Overview
Most modern cosmological models are based on the cosmological principle that our observational location in the universe is in no way unusual or special; on a large enough scale, the universe looks the same in all directions (isotropy) and from every location (homogeneity).
The 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. While 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.
Λ (Lambda) stands for the cosmological constant which is currently associated with a vacuum energy or dark energy inherent in empty space that explains the current accelerating expansion of space against the attractive (collapsing) effects of gravity from matter. A cosmological constant has negative pressure, ; this contributes to the stress-energy tensor in general relativity and therefore causes accelerating expansion. The cosmological constant is denoted as, which is interpreted as the fraction of the total mass-energy density of a flat universe that is attributed to dark energy. Currently, about 73% of the energy density of the present universe is estimated to be dark energy.
Cold dark matter is a form of matter necessary to account for gravitational effects observed in very large scale structures (anomalies in the rotation of galaxies, the gravitational lensing of light by galaxy clusters, enhanced clustering of galaxies) that cannot be accounted for by the quantity of observed matter. Dark matter is described as being cold (i.e. its velocity is non-relativistic at the epoch of radiation-matter equality), non-baryonic (consisting of matter other than protons and neutrons), dissipationless (cannot cool by radiating photons) and collisionless (i.e., the dark matter particles interact with each other and other particles only through gravity and possibly the weak force). The dark matter component is currently estimated to constitute about 23% of the mass-energy density of the universe.
The remaining 4.5% comprises all ordinary matter observed as atoms, chemical elements, gas and plasma, the stuff of which visible planets, stars and galaxies are made.
Also, the energy density includes a very small fraction (~ 0.01%) in cosmic microwave background radiation, and not more than 0.5% in relic neutrinos. While very small today, these were much more important in the distant past, dominating the matter at redshift > 3200.
The model includes a single originating event, the "Big Bang" or initial singularity, which was not an explosion but the abrupt appearance of expanding space-time 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 current 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 is also necessary to address the "horizon problem" in the CMB. Indeed, it seems likely that the universe is larger than the observable particle horizon.
The model uses the FLRW metric, the Friedmann equations and the cosmological equations of state to describe the observable universe from right after the inflationary epoch to present and future.
Read more about this topic: Lambda-CDM Model