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Swiss cheese expansion

  1. Aug 12, 2008 #1


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    arXiv:0808.1080 (cross-list from astro-ph) [ps, pdf, other]
    Title: Luminosity distance in "Swiss cheese" cosmology with randomized voids: I. Single void size
    Authors: R. Ali Vanderveld, Eanna E. Flanagan, Ira Wasserman
    Comments: 6 pages, 2 figures, revtex4
    Subjects: Astrophysics (astro-ph); General Relativity and Quantum Cosmology (gr-qc)

    Recently there have been suggestions that the Type Ia supernova data can be explained using only general relativity and cold dark matter with no dark energy. In "Swiss cheese" models of the Universe, the standard Friedmann-Robertson-Walker picture is modified by the introduction of mass compensating spherical inhomogeneities, typically described by the Lemaitre-Tolman-Bondi metric. If these inhomogeneities correspond to underdense cores surrounded by mass-compensating overdense shells, then they can modify the luminosity distance-redshift relation in a way that can mimic accelerated expansion. It has been argued that this effect could be large enough to explain the supernova data without introducing dark energy or modified gravity. We show that the large apparent acceleration seen in some models can be explained in terms of standard weak field gravitational lensing together with insufficient randomization of void locations. The underdense regions focus the light less than the homogeneous background, thus dimming supernovae in a way that can mimic the effects of acceleration. With insufficient randomization of the spatial location of the voids and of the lines of sight, coherent defocusing can lead to anomalously large demagnification effects. We show that a proper randomization of the voids and lines of sight reduces the effect to the point that it can no longer explain the supernova data.

    I only understand the general idea of this but some will be more able to understand it.
  2. jcsd
  3. Aug 12, 2008 #2
    It sounds similar to the ideas of David Wiltshire who claimed that the ”lumpiness” of the universe can explain the observations of cosmology without requiring dark energy. He used equations developed by Thomas Buchert that are designed to cope with the complication of assuming a inhomogeneous universe. to calculate how time varies in voids compared to denser areas of the universe. A diagram in New Scientist illustrates Wiltshire’s idea with an embedding diagram showing light paths from supernovae travelling in meandering paths across the topology rather than in straight lines as is assumed in calculations based on a homogenous universe. Wiltshire describes the effect in terms of time dilation and clocks running faster in voids although the magnitude of the time effect he is claiming to explain the accelerating expansion as an apparent effect seems rather large. As far as I can tell from the sources I have looked at, Wiltshire does not really explain how his idea affects angular distance versus luminosity distance which is an important quantity used in estimating supernova distances or how his idea affects CMB calculations.

    I note Vanderveld is basically dismissing the swiss cheese model as an alternative explanation to dark energy.
    Last edited: Aug 12, 2008
  4. Aug 12, 2008 #3
    Hi Kev and Wolram,
    Good article. One more theoretical alternative to dark energy is apparently put to rest.

    I'm not an advocate of Wiltshire, but I think it's fair to say that Wiltshire's theory does not depend on inhomogeneous lensing of photons passing through voids enroute; as you say it depends primarily on clocks running much faster in voids.

  5. Aug 12, 2008 #4
    I was just making the observation that both the "Swiss cheese" and Wiltshire ideas claim that acceleration can be explained by the large scale structures of the universe making the universe a lot different from the homogenous models that are usually assumed in cosmology. It certainly makes the calculations a lot more difficult. The inhomogenuity might alternatively explain the large scatter in surpernova data away from the "best fit" standard model curve and might make it necessary to obtain a lot more supernova data at high red shifts to come to any definite conclusions that are statistically valid. It might also be relevnt to why supernova data is in such poor concordance with data from other sources such as CMP and cluster data which is at yet unexplained.
  6. Aug 12, 2008 #5
    Hi Kev,

    Sorry, I was nitpicking.

  7. Aug 12, 2008 #6


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    Not sure where you are coming from, kev. Can you clarify how CMB and cluster data is discordant with supernova data? The Perlmutter study is pretty convincing, IMO.
  8. Aug 13, 2008 #7
    Hi Chronos,

    Have a look at the attached image which shows how the concordance diagrams should look if the supernova data really was in accordance with the the other data and contrast my diagram with the concordance diagrams using http://www.astro.ucla.edu/~wright/triptych-SNe-CMB-BO-H0-75.gif" [Broken]

    The centre of the supernova error ellipses should coincide with where the other data cross over, but in order to do that I have had to artificially adjust the supernova data in the left diagram to agree with other data if Omega(total) is assumed to be about 1.02

    In the right hand diagram I have had to move all the other datasets to coincide with the supernova data which by itself suggests Omega(total) is about 1.30. That also requires adjusting the Hubble parameter in the second diagram to about 60 which is indicated by the vertical blue line. The vertical line also represents Omega(mass) and that is sometimes estimated from cluster data and includes normal matter and dark matter. Omega(mass) has had to be adjusted to about 0.4 to agree with the supernova data which differs from the value of under 0.3 for the standard LCDM model. The CMB line has had to be moved considerably too. The slightly tilted magenta lines represents data from Baryon Acoustic Oscillations. The supernova data also suggests lambda is about 0.9 which is significantly larger than the value of about 0.7 stated for the standard LCDM model.

    Also have a look at this http://www.astro.ucla.edu/~wright/dDM-vs-z-Union-2008-75.gif" [Broken] diagram by Ned .The binned supernova data at about Z=1.15 is so far off the best fit lines that even the error bar does not come anywhere near the model lines. The solid magenta curve which represents the flat dark energy model (which is pretty much the standard LCDM model) depends on the binned supernova data at about Z=1.6 which has a huge error bar. If the binned supernova data at Z=1.6 is ignored then the dashed magenta line is the better fit and this is the line Ned calls the "Closed Dark Energy Model". Although Ned does not state what value of Omega(total) he is using for the closed model it looks more like the figure of 1.3 that I mentioned earlier than the standard figure of about 1.02 +/- 0.2 or even 1.01 +/- 0.1 that is often quoted.

    The next Ned diagram shows http://www.astro.ucla.edu/~wright/dDM-vs-z-29Dec06.gif" [Broken] The best fit dark energy closed model for the supernova data is a long way of the best fit flat model for the GRB data. There is also a large deviation of the flat model from the GRB data at Z<1.0 so again it is hard to draw a definitive conclusion. Ned also shows a dashed blue line that suggests an evolving supernova model brings the supernova data into better agreement with the GRB data and the flat model.

    Also note that the first Ned Wright diagram I mentioned earlier (that is located at the bottom of his supernova cosmology webpage) shows Ned's attempts to get the various data sets to agree by adjusting the equation of state parameter (w). He does not succeed in getting the supernova data to exactly agree with the CMB/BOA/Hubble datasets for any value of w. The small green ellipse at the centre of the supernova error ellipses never coincides with the other datasets. It is a pity Ned does not show the GRB data on the concordance diagrams but I would be willing to bet it matches the other 3 datasets much better than the supernova data.

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    Last edited by a moderator: May 3, 2017
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