Acosmological horizon is one of two boundaries in three dimensional space, theparticle horizon or theevent horizon. The particle horizon divides space into those points reached by light traveling to an observer from those points too distant for light to have been observed. The particle horizon is the boundary of theobservable universe. The event horizon includes all possible future observations: points outside the event horizon can never be observed. The event horizon is the boundary of all future observable universes.^[1] These boundaries are a consequence ofgeneral relativity, theexpanding universe, and the physics ofBig Bangcosmology.

The particle horizon, also called the comoving particle horizon,^[2] is the maximum distance from which light from particles could have traveled to the observer in theage of the universe. 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. When cosmologists say "horizon" they almost always mean the particle horizon.^[3]

In an empty, homogeneous, and isotropic universe the proper distance to the horizon at timet is$${\displaystyle d_H(t)=R(t){\int }_0^t\frac{d{t}^{\prime }}{R(t^{\prime })}}$$whereR is thecosmological scale factor with dimensions of length.^[4]: 36

In terms of comoving distance, the particle horizon is equal to the conformal time that has passed since the Big Bang, times the speed of light. In general, the conformal time at a certain time is given in terms of the normalized^[3]: 75 scale factor${\displaystyle a=R(t)/R(t=0)}$ by,$${\displaystyle \eta (t)={\int }_0^t\frac{d{t}^{\prime }}{a(t^{\prime })}}$$

The particle horizon is the boundary between two regions at a point at a given time: one region defined by events that have already been observed by an observer, and the other by events which cannot be observedat that time. It represents the furthest distance from which we can retrieve information from the past, and so defines the observable universe.^[1]

The particle horizon differs from the cosmicevent horizon, in that the particle horizon represents the largestcomoving distance from which light could have reached the observer by a specific time, while the cosmic event horizon is the largest comoving distance from which light emitted now canever reach the observer in the future.^[5] The current distance to our cosmic event horizon is about five gigaparsecs (16 billion light-years), well within our observable range given by the particle horizon.^[6]

In general, the proper distance to the event horizon at time${\displaystyle t}$ is given by^[7]$${\displaystyle d_e(t)=a(t){\int }_t^{t_{\text{max}}}\frac{cd{t}^{\prime }}{a(t^{\prime })}}$$where${\displaystyle t_{\text{max}}}$ is the time-coordinate of the end of the universe, which would be infinite in the case of a universe that expands forever.

For our case, assuming thatdark energy is due to acosmological constantΛ, there will be a minimum Hubble parameterH_e and a maximum horizond_e which is often referred to as the only particle horizon:$${\displaystyle max(d_e)=\frac{c}{H_e}=c\sqrt{\frac{3}{\mathrm{\Lambda }}}=\frac{c}{\sqrt{{\mathrm{\Omega }}_{\mathrm{\Lambda }}}{H}_0}=17.55\text{Gly}.}$$

The current concordance orLambda-CDM model of cosmology is based on anaccelerating universe. Extrapolating the model into the far future predicts an universe consisting solely of our Milky Way. Light from distant galaxies will beredshifted so much as become invisible. Thus observational evidence for cosmology, including the particle horizon, will be unverifiable.^[8]

While not technically "horizons" in the sense of an impossibility for observations due to relativity or cosmological solutions, there are practical horizons which include the optical horizon, set at thesurface of last scattering. This is the farthest distance that any photon can freely stream.^[2] TheHubble sphere is also called the "photon horizon".^[9]: 466 Similarly, there is a "neutrino horizon" set for thefarthest distance a neutrino can freely stream and a gravitational wave horizon at the farthest distance thatgravitational waves can freely stream. The latter is predicted to be a direct probe of the end ofcosmic inflation.

The nature of cosmological horizons was clarified byWolfgang Rindler in 1956. He distinguished instantaneous events like a supernova fromworld lines, a string of events like light from a durable object like galaxy. The behavior of world lines became the basis for splitting the observable and unobservable universe.^[9]: 438

• Killing horizon

• Physical cosmology
• Physical horizons

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