radiation-dominated era
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The relative expansion of the
universe The universe is all of space and time and their contents, including planets, stars, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development of the universe. ...
is parametrized by a
dimensionless A dimensionless quantity (also known as a bare quantity, pure quantity, or scalar quantity as well as quantity of dimension one) is a quantity to which no physical dimension is assigned, with a corresponding SI unit of measurement of one (or 1) ...
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, 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 univ ...
, 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 General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics ...
, which are presented in the case of a locally isotropic, locally homogeneous universe by the
Friedmann equations The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann ...
. The
Hubble parameter 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 defined as: :H(t) \equiv where the dot represents a time
derivative In mathematics, the derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value). Derivatives are a fundamental tool of calculus. ...
. 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 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 ...
. 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 The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...
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 (cosmology), Inflation, and until about 47,000 years cosmic time, after the Big Bang, the dynamics of the early universe were set by radiation (referring generally to the constituents of the universe which moved special relativity, relativistically, principally photons and neutrinos). For a radiation-dominated universe the evolution of the scale factor in the
Friedmann–Lemaître–Robertson–Walker metric The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...
is obtained solving the
Friedmann equations The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann ...
: :a(t)\propto t^. \,


Matter-dominated era

Between about 47,000 years and 9.8 billion years cosmic time, 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 was about 47,000 years old (redshift 3600), mass–energy equivalence, mass–energy density surpassed the radiant energy, radiation energy, although the universe remained optical depth, 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 (cosmology), recombination), at which the photons which compose the cosmic microwave background radiation 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 The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...
is easily obtained solving the
Friedmann equations The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann ...
: :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, matter-dominated era and the #Radiation-dominated era, radiation-dominated era. 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 Inflation_(cosmology), cosmic inflation, 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 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 univ ...
. 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 The Friedmann–Lemaître–Robertson–Walker (FLRW; ) metric is a metric based on the exact solution of Einstein's field equations of general relativity; it describes a homogeneous, isotropic, expanding (or otherwise, contracting) universe tha ...
is easily obtained solving the
Friedmann equations The Friedmann equations are a set of equations in physical cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity. They were first derived by Alexander Friedmann ...
: :a(t)\propto \exp(H_0t) Here, the coefficient H_0in the exponential, the Hubble constant, is :H_0 = \sqrt = \sqrt. This exponential dependence on time makes the spacetime geometry identical to the de Sitter universe, 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#Positive_value, cosmological constant, 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 *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