This plot shows the confidence areas for the Hubble constant (h) and the matter density parameter (Ωm), obtained from the Planck experiment on the one hand (black contours), and from the Hubble diagram on the other hand (colored areas). The green area, obtained by interpreting the Hubble diagram using a very clumpy Swiss-cheese model, is clearly in better agreement with Planck than the blue area, obtained with the standard FL interpretation. Credit: Fleury, et al. ©2013 American Physical Society

(Phys.org) —In Jonathan Swift's 1726 book "Travels into Several Remote Nations of the World. In Four Parts," the miniature Lilliputians experience the world very differently from the giant Brobdingnagians.

Because they see the world on different scales, the two types of creatures use maps with different resolutions. Using this analogy, physicists from France have proposed that we need maps of the Universe with different resolutions depending on the resolution of our experiments. The physicists show that using an alternative "map" (or model) to interpret the Hubble diagram—which is based on high-resolution supernova observations—produces results that more closely match the results from low-resolution cosmic microwave background (CMB) observations than when using a traditional model.

The physicists, Pierre Fleury, Hélѐne Dupuy, and Jean-Philippe Uzan, at the Institut d'Astrophysique de Paris (CNRS) and the Institut de Physique Théorique (CEA), have published a paper on interpreting cosmological observations with different models in a recent issue of Physical Review Letters.

"Our work emphasizes the model-dependence of the interpretation of cosmological observations, by showing explicitly the impact of taking the small-scale inhomogeneity of our Universe into account," Fleury told Phys.org. "Thus, we may need to refine our standard cosmological model in order to consistently interpret all the current high-accuracy observations together."

In their work, the scientists were confronting a problem from a recent analysis of the results from the Planck experiment. Two areas that the Planck experiment is investigating are the average density of matter in the Universe and the speed at which galaxies are receding due to the expansion of the Universe. These areas are measured by the matter density parameter and the Hubble parameter, respectively. Knowing accurate values of these parameters will enable scientists to better understand the composition and fate of the Universe, among other things.

However, the problem is that the Hubble diagram and the CMB produce slightly different best fits for the values of the matter density parameter and Hubble parameter, and they cannot both be correct. Currently, both the supernova experiments used to construct the Hubble diagram and the CMB experiments are interpreted using the same "map" to describe the Universe, which is the Friedmann-Lemaître (FL) geometry. The FL geometry describes the Universe as homogeneous and isotropic, in strict accordance with the cosmological principle.

Fleury, Dupuy, and Uzan wondered if perhaps the FL geometry is too simple to accurately interpret the supernova observations. Noting that the supernova experiments involve light beams with a much smaller angular size than the light beams involved by the CMB experiments, the physicists investigated what would happen if they interpreted the supernova observations using a model that describes the Universe as clumpier.

So the physicists turned to a model proposed by Einstein and Straus in 1945 called the Swiss-cheese model. In this model, clumps of matter (that model galaxies, for example), each lying at the center of a spherical void, are embedded in an otherwise homogeneous FL spacetime.

Compared to a strictly homogeneous universe, the Swiss-cheese model is characterized by the size of the voids and the fraction of the remaining FL regions. The traditional FL geometry is the extreme instance of the Swiss-cheese model with no voids. On the other end of the spectrum is the case where matter is exclusively in the form of clumps inside voids.

Interpreting the supernova observations with a Swiss-cheese model gives different results because the inhomogeneity of the distribution of matter causes gravitational lensing. Since the light traveling from the supernovae to Earth rarely cross clumps of matter, it essentially experiences an underdense universe; consequently, the light beams are defocused—the supernovae appears fainter, that is, farther—compared to the case in which light would travel through a strictly homogeneous universe.

The physicists' calculations revealed that, using a very clumpy Swiss-cheese model to interpret the Hubble diagram can shift the best fit values of the matter density parameter—but not the Hubble parameter—to be in much closer agreement with the values obtained from the CMB observations.

Why is there still disagreement on the Hubble parameter? The physicists explain that supernova observations alone cannot fully constrain the Hubble diagram, since other factors also play a role.

Alleviating the tension between the best fits for the Hubble parameter remains an open problem.

One speculative possibility is that our local environment is underdense compared to the rest of the Universe, and accounting for this underdensity could help explain the disagreement.

Overall, the idea of using scale-dependent models to interpret different observations could have far-reaching effects throughout the study of cosmology.

"Our analysis, though relying on a particular class of models, indicates that the FL geometry is probably too simplistic to describe the Universe for certain types of observations, given the accuracy reached today," the physicists wrote. "In the end, a single metric may not be sufficient to describe all the cosmological observations, just as Lilliputians and Brobdingnag's giants cannot use a map with the same resolution to travel. A better cosmological model probably requires an atlas of maps with various smoothing scales, determined by the observations at hand. Other observations, such as lensing, may help to characterize the distribution and the geometry of voids, in order to construct a better geometrical model. For the first time, the standard FL background geometry may be showing its limits to interpret the cosmological data with the accuracy they require."

In the future, the physicists plan to further investigate the possibility of a cosmological model that involves an atlas of maps.

"Our future plans in this area are twofold," Fleury said. "On the one hand, we try to construct models for the spacetime geometry of the Universe which would be more realistic than the simple Swiss-cheese model we started with. On the other hand, we are interested in using other types of observations, e.g., weak gravitational lensing, which would be able to distinguish between the standard model of cosmology and alternative ones."

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More information: Pierre Fleury, et al. "Can All Cosmological Observations Be Accurately Interpreted with a Unique Geometry?" PRL 111, 091302 (2013). Journal information: Physical Review Letters Pierre Fleury, et al. "Can All Cosmological Observations Be Accurately Interpreted with a Unique Geometry?"111, 091302 (2013). DOI: 10.1103/PhysRevLett.111.091302

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