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The Lambda-CDM, Lambda cold dark matter, or ΛCDM model is a mathematical model of the Big Bang theory with three major components:

1. a cosmological constant denoted by lambda (Λ) associated with dark energy
2. the postulated cold dark matter denoted by CDM
3. ordinary matter

It is referred to as the standard model of Big Bang cosmology^[1] because it is the simplest model that provides a reasonably good account of:

• the existence and structure of the cosmic microwave background
• the large-scale structure in the distribution of galaxies
• the observed abundances of hydrogen (including deuterium), helium, and lithium
• the accelerating expansion of the universe observed in the light from distant galaxies and supernovae

The model assumes that general relativity is the correct theory of gravity on cosmological scales. It emerged in the late 1990s as a concordance cosmology, after a period of time when disparate observed properties of the universe appeared mutually inconsistent, and there was no consensus on the makeup of the energy density of the universe.

The ΛCDM model can be extended by adding cosmological inflation, quintessence, and other areas of speculation and research in cosmology.

Some alternative models challenge the assumptions of the ΛCDM model. Examples of these are modified Newtonian dynamics, entropic gravity, modified gravity, theories of large-scale variations in the matter density of the universe, bimetric gravity, scale invariance of empty space, and decaying dark matter (DDM).^{[2][3][4][5][6]}

Overview

The ΛCDM model includes an expansion of metric space that is well documented both as the red shift of prominent spectral absorption or emission lines in the light from distant galaxies and as the time dilation in the light decay of supernova luminosity curves. Both effects are attributed to a Doppler shift in electromagnetic radiation as it travels across expanding space. Although this expansion increases the distance between objects that are not under shared gravitational influence, it does not increase the size of the objects (e.g. galaxies) in space. It also allows for distant galaxies to recede from each other at speeds greater than the speed of light; local expansion is less than the speed of light, but expansion summed across great distances can collectively exceed the speed of light.^[7]

The letter Λ (lambda) represents the cosmological constant, which is associated with a vacuum energy or dark energy in empty space that is used to explain the contemporary accelerating expansion of space against the attractive effects of gravity. A cosmological constant has negative pressure, ${\displaystyle p=-\rho c^{2}}$, which contributes to the stress–energy tensor that, according to the general theory of relativity, causes accelerating expansion. The fraction of the total energy density of our (flat or almost flat) universe that is dark energy, ${\displaystyle \Omega _{\Lambda }}$, is estimated to be 0.669 ± 0.038 based on the 2018 Dark Energy Survey results using Type Ia supernovae^[8] or 0.6847 ± 0.0073 based on the 2018 release of Planck satellite data, or more than 68.3 % (2018 estimate) of the mass–energy density of the universe.^[9]

Dark matter is postulated in order to account for gravitational effects observed in very large-scale structures (the "flat" rotation curves of galaxies; the gravitational lensing of light by galaxy clusters; and enhanced clustering of galaxies) that cannot be accounted for by the quantity of observed matter.^[10] The ΛCDM model proposes specifically cold dark matter, hypothesized as:

• Non-baryonic: Consists of matter other than protons and neutrons (and electrons, by convention, although electrons are not baryons)
• Cold: Its velocity is far less than the speed of light at the epoch of radiation–matter equality (thus neutrinos are excluded, being non-baryonic but not cold)
• Dissipationless: Cannot cool by radiating photons
• Collisionless: Dark matter particles interact with each other and other particles only through gravity and possibly the weak force

Dark matter constitutes about 26.5 %^[11] of the mass–energy density of the universe. The remaining 4.9 %^[11] comprises all ordinary matter observed as atoms, chemical elements, gas and plasma, the stuff of which visible planets, stars and galaxies are made. The great majority of ordinary matter in the universe is unseen, since visible stars and gas inside galaxies and clusters account for less than 10 % of the ordinary matter contribution to the mass–energy density of the universe.^[12]

The model includes a single originating event, the "Big Bang", which was not an explosion but the abrupt appearance of expanding spacetime containing radiation at temperatures of around 10¹⁵ K. This was immediately (within 10⁻²⁹ seconds) followed by an exponential expansion of space by a scale multiplier of 10²⁷ or more, known as cosmic inflation. The early universe remained hot (above 10 000 K) for several hundred thousand years, a state that is detectable as a residual cosmic microwave background, or CMB, a very low energy radiation emanating from all parts of the sky. The "Big Bang" scenario, with cosmic inflation and standard particle physics, is the only cosmological model consistent with the observed continuing expansion of space, the observed distribution of lighter elements in the universe (hydrogen, helium, and lithium), and the spatial texture of minute irregularities (anisotropies) in the CMB radiation. Cosmic inflation also addresses the "horizon problem" in the CMB; indeed, it seems likely that the universe is larger than the observable particle horizon.^{[citation needed]}

The model uses the Friedmann–Lemaître–Robertson–Walker metric, the Friedmann equations and the cosmological equations of state to describe the observable universe from approximately 0.1s to the present.^[1]: 605

Cosmic expansion history

The expansion of the universe is parameterized by a dimensionless scale factor ${\displaystyle a=a(t)}$ (with time ${\displaystyle t}$ counted from the birth of the universe), defined relative to the present time, so ${\displaystyle a_{0}=a(t_{0})=1}$; the usual convention in cosmology is that subscript 0 denotes present-day values, so ${\displaystyle t_{0}}$ denotes the age of the universe. The scale factor is related to the observed redshift^[13] ${\displaystyle z}$ of the light emitted at time ${\displaystyle t_{\mathrm {em} }}$ by

${\displaystyle a(t_{\text{em}})={\frac {1}{1+z}}\,.}$

The expansion rate is described by the time-dependent Hubble parameter, ${\displaystyle H(t)}$, defined as

${\displaystyle H(t)\equiv {\frac {\dot {a}}{a}},}$

where ${\displaystyle {\dot {a}}}$ is the time-derivative of the scale factor. The first Friedmann equation gives the expansion rate in terms of the matter+radiation density ${\displaystyle \rho }$, the curvature ${\displaystyle k}$, and the cosmological constant ${\displaystyle \Lambda }$,^[13]

${\displaystyle H^{2}=\left({\frac {\dot {a}}{a}}\right)^{2}={\frac {8\pi G}{3}}\rho -{\frac {kc^{2}}{a^{2}}}+{\frac {\Lambda c^{2}}{3}},}$

where as usual ${\displaystyle c}$ is the speed of light and ${\displaystyle G}$ is the gravitational constant. A critical density ${\displaystyle \rho _{\mathrm {crit} }}$ is the present-day density, which gives zero curvature ${\displaystyle k}$, assuming the cosmological constant ${\displaystyle \Lambda }$ is zero, regardless of its actual value. Substituting these conditions to the Friedmann equation gives

${\displaystyle {\mathrm{\rho <!--\; \rho \; -->}}_{\mathrm{c}\mathrm{r}\mathrm{i}\mathrm{t}}=\frac{3H_0^2}{8\mathrm{\pi <!--\; \pi \; -->}G}=1.87847(23)\times <!--\; \times \; -->{10}^{-<!--\; -\; -->26}{h}^2\text{kg}}$Zdroj:https://en.wikipedia.org?pojem=ΛCDM
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