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N

#### Nzowa Godat

##### JF-Expert Member

Joined
Jun 15, 2011

2,653
170
160

The ΛCDM model is based on

six parameters: physical

baryon density, physical dark

matter density, dark energy

density, scalar spectral index,

curvature fluctuation

amplitude and reionization

optical depth. From these the

other model values, including

the Hubble constant and age of

the universe, can be derived.

Parameter values listed below

are from the Seven-Year

Wilkinson Microwave

Anisotropy Probe

(WMAP) temperature and

polarization observations.[2]

These include estimates based

on data from Baryon Acoustic

Oscillations[3] and Type Ia

supernova luminosity/time

dilation measurements.[4]

Implications of the data for

cosmological models are

discussed in Komatsu et al. [5]

and Spergel et al.[6]

Parameter

Value

Description

t0

years

Age of the universe

H0

km s−1Mpc−1

Hubble constant

Ωbh2

Physical baryon density

Ωch2

Physical dark matter density

Ωb

Baryon density

Ωc

Dark matter density

ΩΛ

Dark energy density

ΔR2

, k0 =

0.002Mpc−1

Curvature fluctuation

amplitude

σ8

Fluctuation amplitude at 8h

−1 Mpc

ns

Scalar spectral index

z*

Redshift at decoupling

t*

years

Age at decoupling

τ

Reionization optical depth

zreion

Redshift of reionization

The "physical baryon density"

Ωbh2 differs from the "baryon

density" Ωb in that the baryon

density gives the fraction of

the critical density made up of

baryons (the critical density is

the total density of matter/

energy needed for the

universe to be spatially flat,

with measurements indicating

that the actual total density

Ω tot is very close if not equal

to this value, see below), while

the physical baryon density is

equal to the baryon density

multiplied by the square of the

reduced Hubble constant h,[7]

where h is related to the

Hubble constant H 0 by the

equation H0 = 100 h (km/s)/

Mpc.[8] Likewise for the

difference between "physical

dark matter density" and

"dark matter density".

Extended models

Possible extensions of the

simplest ΛCDM model are to

allow quintessence rather than

a cosmological constant. In this

case, the equation of state of

dark energy is allowed to

differ from −1. Cosmic

inflation predicts tensor

fluctuations ( gravitational

waves). Their amplitude is

parameterized by the tensor-

to-scalar ratio, which is

determined by the energy

scale of inflation. Other

modifications allow for spatial

curvature (Ω tot may be

different from 1), hot dark

matter in the form of

neutrinos, or a running

spectral index, which are

generally viewed as

inconsistent with cosmic

inflation.

Allowing these parameters will

generally increase the errors

in the parameters quoted

above, and may also shift the

observed values somewhat.

Parameter

Value

Description

Ωtot

Total density

w

Equation of state

r

< 0.24, k0 = 0.002Mpc−1

(2σ

Tensor-to-scalar ratio

d ns / d ln k

, k0 =

0.002Mpc−1

Running of the spectral index

Ωvh2

< 0.0062

Physical neutrino density

Σmν

< 0.58 eV (2σ

Neutrino mass

six parameters: physical

baryon density, physical dark

matter density, dark energy

density, scalar spectral index,

curvature fluctuation

amplitude and reionization

optical depth. From these the

other model values, including

the Hubble constant and age of

the universe, can be derived.

Parameter values listed below

are from the Seven-Year

Wilkinson Microwave

Anisotropy Probe

(WMAP) temperature and

polarization observations.[2]

These include estimates based

on data from Baryon Acoustic

Oscillations[3] and Type Ia

supernova luminosity/time

dilation measurements.[4]

Implications of the data for

cosmological models are

discussed in Komatsu et al. [5]

and Spergel et al.[6]

Parameter

Value

Description

t0

years

Age of the universe

H0

km s−1Mpc−1

Hubble constant

Ωbh2

Physical baryon density

Ωch2

Physical dark matter density

Ωb

Baryon density

Ωc

Dark matter density

ΩΛ

Dark energy density

ΔR2

, k0 =

0.002Mpc−1

Curvature fluctuation

amplitude

σ8

Fluctuation amplitude at 8h

−1 Mpc

ns

Scalar spectral index

z*

Redshift at decoupling

t*

years

Age at decoupling

τ

Reionization optical depth

zreion

Redshift of reionization

The "physical baryon density"

Ωbh2 differs from the "baryon

density" Ωb in that the baryon

density gives the fraction of

the critical density made up of

baryons (the critical density is

the total density of matter/

energy needed for the

universe to be spatially flat,

with measurements indicating

that the actual total density

Ω tot is very close if not equal

to this value, see below), while

the physical baryon density is

equal to the baryon density

multiplied by the square of the

reduced Hubble constant h,[7]

where h is related to the

Hubble constant H 0 by the

equation H0 = 100 h (km/s)/

Mpc.[8] Likewise for the

difference between "physical

dark matter density" and

"dark matter density".

Extended models

Possible extensions of the

simplest ΛCDM model are to

allow quintessence rather than

a cosmological constant. In this

case, the equation of state of

dark energy is allowed to

differ from −1. Cosmic

inflation predicts tensor

fluctuations ( gravitational

waves). Their amplitude is

parameterized by the tensor-

to-scalar ratio, which is

determined by the energy

scale of inflation. Other

modifications allow for spatial

curvature (Ω tot may be

different from 1), hot dark

matter in the form of

neutrinos, or a running

spectral index, which are

generally viewed as

inconsistent with cosmic

inflation.

Allowing these parameters will

generally increase the errors

in the parameters quoted

above, and may also shift the

observed values somewhat.

Parameter

Value

Description

Ωtot

Total density

w

Equation of state

r

< 0.24, k0 = 0.002Mpc−1

(2σ

Tensor-to-scalar ratio

d ns / d ln k

, k0 =

0.002Mpc−1

Running of the spectral index

Ωvh2

< 0.0062

Physical neutrino density

Σmν

< 0.58 eV (2σ

Neutrino mass