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57-509: The two models were proposed in two articles in 1999 by Lisa Randall and Raman Sundrum because they were dissatisfied with the universal extra-dimensional models then in vogue. Such models require two fine tunings; one for the value of the bulk cosmological constant and the other for the brane tensions . Later, while studying RS models in the context of the anti-de Sitter / conformal field theory (AdS/CFT) correspondence , they showed how it can be dual to technicolor models . The first of

114-478: A bad conscience. ... I am unable to believe that such an ugly thing is actually realized in nature". Einstein's static universe is unstable against matter density perturbations. Furthermore, without the cosmological constant Einstein could have found the expansion of the universe before Hubble's observations. In 1929, not long after Einstein developed his static theory, observations by Edwin Hubble indicated that

171-428: A cosmological constant of the order of M p l 2 {\textstyle M_{\rm {pl}}^{2}} ( 1 {\textstyle 1} in reduced Planck units). As noted above, the measured cosmological constant is smaller than this by a factor of ~10 . This discrepancy has been called "the worst theoretical prediction in the history of physics". Some supersymmetric theories require

228-470: A cosmological constant on theoretical grounds or found that it arose naturally from the mathematics. For example, Arthur Eddington claimed that the cosmological constant version of the vacuum field equation expressed the " epistemological " property that the universe is "self- gauging ", and Erwin Schrödinger 's pure- affine theory using a simple variational principle produced the field equation with

285-410: A cosmological constant that is exactly zero, which further complicates things. This is the cosmological constant problem, the worst problem of fine-tuning in physics : there is no known natural way to derive the tiny cosmological constant used in cosmology from particle physics . No vacuum in the string theory landscape is known to support a metastable, positive cosmological constant, and in 2018

342-712: A cosmological term. In 1990s, Saul Perlmutter at Lawrence Berkeley National Laboratory, Brian Schmidt of the Australian National University and Adam Riess of the Space Telescope Science Institute were searching for type Ia supernovas. By that time, they expected to observe the deceleration of the supernovas caused by the gravitation attraction of mass according to Einstein's gravitational theory. The first reports published in July 1997 from Supernova Cosmology Project used

399-474: A different value. The value w = −1.028 ± 0.032 , measured by the Planck Collaboration (2018) is consistent with −1 , assuming w does not change over cosmic time. Observations announced in 1998 of distance–redshift relation for Type Ia supernovae indicated that the expansion of the universe is accelerating, if one assumes the cosmological principle . When combined with measurements of

456-424: A group of four physicists advanced a controversial conjecture which would imply that no such universe exists . One possible explanation for the small but non-zero value was noted by Steven Weinberg in 1987 following the anthropic principle . Weinberg explains that if the vacuum energy took different values in different domains of the universe, then observers would necessarily measure values similar to that which

513-408: A hundred times the currently accepted value. In 1992, Weinberg refined this prediction of the cosmological constant to 5 to 10 times the matter density. This argument depends on the vacuum energy density being constant throughout spacetime, as would be expected if dark energy were the cosmological constant. There is no evidence that the vacuum energy does vary, but it may be the case if, for example,

570-404: A result of the cosmological principle not applying in the late universe. As was only recently seen, by works of 't Hooft , Susskind and others, a positive cosmological constant has surprising consequences, such as a finite maximum entropy of the observable universe (see Holographic principle ). A major outstanding problem is that most quantum field theories predict a huge value for

627-547: A universe that contracts slightly will continue contracting. However, the cosmological constant remained a subject of theoretical and empirical interest. Empirically, the cosmological data of recent decades strongly suggests that our universe has a positive cosmological constant. The explanation of this small but positive value is a remaining theoretical challenge, the so-called cosmological constant problem . Some early generalizations of Einstein's gravitational theory, known as classical unified field theories , either introduced

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684-464: A very similar theme. He showed that if the Universe is considered as a thin shell (a mathematical synonym for "brane") expanding in 5-dimensional space, then there is a possibility to obtain one scale for particle theory corresponding to the 5-dimensional cosmological constant and Universe thickness, and thus to solve the hierarchy problem . It was also shown that four-dimensionality of the Universe

741-530: Is a professor of computer science at Georgia Tech . Lisa is an avid climber. A rockface along the Mill Creek near Dumont in Colorado , is named Lisa Randall Wall after her by a local climbing society. In a climbing accident, after falling from the cliff despite proper safety measures, she injured her heel. Cosmological constant In cosmology , the cosmological constant (usually denoted by

798-583: Is around the Planck scale , W is the warp factor, and Wk is around a TeV . The boundary at y = 1/ k is called the Planck brane , and the boundary at y = 1/( Wk ) is called the TeV brane . The particles of the standard model reside on the TeV brane. The distance between both branes is only −ln( W )/ k , though. In another coordinate system , so that and The RS2 model uses the same geometry as RS1, but there

855-592: Is based on recent measurements of vacuum energy density, ρ vac = 5.96 × 10  kg/m ≘ 5.3566 × 10  J/m = 3.35 GeV/m . However, due to the Hubble tension and the CMB dipole , recently it has been proposed that the cosmological principle is no longer true in the late universe and that the FLRW metric breaks down, so it is possible that observations usually attributed to an accelerating universe are simply

912-616: Is extremely warped and contains two branes : the Planckbrane (where gravity is a relatively strong force; also called "Gravitybrane") and the Tevbrane (our home with the Standard Model particles; also called "Weakbrane"). In this model, the two branes are separated in the not-necessarily large fifth dimension by approximately 16 units (the units based on the brane and bulk energies). The Planckbrane has positive brane energy, and

969-506: Is no TeV brane. The particles of the standard model are presumed to be on the Planck brane. This model was originally of interest because it represented an infinite 5-dimensional model, which, in many respects, behaved as a 4-dimensional model. This setup may also be of interest for studies of the AdS/CFT conjecture. In 1998/99 Merab Gogberashvili published on arXiv a number of articles on

1026-451: Is observed: the formation of life-supporting structures would be suppressed in domains where the vacuum energy is much larger. Specifically, if the vacuum energy is negative and its absolute value is substantially larger than it appears to be in the observed universe (say, a factor of 10 larger), holding all other variables (e.g. matter density) constant, that would mean that the universe is closed; furthermore, its lifetime would be shorter than

1083-530: Is that people are excited that there is something fundamentally new that has been discovered." Randall has an e-book entitled Higgs Discovery: The Power of Empty Space . Before the Large Hadron Collider was operating, she wrote an article explaining the discoveries that were expected from using it. She was commonly asked about the misconception that the LHC could make black holes that could destroy

1140-409: Is the Planck length . A positive vacuum energy density resulting from a cosmological constant implies a negative pressure, and vice versa. If the energy density is positive, the associated negative pressure will drive an accelerated expansion of the universe, as observed. (See Dark energy and Cosmic inflation for details.) Instead of the cosmological constant itself, cosmologists often refer to

1197-467: Is the result of stability requirement, since the extra component of the Einstein field equations giving the localized solution for matter fields coincides with the one of the conditions of stability. In August 2016, experimental results from the LHC excluded RS gravitons with masses below 3.85 and 4.45 TeV for ˜k = 0.1 and 0.2 respectively and for ˜k = 0.01, graviton masses below 1.95 TeV, except for

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1254-411: The Einstein field equations in the form R μ ν − 1 2 R g μ ν + Λ g μ ν = κ T μ ν , {\displaystyle R_{\mu \nu }-{\tfrac {1}{2}}R\,g_{\mu \nu }+\Lambda g_{\mu \nu }=\kappa T_{\mu \nu },} where

1311-885: The National Academy of Sciences (2008), the American Philosophical Society , and a fellow of the American Physical Society . Randall has helped organize numerous conferences and has been on the editorial board of several major theoretical physics journals. In autumn 2004, she was the most cited theoretical physicist of the previous five years. Randall was featured in Seed magazine 's "2005 Year in Science Icons" and in Newsweek ' s "Who's Next in 2006" as "one of

1368-423: The chameleon particle or the symmetron theory to dark energy, in a laboratory setting, failed to detect a new force. Inferring the presence of dark energy through its interaction with baryons in the cosmic microwave background has also led to a negative result, although the current analyses have been derived only at the linear perturbation regime. It is also possible that the difficulty in detecting dark energy

1425-491: The cosmic microwave background radiation these implied a value of Ω Λ ≈ 0.7, a result which has been supported and refined by more recent measurements (as well as previous works ). If one assumes the cosmological principle, as in the case for all models that use the Friedmann–Lemaître–Robertson–Walker metric , while there are other possible causes of an accelerating universe , such as quintessence,

1482-430: The expansion of the universe is accelerating , implying that the cosmological constant may have a positive value. Since the 1990s, studies have shown that, assuming the cosmological principle , around 68% of the mass–energy density of the universe can be attributed to dark energy. The cosmological constant Λ is the simplest possible explanation for dark energy, and is used in the standard model of cosmology known as

1539-585: The hierarchy problem concerning the relative weakness of gravity, cosmology of dimensions, baryogenesis , cosmological inflation , and dark matter . She contributed to the Randall–Sundrum model , first published in 1999 with Raman Sundrum . Randall was born in Queens , New York City , New York . She graduated from Stuyvesant High School in 1980, where she was a classmate of fellow physicist and science popularizer Brian Greene . She won first place in

1596-630: The hierarchy problem . The warping of the extra dimension is analogous to the warping of spacetime in the vicinity of a massive object, such as a black hole . This warping, or red-shifting, generates a large ratio of energy scales, so that the natural energy scale at one end of the extra dimension is much larger than at the other end: where k is some constant, and η has "−+++" metric signature . This space has boundaries at y = 1/ k and y = 1/( Wk ), with 0 ≤ 1 / k ≤ 1 / ( W k ) {\displaystyle 0\leq 1/k\leq 1/(Wk)} , where k

1653-420: The quantum vacuum . A common assumption is that the quantum vacuum is equivalent to the cosmological constant. Although no theory exists that supports this assumption, arguments can be made in its favor. Such arguments are usually based on dimensional analysis and effective field theory . If the universe is described by an effective local quantum field theory down to the Planck scale , then we would expect

1710-418: The ΛCDM model . According to quantum field theory (QFT), which underlies modern particle physics , empty space is defined by the vacuum state , which is composed of a collection of quantum fields . All these quantum fields exhibit fluctuations in their ground state (lowest energy density) arising from the zero-point energy existing everywhere in space. These zero-point fluctuations should contribute to

1767-479: The 1980 Westinghouse Science Talent Search at the age of 18 and was also named a National Merit Scholar . She attended Harvard University , where she took Math 55 , earned a BA in physics in 1983 and a PhD in theoretical particle physics in 1987 under Howard Georgi . Randall researches particle physics and cosmology at Harvard, where she is a professor of theoretical physics. Her research concerns elementary particles and fundamental forces, and has involved

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1824-420: The 20th century. When T μν is zero, the field equation describes empty space (a vacuum ). The cosmological constant has the same effect as an intrinsic energy density of the vacuum, ρ vac (and an associated pressure ). In this context, it is commonly moved to the right-hand side of the equation using Λ = κρ vac . It is common to quote values of energy density directly, though still using

1881-491: The Greek capital letter lambda : Λ ), alternatively called Einstein's cosmological constant , is a coefficient that Albert Einstein initially added to his field equations of general relativity . He later removed it; however, much later it was revived to express the energy density of space, or vacuum energy , that arises in quantum mechanics . It is closely associated with the concept of dark energy . Einstein introduced

1938-706: The Modern World have both been on New York Times 100 notable books lists. Between the hardback and paperback release of Knocking on Heaven's Door , the quest for the discovery of the Higgs boson was actually completed, a subject discussed in the book. Scientists at the Large Hadron Collider found a particle identified as the Higgs boson. She said about the discovery, that even if people don't understand everything about it, "what an exciting thing it

1995-503: The Ricci tensor R μν , Ricci scalar R and the metric tensor g μν describe the structure of spacetime , the stress–energy tensor T μν describes the energy density, momentum density and stress at that point in spacetime, and κ = 8 πG / c . The gravitational constant G and the speed of light c are universal constants. When Λ is zero, this reduces to the field equation of general relativity usually used in

2052-498: The Tevbrane has negative brane energy. These energies are the cause of the extremely warped spacetime . In this warped spacetime that is only warped along the fifth dimension, the graviton 's probability function is extremely high at the Planckbrane, but it drops exponentially as it moves closer towards the Tevbrane. In this, gravity would be much weaker on the Tevbrane than on the Planckbrane. The RS1 model attempts to address

2109-410: The age of our universe, possibly too short for intelligent life to form. On the other hand, a universe with a large positive cosmological constant would expand too fast, preventing galaxy formation. According to Weinberg, domains where the vacuum energy is compatible with life would be comparatively rare. Using this argument, Weinberg predicted that the cosmological constant would have a value of less than

2166-405: The constant in 1917 to counterbalance the effect of gravity and achieve a static universe , which was then assumed. Einstein's cosmological constant was abandoned after Edwin Hubble confirmed that the universe was expanding. From the 1930s until the late 1990s, most physicists agreed with Einstein's choice of setting the cosmological constant to zero. That changed with the discovery in 1998 that

2223-402: The cosmological constant Λ , but actual calculations give rise to an enormous vacuum energy. The discrepancy between theorized vacuum energy from quantum field theory and observed vacuum energy from cosmology is a source of major contention, with the values predicted exceeding observation by some 120 orders of magnitude, a discrepancy that has been called "the worst theoretical prediction in

2280-467: The cosmological constant as a term in his field equations for general relativity because he was dissatisfied that otherwise his equations did not allow for a static universe : gravity would cause a universe that was initially non-expanding to contract. To counteract this possibility, Einstein added the cosmological constant. However, Einstein was not happy about adding this cosmological term. He later stated that "Since I introduced this term, I had always

2337-473: The cosmological constant is in most respects the simplest solution . Thus, the Lambda-CDM model, the current standard model of cosmology which uses the FLRW metric, includes the cosmological constant, which is measured to be on the order of 10  m . It may be expressed as 10  s (multiplying by c ≈ 10  m ⋅s ) or as 10   ℓ P (where ℓ P is the Planck length). The value

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2394-413: The energy of the universe due to the cosmological constant, i.e., what we would intuitively call the fraction of the universe that is made up of dark energy. Note that this value changes over time: The critical density changes with cosmological time but the energy density due to the cosmological constant remains unchanged throughout the history of the universe, because the amount of dark energy increases as

2451-476: The history of physics!". This issue is called the cosmological constant problem and it is one of the greatest mysteries in science with many physicists believing that "the vacuum holds the key to a full understanding of nature". The cosmological constant was originally introduced in Einstein's 1917 paper entitled “ The cosmological considerations in the General Theory of Reality ”. Einstein included

2508-472: The most promising theoretical physicists of her generation". In 2007, Randall was named one of Time magazine 's 100 Most Influential People ( Time 100 ) under the section for "Scientists & Thinkers". Randall was given this honor for her work regarding the evidence of a higher dimension. Other honors: In an interview she was asked whether she believes in God, she said: Randall's sister, Dana Randall ,

2565-971: The name "cosmological constant". The dimension of Λ is generally understood as length . Using the values known in 2018 and Planck units for Ω Λ = 0.6889 ± 0.0056 and the Hubble constant H 0 = 67.66 ± 0.42 (km/s)/Mpc = (2.192 7664 ± 0.0136) × 10  s , Λ has the value of Λ = 3 ( H 0 c ) 2 Ω Λ = 1.1056 × 10 − 52   m − 2 = 2.888 × 10 − 122 l P − 2 {\displaystyle {\begin{aligned}\Lambda =3\,\left({\frac {\,H_{0}\,}{c}}\right)^{2}\Omega _{\Lambda }&=1.1056\times 10^{-52}\ {\text{m}}^{-2}\\&=2.888\times 10^{-122}\,l_{\text{P}}^{-2}\end{aligned}}} where l P {\textstyle l_{\text{P}}}

2622-539: The planet. She answered that it was "not even conceivable unless space and gravity are very different from what we thought." Randall wrote the libretto of the opera Hypermusic Prologue: A Projective Opera in Seven Planes on the invitation of the composer, Hèctor Parra , who was inspired by her book Warped Passages . Randall is a member of the American Academy of Arts and Sciences (2004) and

2679-477: The ratio between the energy density due to the cosmological constant and the critical density of the universe, the tipping point for a sufficient density to stop the universe from expanding forever. This ratio is usually denoted by Ω Λ and is estimated to be 0.6889 ± 0.0056 , according to results published by the Planck Collaboration in 2018. In a flat universe, Ω Λ is the fraction of

2736-510: The region between 1.75 TeV and 1.85 TeV. Currently, the most stringent limits on RS graviton production. Lisa Randall Lisa Randall HonFInstP (born June 18, 1962) is an American theoretical physicist and Frank B. Baird, Jr. Professor of Science at Harvard University . Her research includes the fundamental forces of nature and dimensions of space. She studies the Standard Model , supersymmetry , possible solutions to

2793-401: The study of a wide variety of models, the most recent involving dimensions . She has also worked on supersymmetry , Standard Model observables, cosmological inflation , baryogenesis , grand unified theories , and general relativity . After her graduate work at Harvard, Randall held professorships at MIT and Princeton University before returning to Harvard in 2001. Professor Randall

2850-467: The supernova observation to support such deceleration hypothesis. But soon they found that supernovas were flying away in an accelerating manner. In 1998, both teams announced this surprising result. It implied the universe is under accelerating expansion. The cosmological constant is needed to explain such acceleration. After this discovery, the cosmological constant was put back to the equation of general relativity. The cosmological constant Λ appears in

2907-419: The two models, called RS1 , has a finite size for the extra dimension with two branes, one at each end. The second, RS2 , is similar to the first, but one brane has been placed infinitely far away, so that there is only one brane left in the model. The model is a braneworld theory developed while trying to solve the hierarchy problem of the Standard Model . It involves a finite five-dimensional bulk that

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2964-469: The universe appears to be expanding; this was consistent with a cosmological solution to the original general relativity equations that had been found by the mathematician Alexander Friedmann , working on the Einstein equations of general relativity. Einstein reportedly referred to his failure to accept the validation of his equations—when they had predicted the expansion of the universe in theory, before it

3021-420: The universe grows but the amount of matter does not. Another ratio that is used by scientists is the equation of state , usually denoted w , which is the ratio of pressure that dark energy puts on the universe to the energy per unit volume. This ratio is w = −1 for the cosmological constant used in the Einstein equations; alternative time-varying forms of vacuum energy such as quintessence generally use

3078-474: The universes that is compatible with some form of intelligent life. Critics claim that these theories, when used as an explanation for fine-tuning, commit the inverse gambler's fallacy . In 1995, Weinberg's argument was refined by Alexander Vilenkin to predict a value for the cosmological constant that was only ten times the matter density, i.e. about three times the current value since determined. An attempt to directly observe and relate quanta or fields like

3135-411: The vacuum energy is (even in part) the potential of a scalar field such as the residual inflaton (also see Quintessence ). Another theoretical approach that deals with the issue is that of multiverse theories, which predict a large number of "parallel" universes with different laws of physics and/or values of fundamental constants. Again, the anthropic principle states that we can only live in one of

3192-408: Was demonstrated in observation of the cosmological redshift —as his "biggest blunder" (according to George Gamow ). It transpired that adding the cosmological constant to Einstein's equations does not lead to a static universe at equilibrium because the equilibrium is unstable: if the universe expands slightly, then the expansion releases vacuum energy , which causes yet more expansion. Likewise,

3249-580: Was the first tenured woman in the Princeton physics department and the first tenured female theoretical physicist at Harvard. ( Melissa Franklin was the first tenured woman in the Harvard physics department.) Randall's books Warped Passages: Unraveling the Mysteries of the Universe's Hidden Dimensions and Knocking on Heaven’s Door: How Physics and Scientific Thinking Illuminate the Universe and

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