Physical cosmology

Universe · Big Bang Age of the universe Timeline of the Big Bang Ultimate fate of the universe Expanding universe Redshift · Hubble's law Metric expansion of space Friedmann equations FLRW metric

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Hubble's law is a statement in physical cosmology which states that the redshift in light coming from distant galaxies is proportional to their distance. Physical cosmology, as a branch of Astronomy, is the study of the large-scale structure of the Universe and is concerned with fundamental questions about its The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. The age of the Universe is the time elapsed between the theory of the Big Bang and the present day This timeline of the Big Bang describes the events according to the Scientific theory of the Big Bang, using the cosmological time parameter of Comoving coordinates The ultimate fate of the universe is a topic in Physical cosmology. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by The metric expansion of space is the averaged increase of metric (i The Friedmann equations are a set of Equations in cosmology that govern the expansion of space in homogeneous and isotropic models Physical cosmology, as a branch of Astronomy, is the study of the large-scale structure of the Universe and is concerned with fundamental questions about its In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by A galaxy is a massive gravitationally bound system consisting of Stars an Interstellar medium of gas and dust, and Dark matter This article is about proportionality the mathematical relation The law was first formulated by Edwin Hubble and Milton Humason in 1929^[1] after nearly a decade of observations. Edwin Powell Hubble ( November 20, 1889 – September 28, 1953) was an American astronomer. Milton Lasell Humason (August 19 1891 &ndash June 18 1972 was as American Astronomer. Observation is either an activity of a living being (such as a Human) which senses and assimilates the Knowledge of a Phenomenon, or the recording of data It is considered the first observational basis for the expanding space paradigm and today serves as one of the most often cited pieces of evidence in support of the Big Bang. The metric expansion of space is the averaged increase of metric (i The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. The most recent calculation of the proportionality constant, using the satellite WMAP began in 2003 and a combination of other astronomical data, yielding a value of 70. 1 ± 1. 3 (km/s)/Mpc. The kilometre ( American spelling: kilometer) symbol km is a unit of Length in the Metric system, equal to one thousand The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units History The first direct measurements of an object at interstellar distances were undertaken by German Astronomer Friedrich Wilhelm Bessel in 1838 In August, 2006, a less accurate figure was obtained independently using data from NASA's orbital Chandra X-ray Observatory: 77 (km/s)/Mpc or about 2. The Chandra X-ray Observatory is a Satellite launched on STS-93 by NASA on July 23, 1999. 5×10⁻¹⁸ s⁻¹ with an uncertainty of ± 15%. ^[2]

Discovery

A decade before Hubble made his observations, a number of physicists and mathematicians had established a consistent theory of the relationship between space and time by using Einstein's field equations of general relativity. Below is a list of famous Physicists Many of these from the 20th and 21st centuries are found on the list of recipients of the Nobel Prize in physics. A mathematician is a person whose primary area of study and research is the field of Mathematics. SpaceTime is a patent-pending three dimensional graphical user interface that allows end users to search their content such as Google Google Images Yahoo! YouTube eBay Amazon and RSS The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the General relativity or the general theory of relativity is the geometric theory of Gravitation published by Albert Einstein in 1916 Applying the most general principles to the nature of the universe yielded a dynamic solution that conflicted with the then prevailing notion of a static universe. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy In physics the term dynamics customarily refers to the time evolution of physical processes

FLRW equations

In 1922, Alexander Friedmann derived his Friedmann equations from Einstein's field equations, showing that the universe might expand at a rate calculable by the equations. Alexander Alexandrovich Friedman or Friedmann (Александр Александрович Фридман ( June 16 1888, Saint Petersburg, Imperial The Friedmann equations are a set of Equations in cosmology that govern the expansion of space in homogeneous and isotropic models The Einstein field equations ( EFE) or Einstein's equations are a set of ten equations in Einstein 's theory of General relativity in which the ^[3] The parameter used by Friedmann is known today as the scale factor which can be considered as a scale invariant form of the proportionality constant of Hubble's Law. The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model is a function of time which represents the relative expansion of the Universe In Physics and Mathematics, scale invariance is a feature of objects or laws that do not change if length scales (or energy scales are multiplied by a common factor This article is about proportionality the mathematical relation Georges Lemaître independently found a similar solution in 1927. Georges Henri Joseph Édouard Lemaître ( July 17, 1894 &ndash June 20, 1966) was a Belgian Roman Catholic Priest The Friedmann equations are derived by inserting the metric for a homogeneous and isotropic universe into Einstein's field equations for a fluid with a given density and pressure. The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface This idea of an expanding spacetime would eventually lead to the Big Bang and Steady State theories of cosmology. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. In cosmology, the Steady State theory (also known as the Infinite Universe theory or continuous creation) is a model developed in 1948 by Fred

Shape of the universe

Before the advent of modern cosmology, there was considerable talk about the size and shape of the universe. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy The shape of the Universe is an informal name for a subject of investigation within Physical cosmology which describes the Geometry of the Universe The Universe is defined as everything that Physically Exists: the entirety of Space and Time, all forms of Matter, Energy In 1920, the famous Shapley-Curtis debate took place between Harlow Shapley and Heber D. Curtis over this issue. This is about the infamous discussion of astronomy For the Dream Theater song about Stem cell research, see The Great Debate (song. Harlow Shapley ( November 2 1885 &ndash October 20 1972) was an American Astronomer. Heber Doust Curtis ( June 27 1872 – January 9 1942) was an American Astronomer. Shapley argued for a small universe the size of the Milky Way galaxy and Curtis argued that the universe was much larger. The Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias sometimes referred to simply The issue would be resolved in the coming decade with Hubble's improved observations.

Cepheid variable stars outside of the Milky Way

Edwin Hubble. Edwin Powell Hubble ( November 20, 1889 – September 28, 1953) was an American astronomer.

Edwin Powell Hubble did most of his professional astronomical observing work at Mount Wilson Observatory, the world's most powerful telescope at the time. The Mount Wilson Observatory (MWO is an Astronomical observatory in Los Angeles County California. His observations of Cepheid variable stars in spiral nebulae enabled him to calculate the distances to these objects. A Cepheid variable (pron ˈse-f(ē-id or ˈsē-f(ē-id or Cepheid is a member of a particular class of Variable stars notable for a fairly tight correlation A nebula (from Latin: "mist" pl nebulae or nebulæ, with ligature or nebulas) is an Interstellar cloud of Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. The Milky Way (a translation of the Latin Via Lactea, in turn derived from the Greek Γαλαξίας (Galaxias sometimes referred to simply The nebulae were first described as "island universes" and it was only later that the moniker "galaxy" would be applied to them.

Combining redshifts with distance measurements

Combining his measurements of galaxy distances with Vesto Slipher's measurements of the redshifts associated with the galaxies, Hubble discovered a rough proportionality of the objects' distances. Vesto Melvin Slipher ( November 11, 1875 &ndash November 8, 1969) was an American Astronomer. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by Though there was considerable scatter (now known to be caused by peculiar velocities), Hubble was able to plot a trend line from the 46 galaxies he studied and obtain a value for the Hubble constant of 500 km/s/Mpc (much higher than the currently accepted value due to errors in his distance calibrations). In Probability theory and Statistics, the variance of a Random variable, Probability distribution, or sample is one measure of In Physical cosmology, the term peculiar velocity refers to the components of a receding Galaxy 's velocity that cannot be explained by Hubble's law. (See cosmic distance ladder for details. The cosmic distance ladder (also known as the Extragalactic Distance Scale) is the succession of methods by which astronomers determine the Distances to celestial )

In 1958, the first good estimate of H₀, 75 km/s/Mpc, was published by Allan Sandage^[4], but it would be decades before a consensus was achieved. Allan Rex Sandage (born June 18 1926 in Iowa City Iowa) is an American Astronomer.

The cosmological constant abandoned

After Hubble's discovery was published, Albert Einstein abandoned his work on the cosmological constant (which he had designed to allow for a static solution to his equations). Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical In Physical cosmology, the cosmological constant (usually denoted by the Greek capital letter Lambda: Λ was proposed by Albert Einstein as a modification He would later term this work his "greatest blunder" since the belief of a static universe prevented him from predicting the expanding universe. Einstein would make a famous trip to Mount Wilson in 1931 to thank Hubble for providing the observational basis for modern cosmology.

Interpretation

The discovery of the linear relationship between redshift, interpreted as recessional velocity, and distance yields a straightforward mathematical expression for Hubble's Law as follows:

where

• v is the recessional velocity, typically expressed in km/s. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by Recessional Velocity is a term used to describe the rate at which an object is moving away typically from Earth.
• H₀ is Hubble's constant and corresponds to the value of H (often termed the Hubble parameter which is a value that is time dependent) in the Friedmann equations taken at the time of observation denoted by the subscript 0. A time-variant system is a System, that is not Time-invariant (TIV This value is the same throughout the universe for a given comoving time. In standard cosmology, ' comoving' distance and ' proper distance' are two closely related distance measures used by cosmologists to define distances between
• D is the comoving proper distance from the galaxy to the observer, measured in megaparsecs (Mpc), in the 3-space defined by given cosmological time. In standard cosmology, ' comoving' distance and ' proper distance' are two closely related distance measures used by cosmologists to define distances between A galaxy is a massive gravitationally bound system consisting of Stars an Interstellar medium of gas and dust, and Dark matter History The first direct measurements of an object at interstellar distances were undertaken by German Astronomer Friedrich Wilhelm Bessel in 1838 (Recession velocity is just v = dD/dt).

Observability of parameters

Strictly speaking, neither v nor D in the formula are directly observable, because they are properties now of a galaxy, whereas our observations refer to the galaxy in the past, at the time that the light we currently see left it.

For relatively nearby galaxies (redshift z much less than unity), v and D will not have changed much, and v can be estimated using the formula v = zc where c is the speed of light. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by This gives the empirical relation found by Hubble.

For distant galaxies, v (or D) cannot be calculated from z without specifying a detailed model for how H changes with time. The redshift is not even directly related to the recession velocity at the time the light set out, but it does have a simple interpretation: (1+z) is the factor by which the universe has expanded while the photon was travelling towards the observer.

Expansion velocity vs relative velocity

In using Hubble's law to determine distances, only the velocity due to the expansion of the universe can be used. Since gravitationally interacting galaxies move relative to each other independent of the expansion of the universe, these relative velocities, called peculiar velocities, need to be accounted for in the application of Hubble's law.

The Finger of God effect is one result of this phenomenon discovered in 1938 by Benjamin Kenneally. In systems that are gravitationally bound, such as galaxies or our planetary system, the expansion of space is (more than) annihilated by the attractive force of gravity. In Mechanics, the virial theorem provides a general equation relating the average total Kinetic energy, \left\langle T \right\rangle of a stable system

Idealized Hubble's Law

The mathematical derivation of an idealized Hubble's Law for a uniformly expanding universe is a fairly elementary theorem of geometry in 3-dimensional Cartesian/Newtonian coordinate space, which, considered as a metric space, is entirely homogeneous and isotropic (properties do not vary with location or direction). In Mathematics, a metric space is a set where a notion of Distance (called a metric) between elements of the set is defined The cosmological principle is an assumption invoked in Cosmology that when applied severely restricts the large variety of possible cosmological theories Simply stated the theorem is this:

Any two points which are moving away from the origin, each along straight lines and with speed proportional to distance from the origin, will be moving away from each other with a speed proportional to their distance apart.

In fact this applies to non-Cartesian spaces as long as they are locally homogeneous and isotropic; specifically to the negatively- and positively-curved spaces frequently considered as cosmological models (see shape of the universe). The shape of the Universe is an informal name for a subject of investigation within Physical cosmology which describes the Geometry of the Universe

The Ultimate fate and age of the universe

The ultimate fate of the universe and the age of the universe can both be determined by measuring the Hubble constant today and extrapolating with the observed value of the deceleration parameter, uniquely characterized by values of density parameters (Ω). The ultimate fate of the universe is a topic in Physical cosmology. The age of the Universe is the time elapsed between the theory of the Big Bang and the present day A so-called "closed universe" (Ω>1) comes to an end in a Big Crunch and is considerably younger than its Hubble age. In Physical cosmology, the Big Crunch is one possible scenario for the Ultimate fate of the universe, in which the Metric expansion of space eventually An "open universe" (Ω≤1) expands forever and has an age that is closer its Hubble age. For the accelerating universe that we inhabit, the age of the universe is coincidentally very close to the Hubble age. The accelerating universe is the observation that the universe appears to be expanding at an accelerated rate

The value of the Hubble parameter changes over time either increasing or decreasing depending on the sign of the so-called deceleration parameter q which is defined by

In a universe with a deceleration parameter equal to zero, it follows that H = 1/t, where t is the time since the Big Bang. The deceleration parameter q in cosmology is a Dimensionless measure of the cosmic acceleration of the expansion of the universe A non-zero, time-dependent value of q simply requires integration of the Friedmann equations backwards from the present time to the time when the comoving horizon size was zero. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space In Physical cosmology, particle horizon is the maximum distance from which particles could have traveled to the observer in the Age of the universe

It was long thought that q was positive, indicating that the expansion is slowing down due to gravitational attraction. This would imply an age of the universe less than 1/H (which is about 14 billion years). For instance, a value for q of 1/2 (once favoured by most theorists) would give the age of the universe as 2/(3H). The discovery in 1998 that q is apparently negative means that the universe could actually be older than 1/H. In fact, estimates of the age of the universe are, by coincidence, very close to 1/H. The age of the Universe is the time elapsed between the theory of the Big Bang and the present day

Olbers' paradox

Main article: Olbers' paradox

The expansion of space summarized by the Big Bang interpretation of Hubble's Law is relevant to the old conundrum known as Olbers' paradox: if the universe were infinite, static, and filled with a uniform distribution of stars (notice that this also requires an infinite number of stars), then every line of sight in the sky would end on a star, and the sky would be as bright as the surface of a star. Olbers' paradox, described by the German Astronomer Heinrich Wilhelm Olbers in 1823 (but not published until 1826 by Bode) and earlier by Olbers' paradox, described by the German Astronomer Heinrich Wilhelm Olbers in 1823 (but not published until 1826 by Bode) and earlier by Infinity (symbolically represented with ∞) comes from the Latin infinitas or "unboundedness The idea of a static universe or "Einstein's universe" is one which demands that space is not expanding nor contracting but rather is dynamically stable A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth Brightness is an attribute of Visual perception in which a source appears to emit or reflect a given amount of Light. However, the night sky is largely dark. Since the 1600s, astronomers and other thinkers have proposed many possible ways to resolve this paradox, but the currently accepted resolution depends in part upon the Big Bang theory and in part upon the Hubble expansion. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. Hubble's law is the statement in Physical cosmology that the Redshift in light coming from distant galaxies is proportional to their distance In a universe that exists for a finite amount of time, only the light of finitely many stars has had a chance to reach us yet, and the paradox is resolved. Additionally, in an expanding universe distant objects recede from us which cause the light emanating from them to be redshifted and diminished in brightness. Recessional Velocity is a term used to describe the rate at which an object is moving away typically from Earth. In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by Although both effects contribute, the redshift is the less important of the two; remember the original paradox was couched in terms of a static universe. ^[5]

Determining the Hubble constant

The value of the Hubble constant is estimated by measuring the redshift of distant galaxies and then determining the distances to the same galaxies (by some other method than Hubble's law). In Physics and Astronomy, redshift occurs when Electromagnetic radiation – usually Visible light – emitted or reflected by The cosmic distance ladder (also known as the Extragalactic Distance Scale) is the succession of methods by which astronomers determine the Distances to celestial Uncertainties in the physical assumptions used to determine these distances have caused varying estimates of the Hubble constant. For most of the second half of the 20th century the value of H₀ was estimated to be between 50 and 90 (km/s)/Mpc.

Disputes over Hubble's constant

The value of the Hubble constant was the topic of a long and rather bitter controversy between Gérard de Vaucouleurs who claimed the value was around 100 and Allan Sandage who claimed the value was near 50. Gérard Henri de Vaucouleurs ( April 25, 1918 &ndash October 7, 1995) was a French Astronomer. Allan Rex Sandage (born June 18 1926 in Iowa City Iowa) is an American Astronomer.

In 1996, a debate moderated by John Bahcall between Gustav Tammann and Sidney van den Bergh was held in similar fashion to the earlier Shapley-Curtis debate over these two competing values. John Norris Bahcall ( December 30 1934 &ndash August 17 2005) was an American astrophysicist. Dr Gustav Tammann was the director of the Astronomical Institute of the University of Basel, Switzerland, European Space Agency member of the Space Sidney van den Bergh (born 20 May 1929, Wassenaar) is a Canadian astronomer This is about the infamous discussion of astronomy For the Dream Theater song about Stem cell research, see The Great Debate (song.

This difference was partially resolved with the introduction of the ΛCDM model of the universe in the late 1990s. &LambdaCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter.

The ΛCDM model

With the ΛCDM model observations of high-redshift clusters at X-ray and microwave wavelengths using the Sunyaev-Zel'dovich effect, measurements of anisotropies in the cosmic microwave background radiation, and optical surveys all gave a value of around 70 for the constant. &LambdaCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. The Sunyaev-Zel'dovich effect (often abbreviated as the SZ effect) is the result of high energy Electrons distorting the Cosmic microwave background radiation

Using Hubble space telescope data

In particular the Hubble Key Project (led by Dr. The Hubble Space Telescope ( HST; also known colloquially as "the Hubble" or just "Hubble" is a space telescope that was carried into Wendy L. Freedman, Carnegie Observatories) gave the most accurate optical determination in May 2001 with its final estimate^[6] of 72±8 (km/s)/Mpc, consistent with a measurement of H₀ based upon Sunyaev-Zel'dovich effect observations of many galaxy clusters having a similar accuracy. The Sunyaev-Zel'dovich effect (often abbreviated as the SZ effect) is the result of high energy Electrons distorting the Cosmic microwave background radiation Galaxy groups and clusters are the largest Gravitationally bound objects to have arisen thus far in the process of cosmic structure formation

Using WMAP data

The most precise cosmic microwave background radiation determinations were 71±4 (km/s)/Mpc, by WMAP in 2003, and 70. 4^{+1. 5}_{−1. 6} (km/s)/Mpc, for measurements up to 2006. ^[7] The five year release from WMAP in 2008 finds 71. 9+2. 6−2. 7 (km/s)/Mpc. The kilometre ( American spelling: kilometer) symbol km is a unit of Length in the Metric system, equal to one thousand The second ( SI symbol s) sometimes abbreviated sec, is the name of a unit of Time, and is the International System of Units History The first direct measurements of an object at interstellar distances were undertaken by German Astronomer Friedrich Wilhelm Bessel in 1838 [1]

These values arise from fitting a combination of WMAP and other cosmological data to the simplest version of the ΛCDM model. If the data is fitted with more general versions, H₀ tends to be smaller and more uncertain: typically around 67±4 (km/s)/Mpc although some models allow values near 63 (km/s)/Mpc. ^[8]

Using Chandra X-ray Observatory data

In August 2006, using NASA's Chandra X-ray Observatory, a team from NASA's Marshall Space Flight Center (MSFC) found the Hubble constant to be 77 (km/s)/Mpc, with an uncertainty of about 15%. August 2006 was a month with thirty-one days On August 10, an alleged plot to detonate ten Airliners over the Atlantic Ocean was revealed to The Chandra X-ray Observatory is a Satellite launched on STS-93 by NASA on July 23, 1999. George C Marshall Space Flight Center (MSFC the original home of NASA, is a lead center for propulsion, Space Shuttle propulsion Shuttle external fuel ^[9] The consistency of the measurements from all these methods lends support to both the measured value of H₀ and the ΛCDM model. &LambdaCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter.

Acceleration of the expansion

A value for q measured from standard candle observations of Type Ia supernovae, which was determined in 1998 to be negative, surprised many astronomers with the implication that the expansion of the universe is currently "accelerating" (although the Hubble factor is still decreasing with time; see the articles on dark energy and the ΛCDM model). A standard candle is an astronomical object that has a known Luminosity. A Type Ia supernova is a sub-category of cataclysmic Variable In Physical cosmology, dark energy is a hypothetical exotic form of Energy that permeates all of space and tends to increase the rate of expansion of the universe &LambdaCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter.

Derivation of the Hubble parameter

Start with the Friedman equation:

where H is the Hubble parameter, a is the scale factor, G is the gravitational constant, k is the normalised spatial curvature of the universe and equal to −1, 0, or +1, and Λ is the cosmological constant. The Friedmann equations are a set of Equations in cosmology that govern the expansion of space in homogeneous and isotropic models The scale factor, parameter of Friedmann-Lemaître-Robertson-Walker model is a function of time which represents the relative expansion of the Universe The gravitational constant, denoted G, is a Physical constant involved in the calculation of the gravitational attraction between objects with mass In Physical cosmology, the cosmological constant (usually denoted by the Greek capital letter Lambda: Λ was proposed by Albert Einstein as a modification

Matter-dominated universe (with a cosmological constant)

If the universe is matter-dominated, then the mass density of the universe ρ can just be taken to include matter so

where is the density of matter today. The Matter-Dominated Era was the epoch in the evolution of the Universe that began after the Radiation-Dominated Era ended when the Universe was about 380000 years old We know for nonrelativistic particles that their mass density decreases proportional to the inverse volume of the universe so the equation above must be true. We can also define (see density parameter for Ω_m)

so ρ = ρ_cΩ_m / a³. The Friedmann equations are a set of Equations in cosmology that govern the expansion of space in homogeneous and isotropic models Also, by definition,

and

where the subscript nought refers to the values today, and a₀ = 1. Substituting all of this in into the Friedman equation at the start of this section and replacing a with a = 1 / (1 + z) gives

Matter- and dark energy-dominated universe

If the universe is both matter-dominated and dark energy-dominated, then the above equation for the Hubble parameter will also be a function of the equation of state of dark energy. The Matter-Dominated Era was the epoch in the evolution of the Universe that began after the Radiation-Dominated Era ended when the Universe was about 380000 years old In Physical cosmology, dark energy is a hypothetical exotic form of Energy that permeates all of space and tends to increase the rate of expansion of the universe In cosmology, the equation of state of a Perfect fluid is characterized by a Dimensionless number w, equal to the ratio of its Pressure So now:

ρ = ρ_m(a) + ρ_de(a),

where ρ_de is the mass density of the dark energy. By definition an equation of state in cosmology is P = wρc², and if we substitute this into the fluid equation, which describes how the mass density of the universe evolves with time,

If w is constant,

Therefore for dark energy with a constant equation of state w, . If we substitute this into the Friedman equation in a similar way as before, but this time set k = 0 which is assuming we live in a spatially flat universe, (see Shape of the Universe)

If dark energy does not have a constant equation-of-state w, then

and to solve this we must parametrize w(a), for example if w(a) = w₀ + w_a(1 − a), giving

Units derived from the Hubble constant

Hubble time

The Hubble constant H₀ has units of inverse time. The shape of the Universe is an informal name for a subject of investigation within Physical cosmology which describes the Geometry of the Universe We can therefore define “Hubble time” as 1 / H₀. The value of Hubble time in the standard cosmological model is 4. &LambdaCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. 35×10¹⁷ s or 13. 8 billion years (Liddle 2003, p. 57).

Hubble length

The Hubble length is a unit of distance in cosmology, defined as c / H₀—the speed of light multiplied by the Hubble time. It is equivalent to 4228 million parsecs or 13. 8 billion light years. (The numerical value of the Hubble length in light years is, by definition, equal to that of the Hubble time in years. )

Hubble volume

The Hubble volume is sometimes defined as a volume of the universe with a comoving size of c / H₀. In standard cosmology, ' comoving' distance and ' proper distance' are two closely related distance measures used by cosmologists to define distances between The exact definition varies: it is sometimes defined as the volume of a sphere with radius c / H₀, or alternatively, a cube of side c / H₀. Some cosmologists even use the term Hubble volume to refer to the volume of the observable universe, although this has a radius approximately 3 times larger. In Big Bang Cosmology, the observable universe is the region of space bounded by a Sphere, centered on the observer that is small enough that

See also

• Age of the universe
• Shape of the universe
  • Hyperbolic geometry (crinkly due to expansion)
  • Euclidean geometry (flat due to a balance)
  • Elliptic geometry (round due to gravity)

Notes

References

• Kutner, Marc (2003). Astronomy: A Physical Perspective. Cambridge University Press. ISBN 0-521-52927-1.  
• Hubble, E. P. . , The Observational Approach to Cosmology (Oxford, 1937)
• Liddle, A (2003). "An Introduction to Modern Cosmology 2nd ed. ", Wiley.

External links

• The Hubble Key Project
• The Hubble Diagram Project