A note on cosmological parameters and the topology of the universe

Rebouças, M. J.; Alcaniz, J. S.

doi:10.1590/s0103-97332005000700012

Braz. J. Phys.

2005

DOI: 10.1590/s0103-97332005000700012

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A note on cosmological parameters and the topology of the universe

M. J. Rebouças

J. S. Alcaniz

Abstract: Given the wealth of increasingly accurate cosmological observations, especially the recent results from the WMAP, and the development of methods and strategies in the search for cosmic topology, it is reasonable to expect that we should be able to detect the spatial topology of the Universe in the near future. Motivated by this, we examine to what extent a possible detection of a nontrivial topology of positively curved universe may be used to place constraints on the matter content of the Universe. We show th… Show more

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Cited by 4 publications

References 18 publications

(28 reference statements)

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Dark energy cosmology with the alternative cosmic microwave background data

Hao¹

2011

J. Cosmol. Astropart. Phys.

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Recently, in a series of works by Liu and Li (L&L), they claimed that there exists a timing asynchrony of −25.6 ms between the spacecraft attitude and radiometer output timestamps in the original raw WMAP time-ordered data (TOD). L&L reprocessed the WMAP data while the aforementioned timing asynchrony has been corrected, and they obtained an alternative CMB map in which the quadrupole dropped to nearly zero. In the present work, we try to see the implications to dark energy cosmology if L&L are right. While L&L claimed that there is a bug in the WMAP pipeline which leads to significantly different cosmological parameters, an interesting question naturally arises, namely, how robust is the current dark energy cosmology with respect to systematic errors and bugs? So, in this work, we adopt the alternative CMB data of L&L as a strawman to study the robustness of dark energy predictions.PACS numbers: 98.80. Es, 95.36.+x, 98.80.Cq, 98.70.Vc

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Dark energy cosmology with the alternative cosmic microwave background data

Hao¹

2011

J. Cosmol. Astropart. Phys.

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Circles-in-the-sky searches and observable cosmic topology in the inflationary limit

2008

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While the topology of the Universe is at present not specified by any known fundamental theory, it may in principle be determined through observations. In particular, a non-trivial topology will generate pairs of matching circles of temperature fluctuations in maps of the cosmic microwave background, the so-called circles-in-the-sky. A general search for such pairs of circles would be extremely costly and would therefore need to be confined to restricted parameter ranges. To draw quantitative conclusions from the negative results of such partial searches for the existence of circles we need a concrete theoretical framework. Here we provide such a framework by obtaining constraints on the angular parameters of these circles as a function of cosmological density parameters and the observer's position. As an example of the application of our results, we consider the recent search restricted to pairs of nearly back-to-back circles with negative results. We show that assuming the Universe to be very nearly flat, with its total matter-energy density satisfying the bounds 0 < |Ω0 − 1| 10 −5 , compatible with the predictions of typical inflationary models, this search, if confirmed, could in principle be sufficient to exclude a detectable non-trivial cosmic topology for most observers. We further relate explicitly the fraction of observers for which this result holds to the cosmological density parameters. 98.80.Es, 98.80.Jk

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Limits of the circles-in-the-sky searches in the determination of cosmic topology of nearly flat universes

2016

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An important observable signature of a detectable nontrivial spatial topology of the Universe is the presence in the cosmic microwave background sky of pairs of matching circles with the same distributions of temperature fluctuations -the so-called circles-in-the-sky. Most of the recent attempts to find these circles, including the ones undertaken by the Planck Collaboration, were restricted to antipodal or nearly antipodal circles with radii λ ≥ 15• . In the most general search, pairs of circles with deviation from antipodality angles 0• ≤ θ ≤ 169• and radii 10 • ≤ λ ≤ 90• were investigated. No statistically significant pairs of matching circles were found in the searches so far undertaken. Assuming that the negative result of general search can be confirmed through analysis made with data from Planck and future cosmic microwave background (CMB) experiments, we examine the question as to whether there are nearly flat universes with compact topology, satisfying Planck constraints on cosmological parameters, that would give rise to circles-in-the-sky whose observable parameters λ and θ fall outside the parameter ranges covered by this general search. We derive the expressions for the deviation from antipodality and for the radius of the circles associated to a pair of elements (γ ,γ −1 ) of the holonomy group Γ which define the spatial section of any positively curved universe with a nontrivial compact topology. We show that there is a critical position that maximizes the deviation from antipodality, and prove that no matter how nearly flat the Universe is, it can always have a nontrivial spatial topology that gives rise to circles whose deviation from antipodality θ is larger than 169• , and whose radii of the circles λ are smaller than 10• for some observers's positions. This makes it apparent that slightly positively curved nearly flat universes with cosmological parameters within Planck bounds can be endowed with a nontrivial spatial topology with values of the observable parameters λ and θ outside the ranges covered by the searches for circles carried out so far with either WMAP or Planck data. Thus, these circles-inthe-sky searches carried out so far are not sufficient to exclude the possibility of a universe with a detectable nontrivial cosmic topology. We present concrete examples of lens spaces universes whose associated circles have both, or at least one value of the observable parameters (λ, θ) outside the ranges covered by these searches. We also present a brief discussion of the implications of our results in view of unavoidable practical limits of the circles-in-the-sky method. 98.80.Es, 98.80.Jk

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A note on cosmological parameters and the topology of the universe

Cited by 4 publications

References 18 publications

Dark energy cosmology with the alternative cosmic microwave background data

Dark energy cosmology with the alternative cosmic microwave background data

Circles-in-the-sky searches and observable cosmic topology in the inflationary limit

Limits of the circles-in-the-sky searches in the determination of cosmic topology of nearly flat universes

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