COSMOLOGY

Eduard MassóUAB/IFAE

International Meeting of Fundamental Physics(“Winter” meeting)Santiago de Compostela, 2007

Program

1. The standard cosmological model

2. The observed universe

3. Inflation. Neutrinos in cosmology

Emphasis on “Particles”

Science, vol. 315, 2007

Our universe is expanding

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressorare needed to see this picture.

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

redshift

co-movingdistancescale

lights-yearsago

today

Co-moving co-ordinates

QuickTime™ and aTIFF (LZW) decompressor

are needed to see this picture.

On top: peculiar (real) velocities

Hubble’s law & Cosmological principle

Universe homogenous & isotropicon large scales

Cosmological principle

QuickTime™ and aPNG decompressor

are needed to see this picture. Hubble parameter

Hubble’s discoveryQuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Hubble’s law: QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

(today)

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

Expansion (or contraction) is inevitable

RG + CP

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Robertson-Walker metric(homogeneity & isotropy)

QuickTime™ and aPNG decompressorare needed to see this picture.Content(matter+radiation)

QuickTime™ and aPNG decompressorare needed to see this picture.Content too (cosm. const.)

QuickTime™ and aPNG decompressorare needed to see this picture.Spatial geometry

QuickTime™ and aPNG decompressorare needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Parameters:

Parametersare relatedby eqs.

Cosmological equations

QuickTime™ and aPNG decompressor

are needed to see this picture.

Friedmann eqs.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

1

2a

1+2a -> 2b

QuickTime™ and aPNG decompressor

are needed to see this picture.

Spatial geometry &Light propagationQuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

OpenFLAT Closed

QuickTime™ and aTIFF (Uncompressed) decompressor

are needed to see this picture.

3D

Spatial geometry &Light propagationQuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Luminosity distance

QuickTime™ and aPNG decompressor

are needed to see this picture.

Measured flux(E/time/area)

Absolute luminosityE/time in rest frame

Luminosity distance

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Hubble’s law

Exact:

QuickTime™ and aPNG decompressorare needed to see this picture.Small z

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

That was kinematics

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.Decelerationparameter

Cosmological constant contribution

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Negativepressure

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.QuickTime™ and aPNG decompressor

are needed to see this picture.

+ any other component

Solution to cosmological eqs.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Equation of state

Assume i - dominance and

RD universe

MD universe.

CCD universe

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Critical density

QuickTime™ and aPNG decompressor

are needed to see this picture.

Define also

(Today)

Define QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Not energy-density contribution

Rewriting Friedmann eqs.QuickTime™ and aPNG decompressor

are needed to see this picture.

Cosmic sum rule

2a today

Notice signs

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

The future QuickTime™ and aPNG decompressor

are needed to see this picture.

+ Initial conditions taken today

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Diff. eq.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressorare needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Eternal Expansion OR Recollapse ?

EE

R

EE

R

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

1

2

3

Distance - RedshiftQuickTime™ and a

Photo - JPEG decompressorare needed to see this picture.

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

Co-moving distance to source:

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

Where:

Can neglect QuickTime™ and aPhoto - JPEG decompressorare needed to see this picture.QuickTime™ and a

Photo - JPEG decompressorare needed to see this picture.

Distance-redshift relation is function of

Age of the universe

look-back time

lifetime

Flat univ.QuickTime™ and aPNG decompressor

are needed to see this picture.

Our univ.QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

QuickTime™ and aPhoto - JPEG decompressor

are needed to see this picture.

(Age crisis: Open universe gave too low lifetime)

Which universe ?

The past universe

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

today

rad

mat

cc

equality

recombination

nucleosynthesis

QuickTime™ and aPNG decompressorare needed to see this picture.

next

The hot universe

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

number density

energy density

pressure

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

distribution

QuickTime™ and aPNG decompressor

are needed to see this picture.

g= deg. of freedom

Equilibrium thermodynamics

Decoupling of species

Expansion:

Interaction:

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressorare needed to see this picture.

rates

QuickTime™ and aPNG decompressorare needed to see this picture.

QuickTime™ and aPNG decompressorare needed to see this picture.

Phase transitionsSymmetry restoring

2n order

1st order

Phase transitions

Conformal time

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Particle HorizonIt is the physical distance photons can travel until a time t

Defines causal distance at a given time t QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

QuickTime™ and aPNG decompressor

are needed to see this picture.

Program

1. The standard cosmological model

2. The observed universe

3. Inflation. Neutrinos in cosmology