Cosmological horizon

Last updated April 22, 2024

A cosmological horizon is a measure of the distance from which one could possibly retrieve information.^[1] This observable constraint is due to various properties of general relativity, the expanding universe, and the physics of Big Bang cosmology. Cosmological horizons set the size and scale of the observable universe. This article explains a number of these horizons.

Particle horizon

The particle horizon, also called the cosmological horizon, the comoving horizon, or the cosmic light horizon, is the maximum distance from which light from particles could have traveled to the observer in the age 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. Due to the expansion of the universe, it is not simply the age of the universe times the speed of light, as in the Hubble horizon, but rather the speed of light multiplied by the conformal time. The existence, properties, and significance of a cosmological horizon depend on the particular cosmological model.

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 scale factor $a$ by,

\eta (t)=\int _{0}^{t}{\frac {dt'}{a(t')}}

or

\eta (a)=\int _{0}^{a}{\frac {1}{a'H(a')}}{\frac {da'}{a'}}\,.

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 observed at that time. It represents the furthest distance from which we can retrieve information from the past, and so defines the observable universe.^[1]

Hubble horizon

Hubble radius, Hubble sphere (not to be confused with a Hubble bubble), Hubble volume, or Hubble horizon is a conceptual horizon defining the boundary between particles that are moving slower and faster than the speed of light relative to an observer at one given time. Note that this does not mean the particle is unobservable; the light from the past is reaching and will continue to reach the observer for a while. Also, more importantly, in the current expansion models, light emitted from the Hubble radius will reach us in a finite amount of time.

It is a common misconception that light from the Hubble radius can never reach us. In models assuming decreasing $H$ with time (some cases of Friedmann universe), while particles on the Hubble radius recede from us with the speed of light, the Hubble radius gets larger over time, so light emitted towards us from a particle on the Hubble radius will be inside the Hubble radius some time later. In such models, only light emitted from the cosmic event horizon or further will never reach us in a finite amount of time.

The Hubble velocity of an object is given by Hubble's law,

v=xH.

Replacing $v$ with speed of light $c$ and solving for proper distance ${\textstyle x}$ we obtain the radius of Hubble sphere as

r_{\text{HS}}(t)={\frac {c}{H(t)}}\,.

In an ever-accelerating universe, if two particles are separated by a distance greater than the Hubble radius, they cannot talk to each other from now on (as they are now, not as they have been in the past). However, if they are outside of each other's particle horizon, they could have never communicated.^[2] Depending on the form of expansion of the universe, they may be able to exchange information in the future. Today,

r_{\text{HS}}(t_{0})={\frac {c}{H_{0}}}\,,

yielding a Hubble horizon of some 4.1 gigaparsecs. This horizon is not really a physical size, but it is often used as useful length scale as most physical sizes in cosmology can be written in terms of those factors.

One can also define a comoving Hubble horizon by simply dividing the Hubble radius by the scale factor

r_{{\text{HS}},\mathrm {comoving} }(t)={\frac {c}{a(t)H(t)}}\,.

Event horizon

The particle horizon differs from the cosmic event horizon, in that the particle horizon represents the largest comoving 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 can ever reach the observer in the future.^[3] 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.^[4]

In general, the proper distance to the event horizon at time $t$ is given by^[5]

d_{e}(t)=a(t)\int _{t}^{t_{\text{max}}}{\frac {cdt'}{a(t')}}

where $t_{\text{max}}$ 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 that dark energy is due to a cosmological constant Λ, there will be a minimum Hubble parameter H_e and a maximum horizon d_e which is often referred to as the only particle horizon:

\max(d_{e})={\frac {c}{H_{e}}}={\sqrt {\tfrac {3}{\Lambda }}}={\frac {c}{{\sqrt {\Omega _{\Lambda }}}H_{0}}}=17.55\ {\textrm {Gly}}.

Future horizon

In an accelerating universe, there are events which will be unobservable as $t\rightarrow \infty$ as signals from future events become redshifted to arbitrarily long wavelengths in the exponentially expanding de Sitter space. This sets a limit on the farthest distance that we can possibly see as measured in units of proper distance today. Or, more precisely, there are events that are spatially separated for a certain frame of reference happening simultaneously with the event occurring right now for which no signal will ever reach us, even though we can observe events that occurred at the same location in space that happened in the distant past.^[6]

While we will continue to receive signals from this location in space, even if we wait an infinite amount of time, a signal that left from that location today will never reach us. The signals coming from that location will have less and less energy and be less and less frequent until the location, for all practical purposes, becomes unobservable. In a universe that is dominated by dark energy which is undergoing an exponential expansion of the scale factor, all objects that are gravitationally unbound with respect to the Milky Way will become unobservable, in a futuristic version of Kapteyn's universe.^[7]

Practical horizons

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 the surface of last scattering. This is the farthest distance that any photon can freely stream. Similarly, there is a "neutrino horizon" set for the farthest distance a neutrino can freely stream and a gravitational wave horizon at the farthest distance that gravitational waves can freely stream. The latter is predicted to be a direct probe of the end of cosmic inflation.

Related Research Articles

The Big Bang is a physical theory that describes how the universe expanded from an initial state of high density and temperature. It was first proposed in 1927 by Roman Catholic priest and physicist Georges Lemaître. Various cosmological models of the Big Bang explain the evolution of the observable universe from the earliest known periods through its subsequent large-scale form. These models offer a comprehensive explanation for a broad range of observed phenomena, including the abundance of light elements, the cosmic microwave background (CMB) radiation, and large-scale structure. The overall uniformity of the universe, known as the flatness problem, is explained through cosmic inflation: a sudden and very rapid expansion of space during the earliest moments. However, physics currently lacks a widely accepted theory of quantum gravity that can successfully model the earliest conditions of the Big Bang.

<span class="mw-page-title-main">Redshift</span> Change of wavelength in photons during travel

In physics, a redshift is an increase in the wavelength, and corresponding decrease in the frequency and photon energy, of electromagnetic radiation. The opposite change, a decrease in wavelength and increase in frequency and energy, is known as a blueshift, or negative redshift. The terms derive from the colours red and blue which form the extremes of the visible light spectrum. The main causes of electromagnetic redshift in astronomy and cosmology are the relative motions of radiation sources, which give rise to the relativistic Doppler effect, and gravitational potentials, which gravitationally redshift escaping radiation. All sufficiently distant light sources show cosmological redshift corresponding to recession speeds proportional to their distances from Earth, a fact known as Hubble's law that implies the universe is expanding.

Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered in 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which used distant type Ia supernovae to measure the acceleration. The idea was that as type Ia supernovae have almost the same intrinsic brightness, and since objects that are farther away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the farther away that an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.

<span class="mw-page-title-main">Hubble's law</span> Observation in physical cosmology

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 away from Earth. The velocity of the galaxies has been determined by their redshift, a shift of the light they emit toward the red end of the visible spectrum. The discovery of Hubble's law is attributed to Edwin Hubble's work published in 1929.

In standard cosmology, comoving distance and proper distance are two closely related distance measures used by cosmologists to define distances between objects. Comoving distance factors out the expansion of the universe, giving a distance that does not change in time due to the expansion of space. Proper distance roughly corresponds to where a distant object would be at a specific moment of cosmological time, which can change over time due to the expansion of the universe. Comoving distance and proper distance are defined to be equal at the present time. At other times, the Universe's expansion results in the proper distance changing, while the comoving distance remains constant.

The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. Initially, it was estimated that there may be 2 trillion galaxies in the observable universe. That number was reduced in 2021 to only several hundred billion based on data from New Horizons. Assuming the universe is isotropic, the distance to the edge of the observable universe is roughly the same in every direction. That is, the observable universe is a spherical region centered on the observer. Every location in the universe has its own observable universe, which may or may not overlap with the one centered on Earth.

The particle horizon is the maximum distance from which light from particles could have traveled to the observer in the age of the universe. Much like the concept of a 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 times the speed of light, but rather the speed of light times the conformal time. The existence, properties, and significance of a cosmological horizon depend on the particular cosmological model.

The Friedmann–Lemaître–Robertson–Walker metric is a metric based on an exact solution of the Einstein field equations of general relativity. The metric describes a homogeneous, isotropic, expanding universe that is path-connected, but not necessarily simply connected. The general form of the metric follows from the geometric properties of homogeneity and isotropy; Einstein's field equations are only needed to derive the scale factor of the universe as a function of time. Depending on geographical or historical preferences, the set of the four scientists – Alexander Friedmann, Georges Lemaître, Howard P. Robertson and Arthur Geoffrey Walker – are variously grouped as Friedmann, Friedmann–Robertson–Walker (FRW), Robertson–Walker (RW), or Friedmann–Lemaître (FL). This model is sometimes called the Standard Model of modern cosmology, although such a description is also associated with the further developed Lambda-CDM model. The FLRW model was developed independently by the named authors in the 1920s and 1930s.

The horizon problem is a cosmological fine-tuning problem within the Big Bang model of the universe. It arises due to the difficulty in explaining the observed homogeneity of causally disconnected regions of space in the absence of a mechanism that sets the same initial conditions everywhere. It was first pointed out by Wolfgang Rindler in 1956.

The expansion of the universe is parametrized by a dimensionless scale factor $. Also known as the cosmic scale factor or sometimes the Robertson Walker scale factor, this is a key parameter of the Friedmann equations.$

The flatness problem is a cosmological fine-tuning problem within the Big Bang model of the universe. Such problems arise from the observation that some of the initial conditions of the universe appear to be fine-tuned to very 'special' values, and that small deviations from these values would have extreme effects on the appearance of the universe at the current time.

The Gödel metric, also known as the Gödel solution or Gödel universe, is an exact solution, found in 1949 by Kurt Gödel, of the Einstein field equations in which the stress–energy tensor contains two terms: the first representing the matter density of a homogeneous distribution of swirling dust particles, and the second associated with a negative cosmological constant.

In physical cosmology, cosmological perturbation theory is the theory by which the evolution of structure is understood in the Big Bang model. Cosmological perturbation theory may be broken into two categories: Newtonian or general relativistic. Each case uses its governing equations to compute gravitational and pressure forces which cause small perturbations to grow and eventually seed the formation of stars, quasars, galaxies and clusters. Both cases apply only to situations where the universe is predominantly homogeneous, such as during cosmic inflation and large parts of the Big Bang. The universe is believed to still be homogeneous enough that the theory is a good approximation on the largest scales, but on smaller scales more involved techniques, such as N-body simulations, must be used. When deciding whether to use general relativity for perturbation theory, note that Newtonian physics is only applicable in some cases such as for scales smaller than the Hubble horizon, where spacetime is sufficiently flat, and for which speeds are non-relativistic.

The expansion of the universe is the increase in distance between gravitationally unbound parts of the observable universe with time. It is an intrinsic expansion, so it does not mean that the universe expands "into" anything or that space exists "outside" it. To any observer in the universe, it appears that all but the nearest galaxies recede at speeds that are proportional to their distance from the observer, on average. While objects cannot move faster than light, this limitation applies only with respect to local reference frames and does not limit the recession rates of cosmologically distant objects.

In cosmology, a Hubble volume (named for the astronomer Edwin Hubble) or Hubble sphere, Hubble bubble, subluminal sphere, causal sphere and sphere of causality is a spherical region of the observable universe surrounding an observer beyond which objects recede from that observer at a rate greater than the speed of light due to the expansion of the universe. The Hubble volume is approximately equal to 10³¹ cubic light years (or about 10⁷⁹ cubic meters).

Distance measures are used in physical cosmology to give a natural notion of the distance between two objects or events in the universe. They are often used to tie some observable quantity to another quantity that is not directly observable, but is more convenient for calculations. The distance measures discussed here all reduce to the common notion of Euclidean distance at low redshift.

Cosmic time, or cosmological time, is the time coordinate commonly used in the Big Bang models of physical cosmology. Such time coordinate may be defined for a homogeneous, expanding universe so that the universe has the same density everywhere at each moment in time. The clocks measuring cosmic time should move along the Hubble flow.

In cosmology, baryon acoustic oscillations (BAO) are fluctuations in the density of the visible baryonic matter of the universe, caused by acoustic density waves in the primordial plasma of the early universe. In the same way that supernovae provide a "standard candle" for astronomical observations, BAO matter clustering provides a "standard ruler" for length scale in cosmology. The length of this standard ruler is given by the maximum distance the acoustic waves could travel in the primordial plasma before the plasma cooled to the point where it became neutral atoms, which stopped the expansion of the plasma density waves, "freezing" them into place. The length of this standard ruler can be measured by looking at the large scale structure of matter using astronomical surveys. BAO measurements help cosmologists understand more about the nature of dark energy by constraining cosmological parameters.

In astrophysics, an event horizon is a boundary beyond which events cannot affect an observer. Wolfgang Rindler coined the term in the 1950s.

In the general theory of relativity, the McVittie metric is the exact solution of Einstein's field equations describing a black hole or massive object immersed in an expanding cosmological spacetime. The solution was first fully obtained by George McVittie in the 1930s, while investigating the effect of the, then recently discovered, expansion of the Universe on a mass particle.

References

1 2 Margalef-Bentabol, Berta; Margalef-Bentabol, Juan; Cepa, Jordi (8 February 2013). "Evolution of the cosmological horizons in a universe with countably infinitely many state equations". Journal of Cosmology and Astroparticle Physics. 015. 2013 (2): 015. arXiv: 1302.2186 . Bibcode:2013JCAP...02..015M. doi:10.1088/1475-7516/2013/02/015. S2CID 119614479.
↑ Dodelson, Scott (2003). Modern Cosmology. Academic Press. p. 146.
↑ Lars Bergström and Ariel Goobar: "Cosmology and Particle Physics", WILEY (1999), page 65. ISBN 0-471-97041-7
↑ Lineweaver, Charles H.; Davis, Tamara M. (March 2005). "Misconceptions about the Big Bang". Scientific American. 292 (3): 36–45. Bibcode:2005SciAm.292c..36L. doi:10.1038/scientificamerican0305-36. ISSN 0036-8733.
↑ Massimo Giovannini (2008). A primer on the physics of the cosmic microwave background . World Scientific. pp. 70–. ISBN 978-981-279-142-9 . Retrieved 1 May 2011.
↑ Krauss, Lawrence M.; Scherrer, Robert J.; Cepa, Jordi (2007). "The return of a static universe and the end of cosmology". General Relativity and Gravitation. 39 (10): 1545. arXiv: 0704.0221 . Bibcode:2007GReGr..39.1545K. doi:10.1007/s10714-007-0472-9. S2CID 123442313.
↑ Krauss, Lawrence M.; Scherrer, Robert J.; Cepa, Jordi (2007). "The return of a static universe and the end of cosmology". General Relativity and Gravitation. 39 (10): 1545. arXiv: 0704.0221 . Bibcode:2007GReGr..39.1545K. doi:10.1007/s10714-007-0472-9. S2CID 123442313.

External links

Klauber, Robert D. (October 9, 2018). "Horizons in Cosmology" (PDF).

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[Berta-1] 1 2 Margalef-Bentabol, Berta; Margalef-Bentabol, Juan; Cepa, Jordi (8 February 2013). "Evolution of the cosmological horizons in a universe with countably infinitely many state equations". Journal of Cosmology and Astroparticle Physics. 015. 2013 (2): 015. arXiv: 1302.2186 . Bibcode:2013JCAP...02..015M. doi:10.1088/1475-7516/2013/02/015. S2CID 119614479.

[2] Dodelson, Scott (2003). Modern Cosmology. Academic Press. p. 146.

[3] Lars Bergström and Ariel Goobar: "Cosmology and Particle Physics", WILEY (1999), page 65. ISBN 0-471-97041-7

[4] Lineweaver, Charles H.; Davis, Tamara M. (March 2005). "Misconceptions about the Big Bang". Scientific American. 292 (3): 36–45. Bibcode:2005SciAm.292c..36L. doi:10.1038/scientificamerican0305-36. ISSN 0036-8733.

[Giovannini-5] Massimo Giovannini (2008). A primer on the physics of the cosmic microwave background . World Scientific. pp. 70–. ISBN 978-981-279-142-9 . Retrieved 1 May 2011.

[6] Krauss, Lawrence M.; Scherrer, Robert J.; Cepa, Jordi (2007). "The return of a static universe and the end of cosmology". General Relativity and Gravitation. 39 (10): 1545. arXiv: 0704.0221 . Bibcode:2007GReGr..39.1545K. doi:10.1007/s10714-007-0472-9. S2CID 123442313.

[7] Krauss, Lawrence M.; Scherrer, Robert J.; Cepa, Jordi (2007). "The return of a static universe and the end of cosmology". General Relativity and Gravitation. 39 (10): 1545. arXiv: 0704.0221 . Bibcode:2007GReGr..39.1545K. doi:10.1007/s10714-007-0472-9. S2CID 123442313.

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