What is Cosmological constant: Definition and 188 Discussions

In cosmology, the cosmological constant (usually denoted by the Greek capital letter lambda: Λ), alternatively called Einstein's cosmological constant, is the energy density of space, or vacuum energy, that arises in Albert Einstein's field equations of general relativity. It is closely associated to the concept of dark energy.Einstein originally introduced the concept in 1917 to counterbalance the effects of gravity and achieve a static universe, a notion which was the accepted view at the time. Einstein abandoned the concept in 1931 after Hubble's confirmation of the expanding universe. From the 1930s until the late 1990s, most physicists assumed the cosmological constant to be equal to zero. That changed with the surprising discovery in 1998 that the expansion of the universe is accelerating, implying the possibility of a positive nonzero value for the cosmological constant.Since the 1990s, studies have shown that 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 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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  1. G

    I Sign of vacuum energy density

    My head is spinning when it comes to the sign of the vacuum energy density and the cosmological constant. The cosmological term can be put at the left or the right side of Einsteins equation, energy density is not pressure and energy density is not action density. There is a historic theory...
  2. S

    I Avoiding structure collapse due to dark energy?

    I had a question about this paper (https://arxiv.org/abs/1401.3742) There, the authors indicate that dark energy competes against gravity in oversdensities and can slow down or even prevent their collapse. I have a simple question about this: Galaxies will in principle evaporate their outer...
  3. S

    I Dark energy and the kinematic Sunyaev-Zeldovich effect?

    I was reading this interesting article about possible effects of dark energy in the formation of large-scale structures which should have an impact on the Sunyaev-Zeldovich effect ("Dark energy imprints on the kinematic Sunyaev-Zel'dovich signal" (https://arxiv.org/abs/1309.1163))There, the...
  4. D

    I QFT vs GR Cosmological Constant

    I am sorry but I can't seem to find the actual estimated value of the cosmological constant that is predicted by quantum field theory. Can anyone help me and tell me the approximation of that value and/or the value of the approximate observed cosmological constant that physicists today think...
  5. N

    I Einstein's General Relativity w/o Cosmological Constant

    I mean, what's "general relativity but without the cosmological constant term" (##G_{\mu \nu}=\kappa T_{\mu \nu}##) called?
  6. AndreasC

    I Exploring the Cosmological Constant Problem & Zero-Point Energy

    Reading the Wikipedia page on it, one reads: But on the other hand, as far as I know and if I'm not mistaken, zero point energy is not a physical thing, and it is merely a mathematical artifact in QFT. Someone correct me if I'm wrong on that. So if that is the case, then why is it a "problem"...
  7. SH2372 General Relativity - Lecture 10

    SH2372 General Relativity - Lecture 10

    0:00 Cosmological redshift 18:08 Solving the Friedmann equations 34:34 Accelerated expansion and the cosmological constant 56:10 Cosmological inflation
    • Orodruin
    • Media item
    • Accelerated expansion Cosmic inflation Cosmological constant Cosmological redshift Friedmann equations
    • Comments: 0
    • Category: Relativity
  8. Buzz Bloom

    I How does the symbol Λ cosmological constant relate to Ω_Λ or ρ_Λ?

    My references are: https://en.wikipedia.org/wiki/Friedmann_equations#Detailed_derivation https://en.m.wikipedia.org/wiki/Cosmological_constant Ω_Λ is a term in the Friedmann equation along with terms for radiation, mass, and curvature. Λ is the coefficient of the term g_μν in the Einstein field...
  9. D

    I Questions about Negative Pressure and Vacuum Energy

    Currently, dark energy is described as a being that exerts a negative pressure while having a positive energy density. {\rho _\Lambda } + 3{P_\Lambda } = {\rho _\Lambda } + 3( - {\rho _\Lambda }) = - 2{\rho _\Lambda } However, there seems to be a problem with the negative pressure assertion...
  10. S

    I If the Universe had a different size, would physics change?

    I found an article by James Bjorken (https://arxiv.org/abs/hep-th/0210202) which argues that universes with different size would have different physics (like different Standard Model parameters). When applying this reasoning to our own universe, Is this pure conjecture? Or is there some truth...
  11. Safinaz

    I The Units of the Cosmological Constant: eV^2

    In natural units, it’s known that the unit of the cosmological constant is ##eV^2##. I don‘t get why in this paper : https://arxiv.org/pdf/2201.09016.pdf page (1), it says the value of ##\Lambda \sim meV^4##, this means ##\Lambda \sim (10^6 ~ eV)^4 \sim 10^{24} eV^4 ##, shoud not the unit ##eV...
  12. Sciencemaster

    I Adapting Schwarzschild Metric for Nonzero Λ

    So, there are a fair amount of metrics designed with a zero value for the cosmological constant in mind. I was wondering if there was some method to modify metrics to account for a nonzero cosmological constant. Say, for instance, the Schwarzschild metric due to its relative simplicity. A...
  13. K

    I Are two-body orbits with a cosmological constant unstable?

    For background, consider this paper, which describes circular orbits for the two-body problem in the presence of a cosmological constant: https://arxiv.org/abs/1906.05861 What they describe is a system with three regimes of behavior: stable circular orbits below a certain radius, unstable...
  14. N

    A Relationship between energy density and cosmological constant

    According to the wiki entry on Planck units, https://en.wikipedia.org/wiki/Planck_units, the energy density of the universe, 1.8 × 10−123, is 1/16th the cosmological constant, 2.9 × 10−122. Is there a theoretical reason for this precise relationship?
  15. M

    A New string formulae for Higgs mass and cosmological constant

    https://arxiv.org/abs/2106.04622 Calculating the Higgs Mass in String Theory Steven Abel, Keith R. Dienes [Submitted on 8 Jun 2021] There are at least two properties of the Higgs mass one might hope to explain with such a fundamental calculation: its criticality, and its participation in...
  16. J

    B Cosmological constant for the Universe's expansion

    Astronomers1) tell us that a 'cosmological constant' can account for the universe's increasing expansion. Representing the universe by a symbolic expanding ring, Fig.a, at an instantaneous radius r the inward gravitational force varies as the inverse square of this radius, giving Fg ~ 1/r^2...
  17. Ranku

    I Spatial flatness and cosmological constant

    Was the universe always spatially flat due to the presence of the cosmological constant, or has it become flatter in the late-time universe?
  18. Cerenkov

    B How does the cosmological constant affect gravitational collapse?

    https://www.physicsforums.com/threads/what-are-the-best-parameters-for-lcdm.831858/ Hello. In the above linked thread from 2015 Science Advisor Chalnoth replies to Earnest Guest. First, the cosmological constant has been a component of General Relativity pretty much from the start. The way...
  19. I

    A Zero-point Energy Contribution Below the Planck energy cutoff

    Is it possible to determine the amount of zero-point energy contributed by all fields below the Planck energy cutoff?
  20. Arman777

    I Some questions related to the Cosmological Constant

    In Barbara Ryden's introduction to cosmology book its written that "Introducing ##\Lambda## into the Poisson's equation allows the universe to be static, if you set ##\Lambda = 4\pi G\rho##" Then later on, in the book energy density of the ##\Lambda## defined as ##\epsilon_{\Lambda} =...
  21. phyzguy

    A New paper on the cosmological constant

    I'd be interested to hear comments from the forum on this paper. Is it a significant step forward? I haven't been able to make up my mind.
  22. Buzz Bloom

    I Question about the Cosmological Constant

    I am hoping someone can explain to me why the constant Λ has units 1/m2. In the article https://en.wikipedia.org/wiki/Cosmological_constant In the Equations section, the following equation is presented. Do tensors have dimensions? If so, can someone tell me what the dimensions are for these...
  23. Ranku

    I Cosmological constant and structure formation

    How much impact does the presence of the cosmological constant have on the formation of structures in the universe? On a larger scale, is there less structure formation because of the presence of the cosmological constant?
  24. R

    Question About Conservation of Energy, the Cosmological Constant and Dark Energy

    I am confused about the cosmological constant and dark energy. In the most accepted theory, energy is created as the vacuum of space expands. This contravenes the conservation of energy. The law of conservation of energy does not hold in curved spacetime but isn't our universe flat spacetime ...
  25. Ranku

    I Exponential expansion and the Cosmological Constant

    The universe will expand exponentially when dark energy completely dominates the energy density of the universe. To clarify, does that make the present expansion 'quasi-exponential'?
  26. K

    I Cosmological Constant Term in Einstein Equations

    One side of the Einstein Equations with a cosmological constant is ##R_{\mu \nu} - (1/2) Rg_{\mu \nu} + \Lambda g_{\mu \nu}##. Question is, why the cosmological constant term appears with a plus sign and without a factor of 1/2 in front of it? I guess it may be because ##\Lambda## is (in...
  27. M

    I Uniqueness theorems for black holes

    I am under the impression, there is no unique solutions to Einstein's field equations for a cosmological constant, or for higher dimensional spacetimes. Has anybody got a counter example for a solution including the cosmo constant to show there are multiple solutions, for example, i know of the...
  28. Demystifier

    A Negative cosmological constant from string theory

    Allegedly, string theory (in it's simplest form) predicts that cosmological constant must be negative (or zero). Can someone explain where does this result come from? A reference would also be welcome.
  29. Cycklops

    B Einstein's Cosmological Constant: Push or Pull?

    Was watching some documentaries and got confused about something. People say that Einstein unintentionally predicted that the universe was expanding, and that he inserted the cosmological constant to represent a force pulling it back in. But other sources seem to imply that the universe was...
  30. F

    A Time-Varying Cosmological Constant Implications in GR

    Hi, I want to be sure i understand correctly the implications of problem 2 in: http://universeinproblems.com/index.php/Time-dependent_Cosmological_Constant "when G is constant, Lambda is also a constant if and only if the ordinary energy-momentum tensor Tμν is also conserved " As far as i...
  31. K

    A Dark energy = cosmological constant, any problems with that?

    So I recently had a conversation with a mathematician friend of mine who studies Einstein's equations, and he asked me this: Why do physicists call it "dark energy"? It isn't like the dark matter problem, where there is almost certainly some massive "stuff" out there gravitationally influencing...
  32. E

    I Cosmological constant problem

    For instance, in introduction in https://www.sciencedirect.com/science/article/pii/S0550321314001400 we can find that vacuum energy is proportional to ##k_{max}^4## where it is written that "If we believe the general relativity up to the Planck scale ##k_{max}=10^{19}GeV##" And so the...
  33. A

    I Exploring the Effects of Dark Energy on Extremely Large Black Holes

    Ordinarily a black hole’s Schwarzschild radius is linearly proportional to its mass. However, wouldn’t there be a deviation from this rule for extremely large black holes? Suppose we assume dark energy is due to a cosmological constant, whose value is the same everywhere (including inside the...
  34. Arman777

    I Deriving the Cosmological Constant

    I am trying to find a paper which explains the derivation of the Cosmological Constant. I looked several books and sources and it only says " The cosmological constant ##Λ## appears in the Friedmann equation as an extra term" or etc. Sometimes It directly puts it in the Friedmann Equation which...
  35. J

    I Are the energy fluctuations in space real or virtual?

    Heisenberg's uncertainty relation says: $$\Delta x \Delta p \ge \hbar$$ If we assume a massless quantum object then we have the relationship ##\Delta E = c\Delta p## so that the above uncertainty relationship becomes $$\Delta E \ge \frac{\hbar c}{\Delta x}.\tag{1}$$ I understand that if we have...
  36. Ranku

    I Cosmological constant and rate of expansion of the universe

    Does the presence of the cosmological constant modify the rate of expansion of the universe even during the earlier deceleratingly expanding phase of the universe?
  37. redtree

    I Metric for Lambdavacuum EFE - Radial Coordinates

    I am having trouble finding the equation for the metric for the Lambdavacuum solution to the EFE in radial coordinates. Any suggestions?
  38. ohwilleke

    I Is suppressed gravitational pull a possible explanation for dark energy?

    One way to get the universe to expand is with dark energy that pulls at the matter of the galaxy separating it or equivalently for space-time to not be perfectly flat. An alternative, in principle, would be for the gravitational pull between objects like galaxies and galactic clusters to be...
  39. A

    A Cosmological constant in the semiclassical limit of quantum gravity

    Why is it the case that, in a semiclassical description of the Einstein-Hilbert action, the cosmological constant is small in Planck units? Why does this mean that $$\ell \gg G$$ for ##\Lambda = - 1/\ell^{2}##?
  40. U

    I Cosmological constant estimation in QFT

    My question is about the interpretation of the large estimated value. In QM we are supposed to think in terms of measurement results and not of ontological properties. So, if QFT predicts a large vacuum energy what is the correct approach? 1. The predicted value is the result you get if you...
  41. Demystifier

    A Why isn't cosmological constant a mass of the graviton?

    The Lagrangian density for cosmological constant is $${\cal L} = \sqrt{g}\Lambda$$ Let us write, schematically, $$g=\eta+h$$ where ##\eta## is the flat Minkowski metric and ##h## is the spin-2 field. Expanding the square root for small ##h## we get something like $${\cal L} = \Lambda + h\Lambda...
  42. W

    I Cosmological constant problem, interesting solution?

    Som news outlets are reporting a potential solution to the cosmological constant problem: https://arxiv.org/pdf/1703.00543.pdf opinions on this paper are much appreciated.
  43. resurgance2001

    I Discover the Latest Cosmological Parameters for the CDM Lambda Concordance Model

    Cosmological paramaters in the cold dark matter Lamda concordance model. I have been trying to find the most uptodate values for Ho , Ohmega m and Ohmega Lamgad I was wondering if anyone knows where I might find the most reliably, widely accepted values for these values that are currently...
  44. Bolhuso

    I Where did the Dark Energy (or similar mechanism) come from?

    Hi all! I'm new to this forum and, as a matter of fact I only recently rediscovered my interest for physics. I am starting to catch up, yet I find that Wikipedia sometimes falls sort for some basic questions, and I was hopping that this community could gently help me understand some concepts...
  45. wolram

    B Cosmological constant vis-a-vis dynamical vacuum: bold challenging the ΛCDM

    I have read this paper, but i do not understand the consequences in the broadest sense.arXiv:1612.02449 [pdf, ps, other] Cosmological constant vis-a-vis dynamical vacuum: bold challenging the ΛCDM Joan Sola Comments: 31 pages, 2 tables, 9 figures. arXiv admin note: text overlap with...
  46. K

    I Scale of a in MOND and cosmological constant

    in 2 recent papers by Lee Smolin and Erik Verlinde it is claimed that the scale of acceleration as required by various MOND theories is on the same order as the cosmological constant both researchers suggest that instead of cold dark matter, or even modified Newtonian dynamics, MOND-like...
  47. C

    B Can Cosmological Constant contract (negative)?

    Hello... Can the cosmological constant become so rigid as to resist the 120 magnitude quantum contribution? Where is the mathematical terms for it in GR EFEs? is the effect like contraction instead of expansion? Because the 120 magnitude quantum contribution should immediately warp spacetime...
  48. J

    I Cosmological Constant Problem: Pre-Req Knowledge for Paper

    My professor wants to give me (and another kid) a problem in quantum cosmology. To that end, he asked me to read through his recent paper that appeared in the Physical Review Letters. He said that I should be able to go through it since all the paper employs is (quantum) scalar field theory...
  49. stevendaryl

    I Question about cosmological constant

    Einstein's field equations, with cosmological constant, can be written as: G_{\mu \nu} + \Lambda g_{\mu \nu} = \kappa T_{\mu \nu} I understand that some physicists think that the cosmological constant, rather than being a free parameter, might instead be an effect of quantum field theory. Does...
  50. mertcan

    I Cosmological Constant: Expanding Universe & Data Contradiction

    hi, I have been watching some "world science festival" videos on youtube, also there were a conversation pertain to whether or not the cosmological constant should be a constant. As far as I know, our universe is expanding with a positive acceleration measuring the red shifts, and it implies...
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