A Quasar Based Search for Hypertorus Cosmology Dylan Menzies, Grant Mathews University of Notre Dame

General relativity says nothing about topology. Maybe 3D topology is not simply connected. Imposing a non-trivial topology can make a non-compact universe compact. In flat space 10 compact topologies are possible. Infinite non-zero compact constant-curvature topologies. Topological dimension scale? Cosmological 3D Topology

2-torus covering space globally homogenous The Hypertorus 3-torus fundamental domain

WMAP quadrupole and octopole Suppression and alignment Tegmark et al march 03 Hypertorus? Use to guide search (l,b) ~ (250°,60°) Hypertorus Evidence

Multipole Suppression

2D CMB methods –Multipole suppression, dT3  0.25 dSLS –Cornish circles, de Oliveira-Costa July 03, rules out T3 –Search for discrete modes could find dT3>1 dSLS eg Rocha 02 Weak bounds so far. Previous Results

3D quasar groups –Bounds weaker dT3  0.02 dSLS –Reliant on redshift –Dropout intolerant Previous Results

Locate axis without z Bidirectional –search up to dSLS Find direction pixels with high number of alignments. z-free test

Based on lambda = , flat (WMAP) Exclude pair if | t1-t2 | >.5 billion yrs (reduces peculiar velocity error as well) Exclude if z1, z2, theta1, theta2 not well related. More Filters

d z-distance relation z

Pixel Track Illustration

Bin by calculated dT3, store max alignments and location of max in each bin. Repeat on several sets decorrelated by random z- redistribution. Use mean and deviation of the bins in these sets as null hypothesis. More Sensitivity

0.01 deg resolution, 20x30 deg search dT3 bin spacing = dSLS 2nd peak suggests dT3 =.38 dSLS, axis = (273.7, 59.1) But decorrelated data not consistent. Results

Sensitive to dropout of below 0.01 over much of dT3 range Results