Difference between revisions of "Cosmological constant"

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'''Cosmological constant''' is constant <math>\Lambda</math> of Einstein field equation  
+
The '''Cosmological constant''' is the constant <math>\Lambda</math> of the Einstein field equation  
:<math>R_{\mu\nu}-(R/2)g_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi T_{\mu\nu}</math>,
+
:<math>R_{\mu\nu}-(R/2)g_{\mu\nu}+\Lambda g_{\mu\nu}=8\pi G T_{\mu\nu}</math>,
where <math>R_{\mu\nu}</math> is Ricci tensor, <math>R</math> is its contraction, <math>g_{\mu\nu}</math> is metric tensor of spacetime, and <math>T_{\mu\nu}</math> is stress-energy tensor.  
+
where <math>R_{\mu\nu}</math> is Ricci's tensor, <math>R</math> is its contraction, <math>g_{\mu\nu}</math> is the metric tensor of spacetime, <math>G</math> is Newton's constant of gravitation, and <math>T_{\mu\nu}</math> is the stress-energy tensor. (The experimentally derived constant <math>G</math> has to appear in both Newton's formulation of gravity and the [[General relativity]] formulation, since they are compatible.)
  
Einstein added this '''cosmological constant''' to his field equation to make the universe stationary (neither expanding nor contracting) which it works when the '''cosmological constant''' has so called Einstein value  
+
Einstein added the cosmological constant term to his gravitational field equations in order to allow the existence of a homogeneous static solutions in the presence of matter, i.e. to make the universe stationary (neither expanding nor contracting). This works when the cosmological constant has the so-called Einstein value:
 
:<math>\Lambda_E=4\pi G \rho/c^2</math>,  
 
:<math>\Lambda_E=4\pi G \rho/c^2</math>,  
where <math>G</math> is Newtonian gravitational constant, <math>\rho</math> is density of space, and <math>c</math> is speed of light in [[vacuum]].
+
where <math>\rho</math> is the mass density of space and <math>c</math> is the speed of light in vacuo.
  
 
==Historical background==
 
==Historical background==
 +
[[Image:600px-Albert Einstein Head.jpg|thumbnail|right|200px|
 +
*"I do not share the crusading spirit of the professional [[Atheism|atheist]] whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth. I prefer an attitude of humility corresponding to the weakness of our intellectual understanding of nature and of our own being." - [[Albert Einstein]]<ref name="Isaacson390">Isaacson, Walter (2008). [http://books.google.com/books?id=cdxWNE7NY6QC&pg=PT390 ''Einstein: His Life and Universe''] (New York: Simon and Schuster), p. 390.  Retrieved from GoogleBooks archive on February 19, 2015.</ref>]]
 
In 1915 Einstein introduced the field equation that placed into balance and found equal the [[Curvature of space|curvature]] at one side and [[Mass (science)|mass]] on the other. He hoped that the equations of [[general relativity]] would determine a single universe model without any beginning or end. For reasons he could never make clear, he found universe so conceived particularly satisfying and he managed to find a solution to his own equations that specified universe of that sort, static and unchanged forever.<ref name="Devils"/>{{#tag:ref|The contemporary atheistic scientists such as [[Stephen Hawking|S.Hawking]] believe there is no room for creator in the universe which has no boundary or edge whereas in universe which had beginning we could suppose it had a creator.<ref name="WhomadeGod">{{cite book
 
In 1915 Einstein introduced the field equation that placed into balance and found equal the [[Curvature of space|curvature]] at one side and [[Mass (science)|mass]] on the other. He hoped that the equations of [[general relativity]] would determine a single universe model without any beginning or end. For reasons he could never make clear, he found universe so conceived particularly satisfying and he managed to find a solution to his own equations that specified universe of that sort, static and unchanged forever.<ref name="Devils"/>{{#tag:ref|The contemporary atheistic scientists such as [[Stephen Hawking|S.Hawking]] believe there is no room for creator in the universe which has no boundary or edge whereas in universe which had beginning we could suppose it had a creator.<ref name="WhomadeGod">{{cite book
 
|author=Edgar Anrews
 
|author=Edgar Anrews
Line 17: Line 19:
 
|isbn=978-0-85234-707-2
 
|isbn=978-0-85234-707-2
 
|url=http://books.google.com/books?id=EOFfAAAACAAJ&dq=Andrews+who+made+God&source=bl&ots=5Ru2cf9HRQ&sig=PilSMEqTMAmqtoUgJ9idnBQpH64&hl=en&sa=X&ei=099xUNuqE43KtAa8uICIDA&redir_esc=y
 
|url=http://books.google.com/books?id=EOFfAAAACAAJ&dq=Andrews+who+made+God&source=bl&ots=5Ru2cf9HRQ&sig=PilSMEqTMAmqtoUgJ9idnBQpH64&hl=en&sa=X&ei=099xUNuqE43KtAa8uICIDA&redir_esc=y
|quote= Stephen Hawking puts it thus: 'So long as the universe had a beginning, we could suppose it had a creator. But if universe is really completely self-contained, having no boundary or edge, it would have neither beginning not end; it would simply be. What place then for creator?'}}</ref> See also: [[Singularity#Antipathy_to_the_idea_of_beginning|Antipathy to the idea of beginning]]|group=note}} A.G. Riess declares that Einstein's original idea was to have constant amount of energy in the space.<ref name="RiessNobel"/> When in 1920s Russian mathematician A.Friedman (1924)<ref name="Friedman">{{cite web
+
|quote= Stephen Hawking puts it thus: 'So long as the universe had a beginning, we could suppose it had a creator. But if universe is really completely self-contained, having no boundary or edge, it would have neither beginning not end; it would simply be. What place then for creator?'}}</ref> See also: [[Singularity#Antipathy to the idea of beginning|Antipathy to the idea of beginning]]|group=note}} A.G. Riess declares that Einstein's original idea was to have constant amount of energy in the space.<ref name="RiessNobel"/> When in 1920s Russian mathematician A.Friedman (1924)<ref name="Friedman">{{cite web
 
|author=Alexander Friedmann
 
|author=Alexander Friedmann
 
|title=Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes
 
|title=Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes
Line 23: Line 25:
 
|volume=21
 
|volume=21
 
|issue=1
 
|issue=1
|pages=326-332
+
|pages=326–332
 
|url=http://adsabs.harvard.edu/abs/1924ZPhy...21..326F
 
|url=http://adsabs.harvard.edu/abs/1924ZPhy...21..326F
 
|doi=10.1007/BF01328280
 
|doi=10.1007/BF01328280
|language=German}}</ref> and Belgian catholic priest and professor of physics G.Lemaître (1927)<ref>{{Cite web|author=G. Lemaître |title=Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques |journal=Annales de la Société Scientifique de Bruxelles |volume=47 |page=49 |month=April |year=1927 |url=http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1927ASSB...47...49L&defaultprint=YES&filetype=.pdf |language=French}}</ref> independently found that Einstein's gravitational field equations of [[General relativity|general relativity]] have non-static cosmological solution<ref name="Devils">{{Cite book
+
|language=German}}</ref> and Belgian catholic priest and professor of physics G.Lemaître (1927)<ref>{{Cite web|author=G. Lemaître |title=Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques |journal=Annales de la Société Scientifique de Bruxelles |volume=47 |page=49 |month=April |year=1927 |url=http://articles.adsabs.harvard.edu/cgi-bin/nph-iarticle_query?1927ASSB...47...49L&defaultprint=YES&filetype=.pdf |language=French}}</ref> independently found that Einstein's gravitational field equations of [[general relativity]] have non-static cosmological solution<ref name="Devils">{{Cite book
 
| author = David Berlinski
 
| author = David Berlinski
 
| title = The Devil’s Delusion
 
| title = The Devil’s Delusion
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|chapter = The Cause
 
|chapter = The Cause
 
| url=http://www.davidberlinski.org/devils-delusion/about.php
 
| url=http://www.davidberlinski.org/devils-delusion/about.php
| quote = }}</ref> implying an [[Expanding universe|expanding ]] or collapsing universe<ref name="DismantlingBB">{{cite book|author=Alex Williams, John Hartnett|title=Dismantling the Big Bang|publisher=Master Books|location=Green Forest, AR, USA|year=2005|pages=110|isbn=978-0-89051-437-5|url=http://books.google.com/books?id=EvN9Gfbox74C&printsec=frontcover&dq=Dismantling+Big&source=bl&ots=uuIXDOw4ld&sig=wWFH6PJy2ZW5JQc8N59jTX5FVd0&hl=en&sa=X&ei=9WlsUJ-cJ8bGtAasp4H4Bg&redir_esc=y#v=snippet&q=CSR&f=false|quote=...his equations were telling [Einstein] that [the universe] had to be either collapsing or expanding...A large value [of cosmological constant] would cause large redshifts and spacial distortion in nearby objects...[the cosmological constant ...involves fine-tuning of over 120 orders of magnitude (quoted Lawrence Krauss)]}}</ref>, Einstein, wishing to cancel out expansion, suggested modification to his field equations by adding a so-called cosmological term.<ref name="CSR">{{cite book  
+
| quote = }}</ref> implying an [[Expanding universe|expanding]] or collapsing universe,<ref name="DismantlingBB">{{cite book|author=Alex Williams, John Hartnett|title=Dismantling the Big Bang|publisher=Master Books|location=Green Forest, AR, USA|year=2005|pages=110|isbn=978-0-89051-437-5|url=http://books.google.com/books?id=EvN9Gfbox74C&printsec=frontcover&dq=Dismantling+Big&source=bl&ots=uuIXDOw4ld&sig=wWFH6PJy2ZW5JQc8N59jTX5FVd0&hl=en&sa=X&ei=9WlsUJ-cJ8bGtAasp4H4Bg&redir_esc=y#v=snippet&q=CSR&f=false|quote=...his equations were telling [Einstein] that [the universe] had to be either collapsing or expanding...A large value [of cosmological constant] would cause large redshifts and spacial distortion in nearby objects...[the cosmological constant ...involves fine-tuning of over 120 orders of magnitude (quoted Lawrence Krauss)]}}</ref> Einstein, wishing to cancel out expansion, suggested modification to his field equations by adding a so-called cosmological term.<ref name="CSR">{{cite book  
 
|author=Moshe Carmeli
 
|author=Moshe Carmeli
 
|title=Cosmological Special Relativity, The Large-Scale Structure of Space, Time and Velocity, 2nd Edition
 
|title=Cosmological Special Relativity, The Large-Scale Structure of Space, Time and Velocity, 2nd Edition
Line 43: Line 45:
 
|isbn=9-789-02-4936-5
 
|isbn=9-789-02-4936-5
 
|quote=
 
|quote=
}}</ref> {{#tag:ref|cf."the 'cosmological constant' ... [also] had the effect of balancing the gravitational attraction that would otherwise cause the universe to collapse"<ref name="WhomadeGod"/>|group=note}} Before long, after Hubble's interpretation of new discoveries as [[expanding universe]] in 1929, the role of cosmological constant aiming to allow static homogeneous solutions to field equations in presence of [[matter]] seemed finished. Einstein consequently called <math>\Lambda</math> ''"the biggest blunder of my life"''.<ref name="CSR"/>
+
}}</ref> {{#tag:ref|cf."the 'cosmological constant' ... [also] had the effect of balancing the gravitational attraction that would otherwise cause the universe to collapse"<ref name="WhomadeGod"/>|group=note}} Before long, after [[Edwin Hubble|Hubble]]'s interpretation of new [[Scientific discovery|discoveries]] as [[expanding universe]] in 1929, the role of cosmological constant aiming to allow static homogeneous solutions to field equations in presence of [[matter]] seemed finished. Einstein consequently called <math>\Lambda</math> ''"the biggest blunder of my life"''.<ref name="CSR"/>
  
 
==Revival of the cosmological constant vs. property of the correct metric==
 
==Revival of the cosmological constant vs. property of the correct metric==
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|iisue=116
 
|iisue=116
 
|doi=10.1086/300499
 
|doi=10.1086/300499
|pages=1009-1038
+
|pages=1009–1038
 
}}</ref> and in December the same year the new discovery of the accelerating universe was declared to be "Breakthrough of the Year" in the journal ''Science''.<ref>{{cite web
 
}}</ref> and in December the same year the new discovery of the accelerating universe was declared to be "Breakthrough of the Year" in the journal ''Science''.<ref>{{cite web
 
|url=http://physicsworld.com/cws/article/news/1998/dec/18/science-chooses-accelerating-universe-as-breakthrough-of-the
 
|url=http://physicsworld.com/cws/article/news/1998/dec/18/science-chooses-accelerating-universe-as-breakthrough-of-the
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|volume=282  
 
|volume=282  
 
|issue=5397  
 
|issue=5397  
|pages=2156-2157
+
|pages=2156–2157
 
|doi=10.1126/science.282.5397.2156a
 
|doi=10.1126/science.282.5397.2156a
 
|quote=In 1998, astronomers peered into the universe and found that it is flying apart ever faster, suggesting that Einstein was right when he posited a mysterious energy that fills "empty" space, and in fact that most of the energy of the universe is in this form. Two independent teams of astronomers found that not only is there too little matter in the universe to ever halt the expansion of the universe on its own, but the outward motion appears to be speeding up, not slowing down. At the same time, the finding raises such profound questions about the nature of space that cosmologists are wondering whether the ultimate fate of the universe can ever be known for certain. We therefore name their findings, which transform our view of the universe and pose fundamental new questions for physics, as Breakthrough of the Year for 1998.
 
|quote=In 1998, astronomers peered into the universe and found that it is flying apart ever faster, suggesting that Einstein was right when he posited a mysterious energy that fills "empty" space, and in fact that most of the energy of the universe is in this form. Two independent teams of astronomers found that not only is there too little matter in the universe to ever halt the expansion of the universe on its own, but the outward motion appears to be speeding up, not slowing down. At the same time, the finding raises such profound questions about the nature of space that cosmologists are wondering whether the ultimate fate of the universe can ever be known for certain. We therefore name their findings, which transform our view of the universe and pose fundamental new questions for physics, as Breakthrough of the Year for 1998.
 
|acessdate=7.10.2012}}</ref>
 
|acessdate=7.10.2012}}</ref>
 
    
 
    
According to [[John Hartnett|J.Hartnett]], it would be fair to state that most cosmologist would like the requirement for cosmological constant to disappear altogether. He interprets its extremely small value as a possible evidence for fine-tuned universe.<ref name="DismantlingBB"/>  
+
According to [[John Hartnett|J.Hartnett]], it would be fair to state that most cosmologists would like the requirement for cosmological constant to disappear altogether. He interprets its extremely small value as a possible evidence for fine-tuned universe.<ref name="DismantlingBB"/>  
 
The 2011 Nobel Laureate in Physics, Brian P. Schmidt was asked in 2011 the question "what is causing the universe to expand at accelerating rate?" which he answered by words that it is a big mystery why space should have energy at all, people around the world are scratching their heads to figure out but as of today there has not been lot progress yet.<ref>{{cite web
 
The 2011 Nobel Laureate in Physics, Brian P. Schmidt was asked in 2011 the question "what is causing the universe to expand at accelerating rate?" which he answered by words that it is a big mystery why space should have energy at all, people around the world are scratching their heads to figure out but as of today there has not been lot progress yet.<ref>{{cite web
 
|title=Nobel Laureates 2011
 
|title=Nobel Laureates 2011
Line 84: Line 86:
 
|accessdate=4.10.2012}}</ref>  
 
|accessdate=4.10.2012}}</ref>  
  
It has been however declared that [[Moshe Carmeli|Carmeli]]'s theory which has no explicit cosmological constant implies its equivalence of <math>\Lambda</math> = 1.934 × 10-35 s-2 and this value is supposed to be in excellent agreement with measurements.<ref name="Cosmological Constant">{{cite web|author=Moshe Carmeli|date=20 November 2002|title=Fundamental Approach to the Cosmological Constant Issue|journal=International Journal of Modern Physics A|volume=17|issue=29|pages=|doi=10.1142/S0217751X02013253|url=www.worldscientific.com/doi/abs/10.1142/S0217751X02013253}}</ref> The 'force' pushing the universe apart, which invokes the ideas about [[dark energy]] is more correctly just a property of the correct metric.<ref name="starlight">{{cite book| last = Hartnett| first = John| authorlink = | title = Starlight, Time and the New Physics| publisher = Creation Ministries International| series = | year = 2007| doi = | isbn = 978-0-949-906687|pages=154|quote=}}</ref>
+
It has been however declared that [[Moshe Carmeli|Carmeli]]'s theory which has no explicit cosmological constant implies its equivalence of <math>\Lambda</math> = 1.934 × 10<sup>−35</sup> s<sup>−2</sup> and this value is supposed to be in excellent agreement with measurements.<ref name="Cosmological Constant">{{cite web|author=Moshe Carmeli|date=20 November 2002|title=Fundamental Approach to the Cosmological Constant Issue|journal=International Journal of Modern Physics A|volume=17|issue=29|pages=|doi=10.1142/S0217751X02013253|url=http://www.worldscientific.com/doi/abs/10.1142/S0217751X02013253}}</ref> The 'force' pushing the universe apart, which invokes the ideas about [[dark energy]] is more correctly just a property of the correct metric.<ref name="starlight">{{cite book| last = Hartnett| first = John| authorlink = | title = Starlight, Time and the New Physics| publisher = Creation Ministries International| series = | year = 2007| doi = | isbn = 978-0-949-906687|pages=154|quote=}}</ref>
  
 
== Notes ==
 
== Notes ==
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{{Reflist}}
 
{{Reflist}}
  
[[Category: Cosmology]]
+
[[Category:Cosmology]]
[[Category: Physics]]
+
[[Category:Physics]]

Latest revision as of 00:58, 13 July 2016

The Cosmological constant is the constant of the Einstein field equation

,

where is Ricci's tensor, is its contraction, is the metric tensor of spacetime, is Newton's constant of gravitation, and is the stress-energy tensor. (The experimentally derived constant has to appear in both Newton's formulation of gravity and the General relativity formulation, since they are compatible.)

Einstein added the cosmological constant term to his gravitational field equations in order to allow the existence of a homogeneous static solutions in the presence of matter, i.e. to make the universe stationary (neither expanding nor contracting). This works when the cosmological constant has the so-called Einstein value:

,

where is the mass density of space and is the speed of light in vacuo.

Historical background

*"I do not share the crusading spirit of the professional atheist whose fervor is mostly due to a painful act of liberation from the fetters of religious indoctrination received in youth. I prefer an attitude of humility corresponding to the weakness of our intellectual understanding of nature and of our own being." - Albert Einstein[1]

In 1915 Einstein introduced the field equation that placed into balance and found equal the curvature at one side and mass on the other. He hoped that the equations of general relativity would determine a single universe model without any beginning or end. For reasons he could never make clear, he found universe so conceived particularly satisfying and he managed to find a solution to his own equations that specified universe of that sort, static and unchanged forever.[2][note 1] A.G. Riess declares that Einstein's original idea was to have constant amount of energy in the space.[4] When in 1920s Russian mathematician A.Friedman (1924)[5] and Belgian catholic priest and professor of physics G.Lemaître (1927)[6] independently found that Einstein's gravitational field equations of general relativity have non-static cosmological solution[2] implying an expanding or collapsing universe,[7] Einstein, wishing to cancel out expansion, suggested modification to his field equations by adding a so-called cosmological term.[8] [note 2] Before long, after Hubble's interpretation of new discoveries as expanding universe in 1929, the role of cosmological constant aiming to allow static homogeneous solutions to field equations in presence of matter seemed finished. Einstein consequently called "the biggest blunder of my life".[8]

Revival of the cosmological constant vs. property of the correct metric

In general, a positive causes acceleration to the universe expansion, whereas negative and ordinary matter tend to decelerate it.[8] When the Supernova Cosmology Project Collaboration and High-Z Supernova Team Collaboration started their research at the beginning of 1990s, both prevailing mainstream cosmological models assumed decelerating universe scenarios. The processing of collected data from research observations however indicated that the universe is accelerating and requires something like non-zero cosmological constant.[4] The first paper on new discovery was submitted in May 1998[9] and in December the same year the new discovery of the accelerating universe was declared to be "Breakthrough of the Year" in the journal Science.[10][11]

According to J.Hartnett, it would be fair to state that most cosmologists would like the requirement for cosmological constant to disappear altogether. He interprets its extremely small value as a possible evidence for fine-tuned universe.[7] The 2011 Nobel Laureate in Physics, Brian P. Schmidt was asked in 2011 the question "what is causing the universe to expand at accelerating rate?" which he answered by words that it is a big mystery why space should have energy at all, people around the world are scratching their heads to figure out but as of today there has not been lot progress yet.[12]

It has been however declared that Carmeli's theory which has no explicit cosmological constant implies its equivalence of = 1.934 × 10−35 s−2 and this value is supposed to be in excellent agreement with measurements.[13] The 'force' pushing the universe apart, which invokes the ideas about dark energy is more correctly just a property of the correct metric.[14]

Notes

  1. The contemporary atheistic scientists such as S.Hawking believe there is no room for creator in the universe which has no boundary or edge whereas in universe which had beginning we could suppose it had a creator.[3] See also: Antipathy to the idea of beginning
  2. cf."the 'cosmological constant' ... [also] had the effect of balancing the gravitational attraction that would otherwise cause the universe to collapse"[3]

References

  1. Isaacson, Walter (2008). Einstein: His Life and Universe (New York: Simon and Schuster), p. 390. Retrieved from GoogleBooks archive on February 19, 2015.
  2. 2.0 2.1 David Berlinski. "The Cause", The Devil’s Delusion. Basic Books, New York, 2009, 77. ISBN 978-0-465-01937-3. 
  3. 3.0 3.1 Edgar Anrews (2010). Who made God? Searching for a theory of everything.. Carlisle, PA, USA: EP Books, 98, 100. ISBN 978-0-85234-707-2. “Stephen Hawking puts it thus: 'So long as the universe had a beginning, we could suppose it had a creator. But if universe is really completely self-contained, having no boundary or edge, it would have neither beginning not end; it would simply be. What place then for creator?'” 
  4. 4.0 4.1 A.G.Riess. Nobel Prize (in Physics 2011) lecture slides on Supernovae Reveal An Accelerating Universe (A Science Adventure Story).
  5. Alexander Friedmann. Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes (German) 326–332. Zeitschrift für Physik. DOI:10.1007/BF01328280.
  6. G. Lemaître (April 1927). Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extra-galactiques (French).
  7. 7.0 7.1 Alex Williams, John Hartnett (2005). Dismantling the Big Bang. Green Forest, AR, USA: Master Books, 110. ISBN 978-0-89051-437-5. “...his equations were telling [Einstein] that [the universe] had to be either collapsing or expanding...A large value [of cosmological constant] would cause large redshifts and spacial distortion in nearby objects...[the cosmological constant ...involves fine-tuning of over 120 orders of magnitude (quoted Lawrence Krauss)]” 
  8. 8.0 8.1 8.2 Moshe Carmeli (2002). Cosmological Special Relativity, The Large-Scale Structure of Space, Time and Velocity, 2nd Edition. World Scientific Publishing, 2, 168. ISBN 9-789-02-4936-5. 
  9. A.G.Riess et al. (1998). Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant 1009–1038. Astrophysics. DOI:10.1086/300499.
  10. Science chooses accelerating universe as "Breakthrough of the Year". IOP Publishing, A website from the Institute of Physics, physicsworld.com (Dec 18, 1998).
  11. James Glanz (18 December 1998). BREAKTHROUGH OF THE YEAR: ASTRONOMY: Cosmic Motion Revealed 2156–2157. Science Magazine. DOI:10.1126/science.282.5397.2156a. “In 1998, astronomers peered into the universe and found that it is flying apart ever faster, suggesting that Einstein was right when he posited a mysterious energy that fills "empty" space, and in fact that most of the energy of the universe is in this form. Two independent teams of astronomers found that not only is there too little matter in the universe to ever halt the expansion of the universe on its own, but the outward motion appears to be speeding up, not slowing down. At the same time, the finding raises such profound questions about the nature of space that cosmologists are wondering whether the ultimate fate of the universe can ever be known for certain. We therefore name their findings, which transform our view of the universe and pose fundamental new questions for physics, as Breakthrough of the Year for 1998.”
  12. Nobel Laureates 2011. nobelprize.org. Retrieved on 4.10.2012.
  13. Moshe Carmeli (20 November 2002). Fundamental Approach to the Cosmological Constant Issue. DOI:10.1142/S0217751X02013253.
  14. Hartnett, John (2007). Starlight, Time and the New Physics. Creation Ministries International, 154. ISBN 978-0-949-906687.