A Quasar Based Search for Hypertorus Cosmology

Dylan Menzies, Grant MathewsUniversity 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 = .7 +- .1, 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

2 4 6 8 10

0.3

0.4

0.5

0.6

0.7d

z-distance relation

0

8.0

z

Pixel Track Illustration

59.4

59.6

59.8

60

60.2

60.4

60.6

60.8

61

61.2

278.5 279 279.5 280 280.5 281 281.5 282 282.5

59.9

60

60.1

60.2

60.3

60.4

60.5

60.6

279 279.5 280 280.5 281 281.5 282

• 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 = 0.002 dSLS

• 2nd peak suggests dT3 = .38 dSLS, axis = (273.7, 59.1)• But decorrelated data not consistent.

Results

-1

0

1

2

3

4

5

6

7

8

1 19 37 55 73 91 109

127

145

163

181

199

217

235

253

271

289

307

325

343

361

379

397

415

433

Series2

Series3

Series4

Series1

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

Results

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

1 15 29 43 57 71 85 99 113

127

141

155

169

183

197

211

225

239

253

267

281

295

309

323

337

351

365

379

393

407

421

435

449

Series1