The particle horizon (also called the cosmological horizon, the comoving horizon (in Dodelson's text), or the cosmic light horizon) is the maximum distance from which light from

particle
In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can be ascribed several physical property, physical or chemical property, chemical p ...

s could have traveled to the observer
An observer is one who engages in observation or in watching an experiment.
Observer may also refer to:
Computer science and information theory
* In information theory, any system which receives information from an object
* State observer in con ...

in the age of the universe
In physical cosmology
Physical cosmology is a branch of cosmology
Cosmology (from Ancient Greek, Greek κόσμος, ''kosmos'' "world" and -λογία, ''-logia'' "study of") is a branch of astronomy concerned with the study of the chro ...

. Much like the concept of a horizon, terrestrial horizon, it represents the boundary between the observable and the unobservable regions of the universe, so its distance at the present epoch defines the size of the observable universe. Due to the expansion of the universe, it is not simply the age of the universe
In physical cosmology
Physical cosmology is a branch of cosmology
Cosmology (from Ancient Greek, Greek κόσμος, ''kosmos'' "world" and -λογία, ''-logia'' "study of") is a branch of astronomy concerned with the study of the chro ...

times the speed of light (approximately 13.8 billion light-years), but rather the speed of light times the conformal time. The existence, properties, and significance of a cosmological horizon depend on the particular physical cosmology, cosmological model.
Conformal time and the particle horizon

In terms of comoving distance, the particle horizon is equal to the conformal time $\backslash eta$ that has passed since the Big Bang, times the speed of light $c$. In general, the conformal time at a certain time $t$ is given by :$\backslash eta\; =\; \backslash int\_^\; \backslash frac,$ where $a(t)$ is the Scale factor (cosmology), scale factor of the Friedmann–Lemaître–Robertson–Walker metric, and we have taken the Big Bang to be at $t=0$. By convention, a subscript 0 indicates "today" so that the conformal time today $\backslash eta(t\_0)\; =\; \backslash eta\_0\; =\; 1.48\; \backslash times\; 10^\backslash text$. Note that the conformal time is ''not'' theage of the universe
In physical cosmology
Physical cosmology is a branch of cosmology
Cosmology (from Ancient Greek, Greek κόσμος, ''kosmos'' "world" and -λογία, ''-logia'' "study of") is a branch of astronomy concerned with the study of the chro ...

, which is estimated around $4.35\; \backslash times\; 10^\backslash text$. Rather, the conformal time is the amount of time it would take a photon to travel from where we are located to the furthest observable distance, provided the universe ceased expanding. As such, $\backslash eta\_0$ is not a physically meaningful time (this much time has not yet actually passed); though, as we will see, the particle horizon with which it is associated is a conceptually meaningful distance.
The particle horizon recedes constantly as time passes and the conformal time grows. As such, the observed size of the universe always increases. Since proper distance at a given time is just comoving distance times the scale factor (with comoving distance normally defined to be equal to proper distance at the present time, so $a(t\_0)\; =\; 1$ at present), the proper distance to the particle horizon at time $t$ is given by
:$a(t)\; H\_p(t)\; =\; a(t)\; \backslash int\_^\; \backslash frac$
and for today $t\; =\; t\_0$
:$H\_p(t\_0)\; =\; c\backslash eta\_0\; =\; 14.4\backslash text\; =\; 46.9\backslash text.$
Evolution of the particle horizon

In this section we consider the Friedmann–Lemaître–Robertson–Walker metric, FLRW cosmological model. In that context, the universe can be approximated as composed by non-interacting constituents, each one being a perfect fluid with density $\backslash rho\_i$, partial pressure $p\_i$ and state equation $p\_i=\backslash omega\_i\; \backslash rho\_i$, such that they add up to the total density $\backslash rho$ and total pressure $p$. Let us now define the following functions: * Hubble function $H=\backslash frac$ * The critical density $\backslash rho\_c=\backslash fracH^2$ * The ''i''-th dimensionless energy density $\backslash Omega\_i=\backslash frac$ * The dimensionless energy density $\backslash Omega=\backslash frac\; \backslash rho\; =\backslash sum\; \backslash Omega\_i$ * The redshift $z$ given by the formula $1+z=\backslash frac$ Any function with a zero subscript denote the function evaluated at the present time $t\_0$ (or equivalently $z=0$). The last term can be taken to be $1$ including the curvature state equation. It can be proved that the Hubble function is given by :$H(z)=H\_0\backslash sqrt$ where $n\_i=3(1+\backslash omega\_i)$. Notice that the addition ranges over all possible partial constituents and in particular there can be countably infinitely many. With this notation we have: :$\backslash text\; H\_p\; \backslash text\; N>2$ where $N$ is the largest $n\_i$ (possibly infinite). The evolution of the particle horizon for an expanding universe ($\backslash dot>0$) is: :$\backslash frac=H\_p(z)H(z)+c$ where $c$ is the speed of light and can be taken to be $1$ (natural units). Notice that the derivative is made with respect to the FLRW-time $t$, while the functions are evaluated at the redshift $z$ which are related as stated before. We have an analogous but slightly different result for event horizon.Horizon problem

The concept of a particle horizon can be used to illustrate the famous horizon problem, which is an unresolved issue associated with the Big Bang model. Extrapolating back to the time of recombination (cosmology), recombination when the cosmic microwave background (CMB) was emitted, we obtain a particle horizon of about which corresponds to a proper size at that time of: Since we observe the CMB to be emitted essentially from our particle horizon ($284\backslash text\; \backslash ll\; 14.4\backslash text$), our expectation is that parts of the cosmic microwave background (CMB) that are separated by about a fraction of a great circle across the sky of (an angular size of $\backslash theta\; \backslash sim\; 1.7^\backslash circ$) should be out of causal contact with each other. That the entire CMB is in thermal equilibrium and approximates a blackbody so well is therefore not explained by the standard explanations about the way the expansion of the universe proceeds. The most popular resolution to this problem is cosmic inflation.See also

*List of cosmological horizons *Observable universeReferences

{{reflist Physical cosmology