes extensions of thismodel and opens up current research in the field: scalar-tensor theories, supersymmetry,the cosmological constant problem and acceleration of the universe, topology of the universe, grand unification and baryogenesis, topological defects and phase transitions,string inspired cosmology including branes and the latest developments. The book provides details of all derivations and leads the student up to the level of research articles.

Patrick Peter and Jean-Philippe Uzan are at the Institut d'Astrophysique de Paris, France.

‘Fills a niche that other recent cosmology texts leave open, namely self-contained derivations in cosmology that span both fundamental issues and applications to the realuniverse that are of great interest to observers.’ Joseph Silk, University of Oxford

‘A remarkable book. Written with great authority and enthusiasm, it gives a comprehensiveview of primordial cosmology today. The style is accessible to a novice for a good introduction, as well as being technically precise enough to be useful for specialists.’

Ted Jacobson, University of Maryland

Primordial Cosmology

Patrick PeterJean-Philippe Uzan

oxford graduate texts

9 780199 209910

2

ogt

PrimordialCosm

ologyPeter&

Uzan

peter&uzan_ppc.qxd 27/2/09 09:11 Page 1

Problèmes de la cosmologie standard


Singularité


O

A”

A

A’

B

B’ B”

Space

Tim

e

Last scattering surface

1°

Decouplingzdec

Horizonat decoupling

O

Infinite redshift

Horizon


Horizon

Ici

Surfacede dernière

diffusionvue d’ici

Surfacede dernière

diffusionvue de B

Surfacede dernière

diffusionvue de A

Photon issu de A Photon issu de B


“plat”

“ouvert”

“fermé”

Platitude


Inflation ... = la panacée !!!

Platitude



Horizon


(Livre A. Linde)


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