Lambda-CDM model

Physical cosmology
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Lambda-CDM model
Dark energy · Dark matter

ΛCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. It is frequently referred to as the standard model of big bang cosmology, since it attempts to explain the existence and structure of the cosmic microwave background, the large scale structure of galaxy clusters and the distribution of hydrogen, helium, lithium, oxygen and also the accelerating expansion of the universe observed in the light from distant galaxies and supernovae. It is the simplest model that is in general agreement with observed phenomena.

Contents

Overview

Historically, the dominant cosmological model previous to the now "standard model" was the Steady State theory, proposed independently in 1948 by H. Bondi & T. Gold and by Fred Hoyle. The universe in this model was flat, infinitely large, infinitely old (homogeneity and isotropy were extended in time as well as space) and was continuously creating matter to stabilize the mass energy density of expanding space. The ΛCDM model is remarkable in that it describes a dynamic, evolving universe, from the initial singularity, inflation, spatial expansion and the creation of all matter through the formation of more than 100 billion visible galaxies from a fixed quantity of matter. It foretells a future in which the metric expansion of space will carry all galaxies away from each other at speeds greater than light, and observers in each galaxy will see only their own galaxy in an otherwise empty universe.[2]

There is currently active research into many aspects of the ΛCDM model, which is very likely to change as new information becomes available. In particular, it is difficult to measure accurately the distance of very far galaxies or supernovae, so that distance related estimates (of stellar or galactic luminosities, or of key parameters such as the Hubble constant) are still uncertain. In addition, ΛCDM has no explicit physical theory for the origin or physical nature of dark matter or dark energy; the nearly scale-invariant spectrum of the CMB perturbations, and their image across the celestial sphere, are believed to result from very small thermal and acoustic irregularities at the point of recombination.

Dark energy Dark matter Hydrogen Helium Star Neutrino
About this image
A clickable pie chart indicating the proportional composition of different mass or energy components of the universe. Roughly ninety-five percent is exotic dark matter and dark energy.(Click here for original image)

Parameters

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 Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) temperature and polarization observations.[3] These include estimates based on data from Baryon Acoustic Oscillations 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 13.72\pm0.12 \times10^9 years Age of the universe
H0 70.5\pm1.3 km s−1 Mpc−1 Hubble constant
Ωb 0.0456\pm0.0015 Baryon density
Ωc 0.228\pm0.013 Dark matter density
ΩΛ 0.726\pm0.015 Dark energy density
Ωtot 1.0050^{+0.0060}_{-0.0061} Total density
ΔR2 2.445\pm0.096\times10^{-9}, k0 = 0.002Mpc−1 Curvature fluctuation amplitude
σ8 0.812\pm0.026 Fluctuation amplitude at 8h−1Mpc
ns 0.960\pm0.013 Scalar spectral index
z* 1090.88\pm0.72 Redshift at decoupling
t* 3.77\pm0.03\times10^5 years Age at decoupling
τ 0.084\pm0.016 Reionization optical depth
zreion 10.9\pm1.4 Redshift of reionization
treion 432^{+90}_{-67}\times10^6 years Age at reionization

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 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
w -0.992^{+0.060}_{-0.061} Equation of state
r <0.22, k0 = 0.002Mpc−1 (2σ) Tensor-to-scalar ratio
α -0.028\pm0.020, k0 = 0.002Mpc−1 Running of the spectral index
Σmν <0.67 eV (2σ) Neutrino mass

Some researchers have suggested that there is a running spectral index, but no statistically significant study has revealed one. Theoretical expectations suggest that the tensor-to-scalar ratio r should be between 0 and 0.3, and the latest results are now within those limits.

See also

References

  1. ↑ Andrew Liddle. An Introduction to Modern Cosmology (2nd ed.). London: Wiley, 2003.
  2. ↑ Lawrence Krauss, "A Universe From Nothing". Presentation to the Atheist Alliance International, Burbank, CA 2009.
  3. ↑ Table 7 of Hinshaw, G. et al. (WMAP Collaboration). (feb 2009). "Five-Year Wilkinson Microwave Anisotropy Probe Observations: Data Processing, Sky Maps, and Basic Results". The Astrophysical Journal Supplement 180: 225–245. doi:10.1088/0067-0049/180/2/225. arXiv:0803.0732. http://adsabs.harvard.edu/abs/2009ApJS..180..225H. 
  4. ↑ M. Kowalski et al. 2008 (Supernova Cosmology Project Collaboration). Improved Cosmological Constraints From New, Old and Combined Supernova Datasets.
  5. ↑ E. Komatsu et al. 2009 (WMAP Collaboration). Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation.
  6. ↑ D. N. Spergel et al. 2003 (WMAP collaboration). First year Wilkinson Microwave Anisotropy Probe (WMAP) observations: determination of cosmological parameters, Astrophys. J. Suppl. 148 175 (2003).

External links