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The relative expansion of the universe is parametrized by a dimensionless scale factor a . Also known as the cosmic scale factor or sometimes the Robertson Walker scale factor, this is a key parameter of the Friedmann equations. In the early stages of the
Big Bang The Big Bang event is a physical theory that describes how the universe expanded from an initial state of high density and temperature. Various cosmological models of the Big Bang explain the evolution of the observable universe from the ...
, most of the energy was in the form of radiation, and that radiation was the dominant influence on the expansion of the universe. Later, with cooling from the expansion the roles of matter and radiation changed and the universe entered a matter-dominated era. Recent results suggest that we have already entered an era dominated by
dark energy In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
, but examination of the roles of matter and radiation are most important for understanding the early universe. Using the dimensionless scale factor to characterize the expansion of the universe, the effective energy densities of radiation and matter scale differently. This leads to a radiation-dominated era in the very early universe but a transition to a matter-dominated era at a later time and, since about 4 billion years ago, a subsequent dark-energy-dominated era.


Detail

Some insight into the expansion can be obtained from a Newtonian expansion model which leads to a simplified version of the Friedmann equation. It relates the proper distance (which can change over time, unlike the
comoving distance In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. ''Proper distance'' roughly corresponds to where a distant object would be at a spec ...
d_C which is constant and set to today's distance) between a pair of objects, e.g. two galaxy clusters, moving with the Hubble flow in an expanding or contracting FLRW universe at any arbitrary time t to their distance at some reference time t_0. The formula for this is: :d(t) = a(t)d_0,\, where d(t) is the proper distance at epoch t, d_0 is the distance at the reference time t_0, usually also referred to as comoving distance, and a(t) is the scale factor. Thus, by definition, d_0=d(t_0) and a(t_0) = 1. The scale factor is dimensionless, with t counted from the birth of the universe and t_0 set to the present
age of the universe In physical cosmology, the age of the universe is the time elapsed since the Big Bang. Astronomers have derived two different measurements of the age of the universe: a measurement based on direct observations of an early state of the universe ...
: 13.799\pm0.021\,\mathrm giving the current value of a as a(t_0) or 1. The evolution of the scale factor is a dynamical question, determined by the equations of general relativity, which are presented in the case of a locally isotropic, locally homogeneous universe by the Friedmann equations. The Hubble parameter is defined as: :H(t) \equiv where the dot represents a time derivative. The Hubble parameter varies with time, not with space, with the Hubble constant H_0 being its current value. From the previous equation d(t) = d_0 a(t) one can see that \dot(t) = d_0 \dot(t), and also that d_0 = \frac, so combining these gives \dot(t) = \frac, and substituting the above definition of the Hubble parameter gives \dot(t) = H(t) d(t) which is just Hubble's law. Current evidence suggests that the expansion rate of the universe is accelerating, which means that the second derivative of the scale factor \ddot(t) is positive, or equivalently that the first derivative \dot(t) is increasing over time. This also implies that any given galaxy recedes from us with increasing speed over time, i.e. for that galaxy \dot(t) is increasing with time. In contrast, the Hubble parameter seems to be decreasing with time, meaning that if we were to look at some fixed distance d and watch a series of different galaxies pass that distance, later galaxies would pass that distance at a smaller velocity than earlier ones. According to the Friedmann–Lemaître–Robertson–Walker metric which is used to model the expanding universe, if at present time we receive light from a distant object with a redshift of ''z'', then the scale factor at the time the object originally emitted that light is a(t) = \frac.


Chronology


Radiation-dominated era

After Inflation, and until about 47,000 years after the Big Bang, the dynamics of the
early universe The chronology of the universe describes the history and future of the universe according to Big Bang cosmology. Research published in 2015 estimates the earliest stages of the universe's existence as taking place 13.8 billion years ago, with ...
were set by radiation (referring generally to the constituents of the universe which moved relativistically, principally photons and neutrinos). For a radiation-dominated universe the evolution of the scale factor in the Friedmann–Lemaître–Robertson–Walker metric is obtained solving the Friedmann equations: :a(t)\propto t^. \,


Matter-dominated era

Between about 47,000 years and 9.8 billion years after the Big Bang, the energy density of matter exceeded both the energy density of radiation and the vacuum energy density. When the
early universe The chronology of the universe describes the history and future of the universe according to Big Bang cosmology. Research published in 2015 estimates the earliest stages of the universe's existence as taking place 13.8 billion years ago, with ...
was about 47,000 years old (redshift 3600), mass–energy density surpassed the radiation energy, although the universe remained optically thick to radiation until the universe was about 378,000 years old (redshift 1100). This second moment in time (close to the time of recombination), at which the photons which compose the
cosmic microwave background radiation In Big Bang cosmology the cosmic microwave background (CMB, CMBR) is electromagnetic radiation that is a remnant from an early stage of the universe, also known as "relic radiation". The CMB is faint cosmic background radiation filling all space ...
were last scattered, is often mistaken as marking the end of the radiation era. For a matter-dominated universe the evolution of the scale factor in the Friedmann–Lemaître–Robertson–Walker metric is easily obtained solving the Friedmann equations: :a(t)\propto t^


Dark-energy-dominated era

In physical cosmology, the dark-energy-dominated era is proposed as the last of the three phases of the known universe, the other two being the
matter-dominated era The relative expansion of the universe is parametrized by a dimensionless scale factor a . Also known as the cosmic scale factor or sometimes the Robertson Walker scale factor, this is a key parameter of the Friedmann equations. In the early st ...
and the
radiation-dominated era The relative expansion of the universe is parametrized by a dimensionless scale factor a . Also known as the cosmic scale factor or sometimes the Robertson Walker scale factor, this is a key parameter of the Friedmann equations. In the early st ...
. The dark-energy-dominated era began after the matter-dominated era, i.e. when the Universe was about 9.8 billion years old. In the era of
cosmic inflation In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch lasted from  seconds after the conjectured Big Bang singularit ...
, the Hubble parameter is also thought to be constant, so the expansion law of the dark-energy-dominated era also holds for the inflationary prequel of the big bang. The
cosmological constant In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...
is given the symbol Λ, and, considered as a source term in the Einstein field equation, can be viewed as equivalent to a "mass" of empty space, or
dark energy In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. The first observational evidence for its existence came from measurements of supernovas, which showed that the univer ...
. Since this increases with the volume of the universe, the expansion pressure is effectively constant, independent of the scale of the universe, while the other terms decrease with time. Thus, as the density of other forms of matter – dust and radiation – drops to very low concentrations, the cosmological constant (or "dark energy") term will eventually dominate the energy density of the Universe. Recent measurements of the change in Hubble constant with time, based on observations of distant supernovae, show this acceleration in expansion rate,The Nobel Prize in Physics 2011
Retrieved 18 May 2017. indicating the presence of such dark energy. For a dark-energy-dominated universe, the evolution of the scale factor in the Friedmann–Lemaître–Robertson–Walker metric is easily obtained solving the Friedmann equations: :a(t)\propto \exp(H_0t) Here, the coefficient H_0in the exponential, the
Hubble constant Hubble's law, also known as the Hubble–Lemaître law, is the observation in physical cosmology that galaxies are moving away from Earth at speeds proportional to their distance. In other words, the farther they are, the faster they are moving a ...
, is :H_0 = \sqrt = \sqrt. This exponential dependence on time makes the spacetime geometry identical to the
de Sitter universe A de Sitter universe is a cosmological solution to the Einstein field equations of general relativity, named after Willem de Sitter. It models the universe as spatially flat and neglects ordinary matter, so the dynamics of the universe are domin ...
, and only holds for a positive sign of the cosmological constant, which is the case according to the currently accepted value of the
cosmological constant In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: ), alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equ ...
, Λ, that is approximately The current density of the observable universe is of the order of and the age of the universe is of the order of 13.8 billion years, or . The Hubble constant, H_0, is (The Hubble time is 13.79 billion years).


See also

*
Cosmological principle In modern physical cosmology, the cosmological principle is the notion that the spatial distribution of matter in the universe is homogeneous and isotropic when viewed on a large enough scale, since the forces are expected to act uniformly throu ...
* Lambda-CDM model * Redshift


Notes


References

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External links


Relation of the scale factor with the cosmological constant and the Hubble constant
{{DEFAULTSORT:Scale Factor (Cosmology) Physical cosmology