[Paper Review] Central symmetry and antisymmetry of the microwave background inhomogeneities on Wilkinson Microwave Anisotropy Probe maps

Iurii Kudriavtcev, D. Semenov|arXiv (Cornell University)|Aug 24, 2010

Cosmology and Gravitation Theories2 references3 citations

TL;DR

This study proposes that microwave background inhomogeneities in WMAP data exhibit central symmetry with both symmetric and antisymmetric components, where temperature deviations at diametrically opposite points on the sky are either identical (symmetric) or opposite (antisymmetric). Using numerical analysis and Mollweide-projection maps, the authors find a global average symmetry coefficient of −4±1%, indicating a slight dominance of antisymmetry, with local variations showing bipolar contributions from both mechanisms, suggesting distinct physical origins in matter motion and density fluctuations at recombination.

ABSTRACT

We performed a visual and numeric analysis of the deviation of the microwave background temperature on WMAP maps. We proved that the microwave background inhomogeneities possess the property of the central symmetry resulting from the two kinds of central symmetry of the opposite signs. After the computer modeling we have established the relation between the coefficient of the central symmetry and the values of the symmetrical and antisymmetrical components of the deviation of the temperature. The obtained distribution of the symmetry coefficient on the map of the celestial sphere in Mollweide projection testifies on a contribution of both kinds of central symmetry which is approximately equal on the average in absolute magnitude but opposite by sign and where one kind of the central symmetry prevails on some sections of the celestial sphere and another kind - on the others. The average resulting value of the symmetry coefficient on the sections with angular measures less than 15-200 varies within the range from -50% to +50% with some prevalence of the antisymmetry - the average coefficient of the central symmetry for the whole celestial sphere is -4 +/- 1%. (antisymmetry 4%). Small scale structure of the distribution indicates that it is the result of the combined action of the mechanisms of the central symmetry and central antisymmetry, close to 100%.

Motivation & Objective

• To investigate whether microwave background inhomogeneities on WMAP maps exhibit central symmetry rather than axisymmetry.
• To test the hypothesis that central symmetry, including both symmetric and antisymmetric components, could explain observed large-scale patterns without violating cosmic isotropy.
• To quantify the relative contributions of symmetric and antisymmetric components using numerical analysis of temperature deviation maps.
• To explore the physical origin of the symmetry patterns, distinguishing between those induced by matter motion and density inhomogeneities at recombination.

Proposed method

• Applied visual and numerical analysis to WMAP maps in Mollweide and Lambert projections to detect central symmetry patterns.
• Defined a central symmetry coefficient ksymm as (|Tsymm| − |Tasymm|)/(|Tsymm| + |Tasymm|), relating it to the difference and sum of absolute values of symmetric and antisymmetric temperature components.
• Used computer modeling to simulate the distribution of symmetry coefficients across the celestial sphere.
• Generated maps of ksymm in Mollweide projection to visualize spatial variations, identifying regions of dominant symmetry or antisymmetry.
• Analyzed unsmoothed fragments of ksymm maps to detect lines of zero symmetric or antisymmetric components, indicating 100% symmetry of one sign.
• Correlated observed patterns with theoretical expectations from a closed 3-sphere universe model, where light rays traverse multiple loops.

Experimental results

Research questions

• RQ1 Does the microwave background in WMAP data exhibit central symmetry rather than axisymmetry, and if so, what are its characteristics?
• RQ2 What is the relative contribution of symmetric and antisymmetric components to the observed temperature deviation patterns on the celestial sphere?
• RQ3 Can the observed symmetry patterns be explained by two distinct physical mechanisms—matter motion and density inhomogeneities—at recombination?
• RQ4 How do the symmetry coefficients vary across different angular scales, and what does this imply about the underlying cosmological dynamics?
• RQ5 What is the global average value of the central symmetry coefficient, and does it indicate a preference for one type of symmetry over the other?

Key findings

• The average central symmetry coefficient over the entire celestial sphere is −4±1%, indicating a slight dominance of antisymmetry.
• On angular scales below 15–20°, the symmetry coefficient varies between −50% and +50%, with local regions showing either symmetric or antisymmetric dominance.
• Small-scale structures in the ksymm map are characterized by lines where Tsymm = 0 or Tasymm = 0, indicating 100% symmetry of one sign, confirming the presence of both mechanisms.
• The distribution of ksymm shows a bipolar pattern, with symmetric and antisymmetric components contributing approximately equally in magnitude but with opposite signs on average.
• The observed symmetry patterns are consistent with a closed universe model where light from recombination travels multiple loops around the 3-sphere, leading to central symmetry in observed temperature deviations.
• The results suggest that temperature deviations are driven by two distinct physical processes: matter motion (inducing antisymmetry) and density inhomogeneities (inducing symmetry) at recombination.