Information about Hubble's Law
physical cosmology which states that the redshift in light coming from distant galaxies is proportional to their distance. The law was first formulated by Edwin Hubble and Milton Humason in 1929[1] after nearly a decade of observations. 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 most recent calculation of the proportionality constant, using the satellite WMAP began in 2003, yielding a value of 71 ± 4 (km/s)/Mpc. In August, 2006, a less accurate figure was obtained independently using data from NASA's orbital Chandra X-ray Observatory: 77 (km/s)/Mpc with an uncertainty of ± 15%.[2]
In 1922, Alexander Friedmann derived his Friedmann equations from the Einstein field equations, showing that the universe might expand at a rate calculable by the equations.[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. Georges Lemaître independently found a similar solution in 1927. 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. This idea of an expanding spacetime would eventually lead to the Big Bang and Steady State theories of cosmology.
Before the advent of modern cosmology, there was considerable talk about the size and shape of the universe. In 1920, the famous Shapley-Curtis debate took place between Harlow Shapley and Heber D. Curtis over this issue. Shapley argued for a small universe the size of the Milky Way galaxy and Curtis argued that the universe was much larger. The issue would be resolved in the coming decade with Hubble's improved observations.
Edwin Hubble did most of his professional astronomical observing work at Mount Wilson Observatory, the world's most powerful telescope at the time. His observations of Cepheid variable stars in spiral nebulae enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. The nebulae were first described as "island universes" and it was only later that the moniker "galaxy" would be applied to them.
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. 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). (See cosmic distance ladder for details.)
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.
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). 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.
where
is the recessional velocity, typically expressed in km/s. H0 is Hubble's constant and corresponds to the value of 
(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. This value is the same throughout the universe for a given conformal time. 
is the proper distance from the galaxy to the observer, measured in megaparsecs (Mpc), in the 3-space defined by given conformal time. (Recession velocity is just v = dD/dt). As the formula implies, in very distant objects, v can be larger than c. This is not a violation of special relativity, because the rules of special relativity only apply precisely within a small region: a special-relativistic description of two widely-separated galaxies would in general be incorrect. (Thus special relativity strictly says, not that no speed can be faster than light, but that nothing can move past another object at a speed faster than light).
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
where c is the speed of light. 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.
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.
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). Simply stated the theorem is this:
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 value of Hubble parameter changes over time either increasing or decreasing depending on the sign of the so-called deceleration parameter
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. A non-zero, time-dependent value of simply requires integration of the Friedmann equations backwards from the present time to the time when the comoving horizon size was zero.
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 14,000 million 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.
For most of the second half of the 20th century the value of
was estimated to be between 50 and 90 (km/s)/Mpc.
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. 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. This difference was partially resolved with the introduction of the Lambda-CDM model of the Universe in the late 1990s. With this 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. In particular the Hubble Key Project (led by Dr. Wendy L. Freedman, Carnegie Observatories) gave the most accurate optical determination in May 2001 with its final estimate of 72±8 (km/s)/Mpc, consistent with a measurement of based upon Sunyaev-Zel'dovich effect observations of many galaxy clusters having a similar accuracy. 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.[6] These values arise from fitting a combination of WMAP and other cosmological data to the simplest version of the Lambda-CDM model. If the data is fitted with more general versions, tends to be smaller and more uncertain: typically around 67±4 (km/s)/Mpc although some models allow values near 63 (km/s)/Mpc.[7]
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%. [8] The consistency of the measurements from all these methods lends support to both the measured value of and the Lambda-CDM model.
(In the metric system, is about 2.3×10−18 s−1; this should not be written as Hertz since the quantity is not a frequency).
A value for 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 Lambda-CDM model).
where is the Hubble parameter, 
is the scale factor, G is the gravitational constant, 
is the geometry of the universe and equal to -1,0 or 1, and 
is the cosmological constant.
can just be taken to include matter so:
where
is the density of matter today. We know for non-relativistic particles their energy density decreases proportional to the volume of the universe so the equation above must be true. We can also define (see Friedmann equations page for an explanation of the density parameter 
):
so
. Also by definition
and
where the subscript zero refers to the values today, and
. Substituting all this in into the Friedman equation at the start of this section and replacing a with 
gives:
where
is the energy density of the dark energy. By definition an equation of state in cosmology is 
, and if we substitute this into the fluid equation, which describes how the 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 
which is assuming we live in a 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 parameterise
, for example if 
, giving:
has units of inverse time. We can therefore define “Hubble time” as 
. The value of Hubble time in the standard cosmological model is 4.35×1017 s or 13.8 billion years, somewhat longer than the current age of the universe.
- the speed of light multiplied by the Hubble time. It is equivalent to 4228 million parsecs or 13800 million light years (the numerical value of the Hubble length in light years is, by definition, equal to that of the Hubble time in years).
. The exact definition varies: it is sometimes defined as the volume of a sphere with radius , or alternatively, a cube of side . 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.
This timeline of cosmological theories and discoveries is a chronological catalog of the evolution of humankind's understanding of the cosmos over the last two-plus millennia.
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)
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. 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.In 1922, Alexander Friedmann derived his Friedmann equations from the Einstein field equations, showing that the universe might expand at a rate calculable by the equations.[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. Georges Lemaître independently found a similar solution in 1927. 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. This idea of an expanding spacetime would eventually lead to the Big Bang and Steady State theories of cosmology.
Before the advent of modern cosmology, there was considerable talk about the size and shape of the universe. In 1920, the famous Shapley-Curtis debate took place between Harlow Shapley and Heber D. Curtis over this issue. Shapley argued for a small universe the size of the Milky Way galaxy and Curtis argued that the universe was much larger. The issue would be resolved in the coming decade with Hubble's improved observations.
Edwin Hubble did most of his professional astronomical observing work at Mount Wilson Observatory, the world's most powerful telescope at the time. His observations of Cepheid variable stars in spiral nebulae enabled him to calculate the distances to these objects. Surprisingly, these objects were discovered to be at distances which placed them well outside the Milky Way. The nebulae were first described as "island universes" and it was only later that the moniker "galaxy" would be applied to them.
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. 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). (See cosmic distance ladder for details.)
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.
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). 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
is the recessional velocity, typically expressed in km/s. H0 is Hubble's constant and corresponds to the value of (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. This value is the same throughout the universe for a given conformal time. is the proper distance from the galaxy to the observer, measured in megaparsecs (Mpc), in the 3-space defined by given conformal time. (Recession velocity is just v = dD/dt). As the formula implies, in very distant objects, v can be larger than c. This is not a violation of special relativity, because the rules of special relativity only apply precisely within a small region: a special-relativistic description of two widely-separated galaxies would in general be incorrect. (Thus special relativity strictly says, not that no speed can be faster than light, but that nothing can move past another object at a speed faster than light).
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
where c is the speed of light. 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.
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.
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). 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 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). A so-called "closed universe" (Ω>1) comes to an end in a Big Crunch and is considerably younger than its Hubble age. 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 value of Hubble parameter changes over time either increasing or decreasing depending on the sign of the so-called deceleration parameter
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. A non-zero, time-dependent value of
simply requires integration of the Friedmann equations backwards from the present time to the time when the comoving horizon size was zero.
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 14,000 million 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.
Olbers' paradox
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). 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
was estimated to be between 50 and 90 (km/s)/Mpc.
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. 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. This difference was partially resolved with the introduction of the Lambda-CDM model of the Universe in the late 1990s. With this 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. In particular the Hubble Key Project (led by Dr. Wendy L. Freedman, Carnegie Observatories) gave the most accurate optical determination in May 2001 with its final estimate of 72±8 (km/s)/Mpc, consistent with a measurement of based upon Sunyaev-Zel'dovich effect observations of many galaxy clusters having a similar accuracy. 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.[6] These values arise from fitting a combination of WMAP and other cosmological data to the simplest version of the Lambda-CDM model. If the data is fitted with more general versions, tends to be smaller and more uncertain: typically around 67±4 (km/s)/Mpc although some models allow values near 63 (km/s)/Mpc.[7]
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%. [8] The consistency of the measurements from all these methods lends support to both the measured value of
and the Lambda-CDM model.
(In the metric system,
is about 2.3×10−18 s−1; this should not be written as Hertz since the quantity is not a frequency).
A value for
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 Lambda-CDM model).
Derivation of the Hubble parameter
Start with the Friedman equation:
where
is the Hubble parameter, is the scale factor, G is the gravitational constant, is the geometry of the universe and equal to -1,0 or 1, and is the cosmological constant.
Matter dominated universe (with a cosmological constant)
If the universe is matter dominated then the energy density of the universe can just be taken to include matter so:
where
is the density of matter today. We know for non-relativistic particles their energy density decreases proportional to the volume of the universe so the equation above must be true. We can also define (see Friedmann equations page for an explanation of the density parameter ):
so
. Also by definition
and
where the subscript zero refers to the values today, and
. Substituting all this in into the Friedman equation at the start of this section and replacing a with 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. So now:
where
is the energy density of the dark energy. By definition an equation of state in cosmology is , and if we substitute this into the fluid equation, which describes how the 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 which is assuming we live in a 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 parameterise
, for example if , giving:
Units derived from the Hubble constant
Hubble time
The Hubble constant has units of inverse time. We can therefore define “Hubble time” as . The value of Hubble time in the standard cosmological model is 4.35×1017 s or 13.8 billion years, somewhat longer than the current age of the universe.
Hubble length
The Hubble length is a unit of distance in cosmology, defined as - the speed of light multiplied by the Hubble time. It is equivalent to 4228 million parsecs or 13800 million 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. The exact definition varies: it is sometimes defined as the volume of a sphere with radius , or alternatively, a cube of side . 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.
See also
- Age of the universe
- Shape of the universe
- Hyperbolic geometry (the space is curved due to expansion)
- Euclidean geometry (the space is "flat" due to a balance)
- Elliptic geometry (the space is curved due to gravity)
Notes
1. ^ Hubble, Edwin, "A Relation between Distance and Radial Velocity among Extra-Galactic Nebulae" (1929) Proceedings of the National Academy of Sciences of the United States of America, Volume 15, Issue 3, pp. 168-173 (Full article, PDF)
2. ^ Chandra Confirms the Hubble Constant (2006-08-08). Retrieved on 2007-03-07.
3. ^ Friedman, A: Über die Krümmung des Raumes, Z. Phys. 10 (1922), 377-386. (English translation in: Gen. Rel. Grav. 31 (1999), 1991-2000.)
4. ^ Huchra, John. . Retrieved on 2007-10-04.
5. ^ S. I. Chase, Olbers' Paradox, entry in the Physics FAQ; see also I. Asimov, "The Black of Night", in Asimov on Astronomy (Doubleday, 1974), ISBN 0-385-04111-X.
6. ^ D. N. Spergel et al. (2007), "Three-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology", Astrophysical Journal Supplement Series 170: 377–408; available online at LAMBDA
7. ^ Results for and other cosmological parameters obtained by fitting a variety of models to several combinations of WMAP and other data are available at the NASA's LAMBDA website.
8. ^ Chandra independently determines Hubble constant in Spaceflight Now
2. ^ Chandra Confirms the Hubble Constant (2006-08-08). Retrieved on 2007-03-07.
3. ^ Friedman, A: Über die Krümmung des Raumes, Z. Phys. 10 (1922), 377-386. (English translation in: Gen. Rel. Grav. 31 (1999), 1991-2000.)
4. ^ Huchra, John. . Retrieved on 2007-10-04.
5. ^ S. I. Chase, Olbers' Paradox, entry in the Physics FAQ; see also I. Asimov, "The Black of Night", in Asimov on Astronomy (Doubleday, 1974), ISBN 0-385-04111-X.
6. ^ D. N. Spergel et al. (2007), "Three-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Implications for Cosmology", Astrophysical Journal Supplement Series 170: 377–408; available online at LAMBDA
7. ^ Results for
and other cosmological parameters obtained by fitting a variety of models to several combinations of WMAP and other data are available at the NASA's LAMBDA website.8. ^ Chandra independently determines Hubble constant in Spaceflight Now
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)
- Final Results from the Hubble Space Telescope Key Project to Measure the Hubble Constant. Freedman et al. The Astrophysical Journal, Volume 553, Issue 1, pp. 47-72.
External links
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 formation and evolution. Cosmology involves itself with studying the motions of the celestial bodies and the first cause.
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The age of the universe, in physics, is the time elapsed between the Big Bang and the present day. Current observations suggest that this is about 13.7 billion years, with an uncertainty of about +/-200 million years.
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Big Bang is the cosmological model of the universe whose primary assertion is that the universe has expanded into its current state from a primordial condition of enormous density and temperature.
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Blue Shift refers to a shortening of a transmitted signal's wavelength, and/or an increase in its frequency. The name comes from the fact that the shorter-wavelength end of the optical spectrum is the blue (or violet) end, hence, when visible light is compacted in
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In standard cosmology, 'comoving' distance or 'proper distance' is one of several distance measures used by cosmologists to define distances between objects.
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Comoving coordinates
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cosmic microwave background radiation (most often abbreviated CMB but occasionally CMBR, CBR or MBR, also referred to as relic radiation) is a form of electromagnetic radiation discovered in 1965 that fills the entire universe [1].
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In physical cosmology, dark energy is a hypothetical form of energy that permeates all of space and tends to increase the rate of expansion of the universe. [1]
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In astrophysics and cosmology, dark matter is hypothetical matter of unknown composition that does not emit or reflect enough electromagnetic radiation to be observed directly, but whose presence can be inferred from gravitational effects on visible matter.
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Friedmann-Lemaître-Robertson-Walker (FLRW) metric is an exact solution of the Einstein field equations of general relativity; it describes a , isotropic expanding or contracting universe.
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The Friedmann equations are a set of equations in cosmology that govern the expansion of space in homogeneous and isotropic models of the universe within the context of general relativity.
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formation of galaxies is still one of the most active research areas in astrophysics; and, to some extent, this is also true for galaxy evolution. Some ideas, however, have gained wide acceptance.
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In physical cosmology, cosmic inflation is the idea that the nascent universe passed through a phase of exponential expansion that was driven by a negative-pressure vacuum energy density.
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large-scale structure refers to the characterization of observable distributions of matter and light on the largest scales (typically on the order of billions of light-years).
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ΛCDM or Lambda-CDM is an abbreviation for Lambda-Cold Dark Matter. It is frequently referred to as the concordance model of big bang cosmology, since it attempts to explain cosmic microwave background observations, as well as large scale structure
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The metric expansion of space is a key part of science's current understanding of the universe, whereby spacetime itself is described by a metric which changes over time in such a way that the spatial dimensions appear to grow or stretch as the universe gets older.
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In physical cosmology, Big Bang nucleosynthesis (or primordial nucleosynthesis) refers to the production of nuclei other than those of H-1 (i.e. the normal, light isotope of hydrogen, whose nuclei consist of a single proton each) during the early phases of the
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redshift occurs when the electromagnetic radiation, usually visible light, that is emitted from or reflected off an object is shifted toward the (less energetic) red end of the electromagnetic spectrum.
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The shape of the Universe is an informal name for a subject of investigation within physical cosmology. Cosmologists and astronomers describe the geometry of the universe which includes both local geometry and global geometry.
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Structure formation refers to a fundamental problem in physical cosmology. The universe, as is now known from observations of the cosmic microwave background radiation, began in a hot, dense, nearly uniform state approximately 13.7 Gyr ago.
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Physical cosmology
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- Age of the universe
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- FLRW metric
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For a timeline of the cosmos (or universe), see .
This timeline of cosmological theories and discoveries is a chronological catalog of the evolution of humankind's understanding of the cosmos over the last two-plus millennia.
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The ultimate fate of the universe is a topic in physical cosmology. Many possible fates are predicted by rival scientific theories, including futures of both finite and infinite duration.
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The Universe is defined as the summation of all particles and energy that exist and the space-time in which all events occur. Based on observations of the portion of the Universe that is observable, physicists attempt to describe the whole of space-time, including all matter and
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General relativity (GR) (aka general theory of relativity (GTR)) is the geometrical theory of gravitation published by Albert Einstein in 1915/16.[1] It unifies special relativity, Newton's law of universal gravitation, and the insight that gravitational
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Particle physics is a branch of physics that studies the elementary constituents of matter and radiation, and the interactions between them. It is also called "high energy physics"
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Quantum gravity is the field of theoretical physics attempting to unify quantum mechanics, which describes three of the fundamental forces of nature, with general relativity, the theory of the fourth fundamental force: gravity.
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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 formation and evolution. Cosmology involves itself with studying the motions of the celestial bodies and the first cause.
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redshift occurs when the electromagnetic radiation, usually visible light, that is emitted from or reflected off an object is shifted toward the (less energetic) red end of the electromagnetic spectrum.
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