الثابت الكوني

Sketch of the timeline of the Universe in the ΛCDM model. The accelerated expansion in the last third of the timeline represents the dark-energy dominated era.

في علم الكون، الثابت الكوني cosmological constant (يرمز له غالبا بالرمز لامبدا: Λ) هو ثابت فيزيائي وضعه العالم ألبرت آينشتاين حتي تتفق معادلاته مع مفهوم أن الكون ثابت و ساكن غير متمدد، و هو ما ثبت خطؤه وألغى أينشتاين هذا الثابت فيما بعد. Much later it was revived and reinterpreted as the energy density of space, or vacuum energy, that arises in quantum mechanics. It is closely associated with the concept of dark energy.

Einstein originally introduced the constant in 1917 to counterbalance the effect of gravity and achieve a static universe, a notion that was the accepted view at the time. Einstein's cosmological constant was abandoned after Edwin Hubble's confirmation 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 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 so-called dark energy. The cosmological constant Λ is the simplest possible explanation for dark energy, and is used in the current standard model of cosmology known as 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 present everywhere in space. These zero-point fluctuations should act as a contribution to the cosmological constant Λ, but when calculations are performed, these fluctuations 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 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".

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 التاريخ

Einstein included 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, soon after Einstein developed his static theory, observations by Edwin Hubble indicated that 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 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 was demonstrated in observation of the cosmological redshift—as his "biggest blunder".

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, 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 a cosmological constant on theoretical grounds or found that it arose naturally from the mathematics. For example, Sir Arthur Stanley 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 a cosmological term.

 تسلسل الأحداث 1915–1998

• In 1915, Einstein publishes his equations of general relativity, without a cosmological constant Λ.
• In 1917, Einstein adds the parameter Λ to his equations when he realizes that his theory implies a dynamic universe for which space is function of time. He then gives this constant a value that makes his Universe model remain static and eternal (Einstein static universe).
• In 1922, the Russian physicist Alexander Friedmann mathematically shows that Einstein's equations (whatever Λ) remain valid in a dynamic universe.
• In 1927, the Belgian astrophysicist Georges Lemaître shows that the Universe is expanding by combining general relativity with astronomical observations, those of Hubble in particular.
• In 1931, Einstein accepts the theory of an expanding universe and proposes, in 1932 with the Dutch physicist and astronomer Willem de Sitter, a model of a continuously expanding Universe with zero cosmological constant (Einstein–de Sitter spacetime).
• In 1998, two teams of astrophysicists, one led by Saul Perlmutter, the other led by Brian Schmidt and Adam Riess, carried out measurements on distant supernovae which showed that the speed of galaxies' recession in relation to the Milky Way increases over time. The universe is in accelerated expansion, which requires having a strictly positive Λ. The universe would contain a mysterious dark energy producing a repulsive force that counterbalances the gravitational braking produced by the matter contained in the universe (see Standard cosmological model).

For this work, Perlmutter, Schmidt, and Riess jointly received the Nobel Prize in physics in 2011.

 المعادلة

Estimated ratios of dark matter and dark energy (which may be the cosmological constant) in the universe. According to current theories of physics, dark energy now dominates as the largest source of energy of the universe, in contrast to earlier epochs when it was insignificant.

يظهر الثابت الكوني Λ في معادلات المجال لأينشتاين بهذا الشكل:

$R_{\mu \nu }-{\textstyle 1 \over 2}R\,g_{\mu \nu }+\Lambda \,g_{\mu \nu }={8\pi G \over c^{4}}T_{\mu \nu }$

حيثR وg يتلائم مع بنية زمكان, T يتلائم مع المادة والطاقة, وG وc هي معاملات تحويل المستخدمة في القياسات التقليدية. عندما Λ تكون بصفر يمكن اختصار المعادلة إلى معادلة المجال للنسبية العامة. عندما تكون T مساوية للصفر فإن معادلة المجال تصف الفضاء الخالي (الفراغ).

 اوميجا لامبدا

تناسب يستخدمه علماء الكون (النسبة بين كثافة الطاقة بسبب الثابت الكوني والكثافة الحرجة للكون) ويرمز له بـ:$\Omega _{\Lambda }$.

 معادلة الحالة

تناسب آخر يستخدمه العلماء, عبارة عن نسبة الضغط على الكون (بفعل طاقة الظلام) إلى الطاقة لوحدة الحجوم.

 التوقعات

  Quantum field theory

انظر أيضاً: Cosmological constant problem

مسألة غير محلولة في physics:

Why does the zero-point energy of the quantum vacuum not cause a large cosmological constant? What cancels it out?

(المزيد من المسائل غير المحلولة في physics)

A major outstanding problem is that most quantum field theories predict a huge value for 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 a cosmological constant of the order of $M_{\rm {pl}}^{2}$ ($1$ in reduced Planck units). As noted above, the measured cosmological constant is smaller than this by a factor of ~10¹²⁰. This discrepancy has been called "the worst theoretical prediction in the history of physics".

Some supersymmetric theories require 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 a group of four physicists advanced a controversial conjecture which would imply that no such universe exists.

 Anthropic principle

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 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 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 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, 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 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.

 Failure to detect dark energy

An attempt to directly observe fields related by the chameleon or the symmetron theories to dark energy in a laboratory 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 is due to the fact that the cosmological constant describes an existing, known interaction (e.g. electromagnetic field).

 اقرأ أيضا

• النظرية النسبية العامة
• Big Rip
• Higgs mechanism
• Lambdavacuum solution
• Naturalness (physics)
• Quantum electrodynamics
• de Sitter invariant special relativity
• Unruh effect

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 للاستزادة

• Michael, E., University of Colorado, Department of Astrophysical and Planetary Sciences, "The Cosmological Constant"
• Ferguson, Kitty (1991). Stephen Hawking: Quest For A Theory of Everything, Franklin Watts. ISBN 0-553-29895-X.
• John D. Barrow and John K. Webb (June 2005). "Inconstant Constants". Scientific American.

 وصلات خارجية

• Michael, E., University of Colorado, Department of Astrophysical and Planetary Sciences, "The Cosmological Constant"
• Carroll, Sean M., "The Cosmological Constant" (short), "The Cosmological Constant"(extended).
• News story: More evidence for dark energy being the cosmological constant
• Cosmological constant article from Scholarpedia
• Copeland, Ed; Merrifield, Mike. "Λ – Cosmological Constant". Sixty Symbols. Brady Haran for the University of Nottingham.