Overview

Extrapolation of the expansion of the universe backwards in time using general relativity yields an infinite density and temperature at a finite time in the past. This singularity signals the breakdown of general relativity. How closely we can extrapolate towards the singularity is debated—certainly not earlier than the Planck epoch. The early hot, dense phase is itself referred to as "the Big Bang", and is considered the "birth" of our universe. Based on measurements of the expansion using Type Ia supernovae, measurements of temperature fluctuations in the cosmic microwave background, and measurements of the correlation function of galaxies, the universe has a calculated age of 13.7 ± 0.2 billion years. The agreement of these three independent measurements strongly supports the ΛCDM model that describes in detail the contents of the universe.
The earliest phases of the Big Bang are subject to much speculation. In the most common models, the universe was filled homogeneously and isotropically with an incredibly high energy density, huge temperatures and pressures, and was very rapidly expanding and cooling. Approximately 10−35 seconds into the expansion, a phase transition caused a cosmic inflation, during which the universe grew exponentially. After inflation stopped, the universe consisted of a quark-gluon plasma, as well as all other elementary particles. Temperatures were so high that the random motions of particles were at relativistic speeds, and particle-antiparticle pairs of all kinds were being continuously created and destroyed in collisions. At some point an unknown reaction called baryogenesis violated the conservation of baryon number, leading to a very small excess of quarks and leptons over antiquarks and anti-leptons—of the order of 1 part in 30 million. This resulted in the predominance of matter over antimatter in the present universe.
The universe continued to grow in size and fall in temperature, hence the typical energy of each particle was decreasing. Symmetry breaking phase transitions put the fundamental forces of physics and the parameters of elementary particles into their present form. After about 10−11 seconds, the picture becomes less speculative, since particle energies drop to values that can be attained in particle physics experiments. At about 10−6 seconds, quarks and gluons combined to form baryons such as protons and neutrons. The small excess of quarks over antiquarks led to a small excess of baryons over antibaryons. The temperature was now no longer high enough to create new proton-antiproton pairs (similarly for neutrons-antineutrons), so a mass annihilation immediately followed, leaving just one in 1010 of the original protons and neutrons, and none of their antiparticles. A similar process happened at about 1 second for electrons and positrons. After these annihilations, the remaining protons, neutrons and electrons were no longer moving relativistically and the energy density of the universe was dominated by photons (with a minor contribution from neutrinos).
A few minutes into the expansion, when the temperature was about a billion (one thousand million; 109; SI prefix giga) Kelvin and the density was about that of air, neutrons combined with protons to form the universe's deuterium and helium nuclei in a process called Big Bang nucleosynthesis. Most protons remained uncombined as hydrogen nuclei. As the universe cooled, the rest mass energy density of matter came to gravitationally dominate that of the photon radiation. After about 380,000 years the electrons and nuclei combined into atoms (mostly hydrogen); hence the radiation decoupled from matter and continued through space largely unimpeded. This relic radiation is known as the cosmic microwave background radiation.

The Hubble Ultra Deep Field showcases galaxies from an ancient era when the universe was younger, denser, and warmer according to the Big Bang theory.
Over a long period of time, the slightly denser regions of the nearly uniformly distributed matter gravitationally attracted nearby matter and thus grew even denser, forming gas clouds, stars, galaxies, and the other astronomical structures observable today. The details of this process depend on the amount and type of matter in the universe. The three possible types of matter are known as cold dark matter, hot dark matter and baryonic matter. The best measurements available (from WMAP) show that the dominant form of matter in the universe is cold dark matter. The other two types of matter make up less than 20% of the matter in the universe.
The universe today appears to be dominated by a mysterious form of energy known as dark energy. Approximately 70% of the total energy density of today's universe is in this form. This dark energy causes the expansion of the universe to accelerate, observed as a slower than expected expansion at very large distances. Dark energy in its simplest formulation takes the form of a cosmological constant term in Einstein's field equations of general relativity, but its composition is unknown and, more generally, the details of its equation of state and relationship with the standard model of particle physics continue to be investigated both observationally and theoretically.
All these observations can be explained by the ΛCDM model of cosmology, which is a mathematical model of the Big Bang with six free parameters. As noted above, there is no compelling physical model for the first 10−11 seconds of the universe. To resolve the paradox of the initial singularity, a theory of quantum gravitation is needed. Understanding this period of the history of the universe is one of the greatest unsolved problems in physics.
The Big Bang theory depends on two major assumptions: the universality of physical laws, and the cosmological principle. The cosmological principle states that on large scales the universe is homogeneous and isotropic.
These ideas were initially taken as postulates, but today there are efforts to test each of them. For example, the first assumption has been tested by observations showing that largest possible deviation of the fine structure constant over much of the age of the universe is of order 10−5. Also, General Relativity has passed stringent tests on the scale of the solar system and binary stars while extrapolation to cosmological scales has been validated by the empirical successes of various aspects of the Big Bang theory.
If the large-scale universe appears isotropic as viewed from Earth, the cosmological principle can be derived from the simpler Copernican principle, which states that there is no preferred (or special) observer or vantage point. To this end, the cosmological principle has been confirmed to a level of 10−5 via observations of the CMB. The universe has been measured to be homogeneous on the largest scales at the 10% level.

FLRW metric
General relativity describes spacetime by a metric, which determines the distances that separate nearby points. The points, which can be galaxies, stars, or other objects, themselves are specified using a coordinate chart or "grid" that is laid down over all spacetime. The cosmological principle implies that the metric should be homogeneous and isotropic on large scales, which uniquely singles out the Friedmann-Lemaître-Robertson-Walker metric (FLRW metric). This metric contains a scale factor, which describes how the size of the universe changes with time. This enables a convenient choice of a coordinate system to be made, called comoving coordinates. In this coordinate system, the grid expands along with the universe, and objects that are moving only due to the expansion of the universe remain at fixed points on the grid. While their coordinate distance (comoving distance) remains constant, the physical distance between two such comoving points expands proportionally with the scale factor of the universe.
The Big Bang is not an explosion of matter moving outward to fill an empty universe. Instead, space itself expands with time everywhere and increases the physical distance between two comoving points. Because the FLRW metric assumes a uniform distribution of mass and energy, it applies to our universe only on large scales—local concentrations of matter such as our galaxy are gravitationally bound and as such do not experience the large-scale expansion of space.

Horizons

An important feature of the Big Bang spacetime is the presence of horizons. Since the universe has a finite age, and light travels at a finite speed, there may be events in the past whose light has not had time to reach us. This places a limit or a past horizon on the most distant objects that can be observed. Conversely, because space is expanding, and more distant objects are receding ever more quickly, light emitted by us today may never "catch up" to very distant objects. This defines a future horizon, which limits the events in the future that we will be able to influence. The presence of either type of horizon depends on the details of the FRW model that describes our universe. Our understanding of the universe back to very early times suggests that there was a past horizon, though in practice our view is limited by the opacity of the universe at early times. If the expansion of the universe continues to accelerate, there is a future horizon as well