Cosmological Constant

  1. What is the current thinking as to the value of the cosmological constant
    given the most recent observations of the universe expansion?
     
  2. jcsd
  3. jmcmurtry wrote:
    >
    > What is the current thinking as to the value of the cosmological constant
    > given the most recent observations of the universe expansion?


    AIP Conf. Proc. 586 316 (2001)
    2.036x10^(-35)/sec^2
    Int. J. Theoret. Phys. 41(1) 131 (2002)
    1.934x10^-35/sec^2
    http://www.qc.fraunhofer.de/qg/lambda
    http://arxiv.org/abs/gr-qc/0609004
    Note length not time units for lambda

    The Lambda-CDM model includes the cosmological constant measured to be
    on the order of 10^(-35)/sec^2, or 10^(-47) GeV^4, or 10^(-29) g/cm^3,
    or about 10^(-120) in reduced Planck units, below.

    http://en.wikipedia.org/wiki/Lambda-CDM_model
    http://super.colorado.edu/~michaele/Lambda/obs.html
    bottom, through 1999
    Mod. Phys. Lett. A 18(08) 561 (2003)

    The conventionally defined cosmological constant "lambda" is
    proportional to the vacuum energy density "rho",

    (lambda) = [8(pi)G/3c^2](rho)

    "rho", less than 10^(-25) kg/m^3, is proportional to the density
    parameter "omega,"

    (omega) = [8(pi)G/3H^2c^2](rho)

    H is the Hubble constant, measured to be 70(+/-)2 km/sec-megaparsec as
    of January 2007.

    Omega breaks down to contributions from matter (omega)_m and the
    vacuum omega)_(lambda).

    (omega)_(lambda) - (omega)_m is between -0.1 and +0.8.

    If one allows zero point fluctuations of the vacuum, 1/2
    photon/allowed EM mode to the Planck energy,

    (rho)_vacuum ~ 10^92 erg/cm^3
    (omega)_(lambda) ~ 10^120

    Even theorists are embarrassed to disappear an omega that big to
    exactly obtain the necessary fractional residue.

    --
    Uncle Al
    http://www.mazepath.com/uncleal/
    (Toxic URL! Unsafe for children and most mammals)
    http://www.mazepath.com/uncleal/lajos.htm#a2
     
  4. On May 2, 4:32 pm, Uncle Al <Uncle...@hate.spam.net> wrote:
    > If one allows zero point fluctuations of the vacuum, 1/2
    > photon/allowed EM mode to the Planck energy,
    >
    > (rho)_vacuum ~ 10^92 erg/cm^3
    > (omega)_(lambda) ~ 10^120
    >
    > Even theorists are embarrassed to disappear an omega that big to
    > exactly obtain the necessary fractional residue.


    It need not be anything more than a self-constitency principle that
    restricts what the actual spectrum of fermions and bosons must be. In
    that case, this goes from a liability to a major asset.

    Finiteness for a total ZPE can be obtained if
    sum_b m_b^n = sum_f m_f^n
    over all boson modes (b) and fermion modes (f), for n = 0 , 2, 4;
    where m_b or m_f is the mass associated with the respective mode.
    Making it small requires further constraining the respective mass
    spectra.

    If you explain away mass as a dynamic effect of the Higgs, then this
    becomes a constraint on the couplings of the fermions and bosons to
    the Higgs.

    The cosmological constant already arises from non-Abelian Yang-Mills
    fields through the contribution
    Lambda = 1/4 sum f^{abc} f_{abc}
    where the structure constants f_{ab}^c are with indices raised and
    lowered by the gauge group metric k_{ab}.

    In a U(1) theory, k_{ab} is just (epsilon_0 c), the vacuum
    permittivity. If you assume k is constant, then the scale of the
    Lambda contribution becomes fixed, and you're in the middle of the
    "fine tuning problem".

    If, on the other hand, k is variable; then this contribution can vary
    and become asymptotically small or zero. The fine-tuning issue is
    potentially evaded. Moreover, you also acquire extra contributions to
    the Lagrangian involving the gradient of k -- "dark energy" terms.
    Since you're lowering 2 indices, and raising only one, Lambda then
    scales proportionally with k.

    The k metric components are equivalent to the Jordan-Brans-Dicke
    scalars; and also to dilatons (the dilaton is equivalent to the
    logarithm of the determinant of the k metric). In terms of the Maxwell
    U(1) field, k is just the dielectric coefficient of the vacuum; so
    that the extra terms are none other than the representation of the
    dielectric energy stored in the vacuum(!) I.e., a vindication of
    Maxwell's notion of a universal dielectric medium.

    Some (or maybe even most) quintessence models use Jordan-Brans-Dicke
    scalars (or scalar-tensor-matter) as their basis. If you want to
    revert this back to the Kaluza-Klein representation k = g_{55} or k =
    (g_{ab};a,b=5,6,...), a confirmation of a link between the
    cosmological constant and vacuum energy to the extra terms arising the
    gauge group's metric would represent an indirect confirmation of the
    geometric interpretation of the gauge fields as extra-dimensional
    gravity; and of the general notion of physical extra dimensions.

    The effective Lagrangians mentioned above are those which come out of
    the total metric
    h_{mn} = e^{2U} g_{mn} + k_{ab} A^a_m A^b_n
    h_{mb} = k_{ab} A^a_m
    h_{an} = k_{ab} A^b_n
    h_{ab} = k_{ab}
    where different choices of U can be used to define what the effective
    "base space" metric is. The choice e^{2U} = k^{-1/2} for a 4-D base
    space gives you an Einstein-Hilbert Lagrangian of the form root(|h|)
    R_h = root(|g|) R_g + ... Otherwise, you get a power of k out in front
    for the leading term (which is sometimes used to model a variable G).
     
  5. In article <ZsvZh.1996$KP1.1795@trnddc02>, jmcmurtry <nospam@alo.com>
    writes:

    > What is the current thinking as to the value of the cosmological constant
    > given the most recent observations of the universe expansion?


    It has the observed value. Prior to having measured a value
    observationally, various pundits put forward (conflicting) arguments as
    to why it had to have a particular value (such as very near 0).

    Or do you mean thinking as to why it has the value it does? It would
    have been interesting if someone had predicted the value beforehand, but
    no-one did, thus lending credence to the idea that none of the
    predictions was really worth considering in the first place. I wouldn't
    be surprised if the weak anthropic principle comes out as the best
    explanation.

    Of course, as Martin Rees has pointed out, the recent obsession with the
    values of the cosmological parameters (i.e. not just measuring them, but
    deriving them from more fundamental arguments) might go the same way
    Kepler's obsession with the planetary orbital radii went, i.e. it turned
    out they were just due to chance, anthropic arguments (in the case of
    the Earth) and some simple physics (orbital resonances) and don't have
    any "deeper" meaning.
     
  6. On May 4, 4:27 pm, hel...@astro.multiCLOTHESvax.de (Phillip Helbig---
    remove CLOTHES to reply) wrote:
    > might go the same way
    > Kepler's obsession with the planetary orbital radii went, i.e. it turned
    > out they were just due to chance


    The jury's still out on that. Complex dynamics can entail regularities
    not easily seen or predicted from the fundamental laws. This is
    already observed, for instance, in the patterns seen in Saturn's
    rings; the various resonances seen between orbits and/or rotation
    periods of the celestial bodies; etc.

    It may simply be the case that a (quasi-)stable long-term requires or
    exists only as you approach certain configurations, such as that
    approximated by Bode's Law.
     
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