slide1 n.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Cosmic Microwave Background and determination of cosmological parameters PowerPoint Presentation
Download Presentation
Cosmic Microwave Background and determination of cosmological parameters

Loading in 2 Seconds...

play fullscreen
1 / 33

Cosmic Microwave Background and determination of cosmological parameters - PowerPoint PPT Presentation


  • 111 Views
  • Uploaded on

表紙. Cosmic Microwave Background and determination of cosmological parameters. 全天マップ1. Full sky map of microwave background radiation #1. T =2.725K Cosmic Microwave Background CMB. 一様等方宇宙. Hubble parameter. Density parameter. cosmological constant (dark energy).

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

Cosmic Microwave Background and determination of cosmological parameters


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
slide2

Cosmic Microwave Background and

determination of cosmological parameters

slide3
全天マップ1

Full sky map of microwave background radiation #1

T=2.725K

Cosmic Microwave Background

CMB

slide4
一様等方宇宙

Hubble parameter

Density parameter

cosmological constant

(dark energy)

Standard Inflation predicts with high accuracy.

The Universe is globally isotropic and homogeneous

Scale factor

Curvature

slide5

1022m

1012m

cluster

階層

1020m

Solar system

galaxy

107m

1024m

1m

Earth

supercluster

Hierarchical Structures of the Universe

slide6

Large-Scale Structures

Present Power Spectrum

Power Spectrum

of Initial Fluctuation

Anisotropies in cosmic

microwave background

Angular Power Spectrum

Hierarchical Structures in the present Universe

grew out of linear perturbations under the gravity

Linear perturbation

Potential fluctuation

Curvature fluctuation

Cosmological

Parameters

H, W, L,...

slide7

Full sky map of microwave background radiation #2

COBE

COsmic

Background

Explorer

1993

WMAP

Wilkinson

Microwave

Anisotropy

Probe

2003

slide8

WMAP

2001/6/30

2002/4: first full-sky map

2002/10: second map

2001/7/30

2001/10/1

size 5m、weight 840kg

slide10

Full Sky Map of Cosmic Microwave Background Radiation

-200 T(μK) +200

Temperature fluctuation is Gaussian distributed.

Power spectrum determines the statistical distribution.

slide11

Two dimensional angular quantities: Spherical harmonics expansion

Angular scaleθ:

Angular Power Spectrum:

Angular Correlation Function:

Three dimensional spatial quantities: Fourier expansion

Length scale r:

Power Spectrum:

Correlation Function:

slide12

Before WMAP

After WMAP

So many data points!

slide13

Cosmological Parameters beofore WMAP

  • Luminosity density and average M/L of galaxies
  • Cluster baryon fraction from X-ray emissivity and

baryon density from primordial nucleosynthesis

  • Shape parameter of the transfer function of CDM

scenario of structure formation

  • Many others
slide14

log(dL)

z

Cosmological Parameters beofore WMAP

  • Type Ia Supernovae m-z relation
slide16

Hubble parameter was determined by HST key project.

HST Key Project

  • CepheidsH0=75±10km/s/Mpc
  • SNIa H0=71±2(stat)±6(syst)km/s/Mpc
  • Tully-Fisher H0=71±3±7km/s/Mpc
  • Surface Brightness Fluctuation H0=70±5±6km/s/Mpc
  • SNII H0=72±9±7km/s/Mpc
  • Fundamental Plane of Elliptical Galaxies

H0=82±6±9km/s/Mpc

SummaryH0=72±8km/s/Mpc

(Freedman et al ApJ 553(2001)47)

slide17

H0=72±8km/s/Mpc,

centered around

Observation:

from globular cluster

from cosmological nuclear chronology

Cosmological Parameters beofore WMAP

Concordance Model

as predicted by Inflation

Cosmic age

slide18

Cosmological Parameters with ERROR BARS

1st year result

Concordance Model was confirmed with high accuracy.

(with the help of the HST value of Hubble parameter.)

slide19

ΛCDM model fits the overall feature of the angular power spectrum

6 Parameters

Normalization of

Fluctuations

Spectral index

Baryon density

Dark matter density

Cosmological Constant

Hubble parameter

in

Spatially Flat Universe

899 data points are fit.

Approximately scale-invariant spectrum, which is

predicted by standard inflation models, fits the data.

But we may also find several interesting features beyond a

simple power-law spectrum…

slide21

We consider temperature fluctuation averaged over photon energy

in Fourier and multipole spaces.

h :conformal time

direction vector of photon

Physics of CMB anisotropy

The Boltzmann equation for photon distribution

in a perturbed spacetime

Collision term due to

the Thomson scattering

free electron density

slide22

conformal time

Euler equation for baryons

Metric perturbation generated during inflation

:Poisson equation

Boltzmann eq. can be transformed to an integral equation.

directionally averaged

Boltzmann equation

collision term

Baryon (electron) velocity

slide23

If we treat the decoupling to occur instantaneously at ,

no scattering

many

scattering

1

Visibility function

now

Last scattering surface

Propagation

Optical depth

slide24

Integrated Sachs-

Wolfe effect

Observable quantity

on Last scattering surface

small scale

: Temperature fluctuations

:Doppler effect

:Gravitational Redshift Sachs-Wolfe effect

Large scale

They can be calculated from the Boltzman/Euler/Poisson eqs., if the initial

condition of F (k,ti)and cosmological parameters are given.

In reality, decoupling requires finite time and the LSS has a finite

thickness. Short-wave fluctuations that oscillate many times during it

damped by a factor with corresponding to 0.1deg.

slide25

Behavior of photon-baryon fluid in the tight coupling regime

Small scales:        below sound horizon (Jeans scale)

Oscillatory   (       is the sound speed.)

Large scales:       

Specifically they are given by the solution of the following eqn.

source term is given by

metric perturbation.

Initial condition of is also given by

generated during inflation (if adiabatic fluc.)

Inflation

We need to calculate and at the Last scattering surface

when photons and baryons are decoupled.

slide26

r

LSS

d

Θ~π/l

Observer

図のような幾何学的関係からフーリエ空間の量がmultipole  空間

の角度パワースペクトル  に関係づけられる。

Fourier modes are related

with angular multipoles

as depicted in the figure.

~2π/k

l~kdにピーク

slide27

Sound horizon at LSS

corresponds to about 1 degree,

which explains the location of

the peak

小スケールで振動

Gravitational

一般相対論的

重力赤方偏移

流体力学的揺らぎ

大スケールで

ほぼ一定

hydorodynamical

slide28

The shape of the angular power

spectrum depends on

(spectral indexetc)as well as the

values of cosmological parameters.

(     corresponds to the scale-

invariant primordial fluctuasion.)

Increasing baryon density relatively lowers radiation pressure,

which results in higher peak.

Decreasing Ω(open Universe)makes opening angle smaller

so that the multipole l at the peak is shifted to a larger value.

Smaller Hubble parameter means more distant LSS with

enhanced early ISW effect.

Λalso makes LSS more distant, shifting the peak toward

right with enhanced Late ISW effect.

slide29

Thick line

0.05

0.03

0.01

1 0.5 0.3

Old standard CDM

model.

0.7

0.3

0

0.3

0.5

0.7

slide32

Fundamental Questions

What is dark matter ?

What is dark energy ?

How inflation occurred ?

What were there before inflation ?

are yet to be answered!