Open pageGeneralizing ΛCDM withTopological Quintessence  L. Perivolaropoulos         BW2011Observational Constraints      ...
Main Points    The consistency level of ΛCDM with geometrical data probes has been                 increasing with time du...
Direct Probes of the Cosmic Metric:            Geometric Observational Probes Direct Probes of H(z): Luminosity Distance (...
Geometric ConstraintsParametrize H(z):                                                                                    ...
Geometric Probes: Recent SnIa DatasetsQ1: What is the Figure of Merit of each dataset?Q2: What is the consistency of each ...
z                                                                                                                         ...
Figures of Merit        The Figure of Merit: Inverse area of the 2σ CPL parameter contour.        A measure of the effecti...
From LP, 0811.4684,                                                                                    I. Antoniou, LP, JC...
Proximity of Axes Directions       I. Antoniou, LP,                                              JCAP 1012:012, 2010,     ...
Proximity of Axes Directions    Q: What is the probability that these           Simulated 6 Random Directions:  independen...
Distribution of Mean Inner Product of Six              Preferred Directions (CMB included)                              Th...
Models Predicting a Preferred Axis•     Anisotropic dark energy equation of state (eg vector fields)         (T. Koivisto ...
Simplest Model: Lematre-Tolman-Bondi Local spherical underdensity of matter (Void), no dark energy                        ...
Shifted Observer: Preferred DirectionLocal spherical underdensity of matter (Void)  Ω M −out = 1                          ...
Constraints: Union2 Data – Central Observer       Metric:                 FRW limit:       A ( r, t ) = r a ( t ) , k ( r ...
Constraints: Union2 Data – Central Observer                                                                               ...
Inhomogeneous Dark Energy: Why Consider?         Coincidence Problem: Why Now?        Time Dependent Dark Energy          ...
Topological QuintessenceGlobal Monopole with Hubble scale Core (Topological Quintessence)                                 ...
Evolution of the MetricSpherically Symmetric Metric:       Evolution:               η = 0.6 m pl   ρ rad ( ti ) = 0.1 ρ va...
Toy Model: Generalized LTB                (Inhomogeneous Dark Energy)     Isotropic Inhomogeneius Fluid        with anisot...
Constraints for On-Center Observer                               ΛCDM limit   Geodesics:                                  ...
Off-Center Observer: Union2 ConstraintsMinimized with respect to        (lc,bc)  Minor improvement (if any) in quality of ...
ff-Center Observer: CMB multipoles alignmen                                     23
Summary  Early hints for deviation from the cosmological principle and statistical  isotropy are being accumulated. This a...
Constraints for On-Center Observer                                          ΛCDM limit   Geodesics:                       ...
Off-Center Observer                            ( l, b)                                           Geodesics                ...
Off-Center Observer: Union2 ConstraintsMinimized with respect to        (lc,bc)  Minor improvement (if any) in quality of ...
Off-Center Observer: CMB dipole Constraints                                               Last Scattering                 ...
Off-Center Observer: CMB dipole Constraints       Problem with Copernican Principle ((robs/r0 )3< 10-5).         Expected ...
Approaches in Cosmology Research                                            A1:        a.          Focus on majority of da...
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L. Perivolaropoulos, Topological Quintessence

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The SEENET-MTP Workshop BW2011
Particle Physics from TeV to Plank Scale
28 August – 1 September 2011, Donji Milanovac, Serbia

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L. Perivolaropoulos, Topological Quintessence

  1. 1. Open pageGeneralizing ΛCDM withTopological Quintessence L. Perivolaropoulos BW2011Observational Constraints http://leandros.physics.uoi.gr Department of Physics University of Ioannina Collaborators: I. Antoniou (Ioannina) J. Bueno-Sanchez (Madrid) J. Grande (Barcelona) S. Nesseris (Niels-Bohr Madrid) 1
  2. 2. Main Points The consistency level of ΛCDM with geometrical data probes has been increasing with time during the last decade. There are some puzzling conflicts between ΛCDM predictions and dynamical data probes (bulk flows, alignment and magnitude of low CMB multipoles, alignment of quasar optical polarization vectors, cluster halo profiles)Most of these puzzles are related to the existence of preferred anisotropy axes which appear to be surprisingly close to each other! The simplest mechanism that can give rise to a cosmological preferred axis is based on an off-center observer in a spherical energy inhomogeneity (dark matter or dark energy). Topological Quintessence is a physical mechanism that can induce breaking of space translation invariance of dark energy. 2
  3. 3. Direct Probes of the Cosmic Metric: Geometric Observational Probes Direct Probes of H(z): Luminosity Distance (standard candles: SnIa,GRB): L z dz ᄁ l= d L ( z )th = c ( 1 + z ) ᄁ flat 4π d L 0 H ( z ) ᄁ 2 SnIa Obs dL ( z ) SnIa : z ᄁ (0,1.7] GRB GRB : z ᄁ [0.1, 6] Significantly less accurate probes S. Basilakos, LP, MBRAS ,391, 411, 2008 arXiv:0805.0875Angular Diameter Distance (standard rulers: CMB sound horizon, clusters): c z dz ᄁ dA ( z) r dA ( z) = s d A ( z )th = ᄁ rs θ ( 1 + z ) 0 H ( zᄁ )Ο θ BAO : z = 0.35, z = 0.2 CMB Spectrum : z = 1089 3
  4. 4. Geometric ConstraintsParametrize H(z): ΛCDM ᄁ ( w0 , w1 ) = ( −1, 0 ) z w ( z ) = w0 + w1 1+ z Chevallier, Pollarski, Linder � 10 ( d L , A ( zi )obs ) − 5log ( d L, A ( zi ; w0 , w1 ) th ) � 2 N 5log χ ( Ω m , w0 , w1 ) = ¥ � 2 � = minMinimize: i =1 σi2 4
  5. 5. Geometric Probes: Recent SnIa DatasetsQ1: What is the Figure of Merit of each dataset?Q2: What is the consistency of each dataset with ΛCDM?Q3: What is the consistency of each dataset with Standard Rulers? J. C. Bueno Sanchez, S. Nesseris, LP, 5 JCAP 0911:029,2009, 0908.2636
  6. 6. z w( z ) = w0 + w1Ω0 m = 0.28 Figures of Merit 1+ z The Figure of Merit: Inverse area of the 2σ CPL parameter contour. A measure of the effectiveness of the dataset in constraining the given parameters. 6 6 6 6 ESSENC GOLD06 UNION 4 SNLS 4 4 4 E 2 2 2 2w1 0 0 w1 0 0 w1 w1 w1  2  2  2  2  4  4  4  4  6  6  6  6  2 .0  1 .5  1 .0  0 .5 0 .0  2 .0  1 .5  1 .0  0 .5 0 .0  2 .0  1 .5  1 .0  0 .5 0 .0  2 .0  1 .5  1 .0  0 .5 0 .0 w0 w 0 w0 w 0 w0 w 0 w0 w 0 6 6 6 CONSTITUTION UNION2 WMAP5+SDSS5 WMAP5+SDSS7 4 4 4 2w1 2 2 0 0 w1 w1 0 w1  2  2  2  4  4  4  6  6 6  6  2 .0  1 .5  1 .0  0 .5 0 .0  2 .0  1 .5  1 .0  0 .5 0 .0 w0  2 .0  1 .5  1 .0  0 .5 0 .0 w 0 w0 w0 w 0 w0 w0
  7. 7. Figures of Merit The Figure of Merit: Inverse area of the 2σ CPL parameter contour. A measure of the effectiveness of the dataset in constraining the given parameters. C U2 SDSS MLCS2k2 G06 U1 SDSS SALTII SNLS ESDSS5 Percival et. al.SDSS7 Percival et. al. 7
  8. 8. From LP, 0811.4684, I. Antoniou, LP, JCAP 1012:012, Puzzles for ΛCDM 2010, arxiv:1007.4347Large Scale Velocity Flows R. Watkins et. al. , Mon.Not.Roy.Astron.Soc.392:743-756,2009, 0809.4041. A. Kashlinsky et. al. Astrophys.J.686:L49-L52,2009 arXiv:0809.3734 - Predicted: On scale larger than 50 h-1Mpc Dipole Flows of 110km/sec or less. - Observed: Dipole Flows of more than 400km/sec on scales 50 h-1Mpc or larger. - Probability of Consistency: 1%Alignment of Low CMB Spectrum Multipoles M. Tegmark et. al., PRD 68, 123523 (2003), Copi et. al. Adv.Astron.2010:847541,2010. - Predicted: Orientations of coordinate systems that maximize planarity ( all 2 + )al −l 2 of CMB maps should be independent of the multipole l . - Observed: Orientations of l=2 and l=3 systems are unlikely close to each other. - Probability of Consistency: 1%Large Scale Alignment of QSO Optical Polarization Data D. Hutsemekers et. al.. AAS, 441,915 (2005), astro-ph/0507274 - Predicted: Optical Polarization of QSOs should be randomly oriented - Observed: Optical polarization vectors are aligned over 1Gpc scale along a preferred axis. - Probability of Consistency: 1%Cluster and Galaxy Halo Profiles: Broadhurst et. al. ,ApJ 685, L5, 2008, 0805.2617, S. Basilakos, J.C. Bueno Sanchez, LP., 0908.1333, PRD, 80, 043530, 2009. - Predicted: Shallow, low-concentration mass profiles - Observed: Highly concentrated, dense halos 8 - Probability of Consistency: 3-5%
  9. 9. Proximity of Axes Directions I. Antoniou, LP, JCAP 1012:012, 2010, arxiv: 1007.4347 Q: What is the probability that these independent axes lie so close in the sky?Calculate: Compare 6 real directions with 6 random directions 9
  10. 10. Proximity of Axes Directions Q: What is the probability that these Simulated 6 Random Directions: independent axes lie so close in the sky?Calculate: 6 Real Directions (3σ away from mean value): Compare 6 real directions with 6 random directions 10
  11. 11. Distribution of Mean Inner Product of Six Preferred Directions (CMB included) The observed coincidence of the axes is a statistically very unlikely event. 8/1000 larger than real datarequencies < |cosθij|>=0.72 (observations) 11 <cosθij>
  12. 12. Models Predicting a Preferred Axis• Anisotropic dark energy equation of state (eg vector fields) (T. Koivisto and D. Mota (2006), R. Battye and A. Moss (2009))• Fundamentaly Modified Cosmic Topology or Geometry (rotating universe, horizon scale compact dimension, non-commutative geometry etc) (J. P. Luminet (2008), P. Bielewicz and A. Riazuelo (2008), E. Akofor, A. P. Balachandran, S. G. Jo, A. Joseph,B. A. Qureshi (2008), T. S. Koivisto, D. F. Mota, M. Quartin and T. G. Zlosnik (2010))• Statistically Anisotropic Primordial Perturbations (eg vector field inflation) (A. R. Pullen and M. Kamionkowski (2007), L. Ackerman, S. M. Carroll and M. B. Wise (2007), K. Dimopoulos, M. Karciauskas, D. H. Lyth and Y. Ro-driguez (2009))• Horizon Scale Primordial Magnetic Field. (T. Kahniashvili, G. Lavrelashvili and B. Ratra (2008), L. Campanelli (2009), J. Kim and P. Naselsky (2009))• Horizon Scale Dark Matter or Dark Energy Perturbations (eg few Gpc void) (J. Garcia-Bellido and T. Haugboelle (2008), P. Dunsby, N. Goheer, B. Osano and J. P. Uzan (2010), T. Biswas, A. Notari and W. Valkenburg (2010)) 12
  13. 13. Simplest Model: Lematre-Tolman-Bondi Local spherical underdensity of matter (Void), no dark energy Ω M −out = 1 r0 Ω M −in ᄁ 0.2 Central Observer H in ( z ) H out ( z ) Faster expansion rate at low redshifts (local space equivalent to recent times) 13
  14. 14. Shifted Observer: Preferred DirectionLocal spherical underdensity of matter (Void) Ω M −out = 1 Preferred r0 Direction Ω M −in ᄁ 0.2 Observer robs H in ( z ) H out ( z ) Faster expansion rate at low redshifts (local space equivalent to recent times) 14
  15. 15. Constraints: Union2 Data – Central Observer Metric: FRW limit: A ( r, t ) = r a ( t ) , k ( r ) = k k ( r) 0 1 − ΩΜ ( r ) = − H 0 ( r ) A ( r, t0 ) 2 2 Cosmological Equation: 1 Geodesics: Luminosity Distance: M 15
  16. 16. Constraints: Union2 Data – Central Observer Advantages: χ 2 ( Ω M −in = 0.2, r0 = 1.86Gpc ) ᄁ 556 1. No need for dark energy. 2. Natural Preferred Axis. ( Ω M −in = 0.2, r0 = 1.86Gpc ) 3. Coincidence Problem Problems: 1. No simple mechanism to create such large voids. 2. Off-Center Observer produces too large CMB Dipole. 3. Worse Fit than LCDM. χ 2 ΛCDM ( Ω 0 m = 0.27 ) ᄁ541 J. Grande, L.P., Phys. Rev. D 84, 023514 (2011). Ω M −in 16
  17. 17. Inhomogeneous Dark Energy: Why Consider? Coincidence Problem: Why Now? Time Dependent Dark Energy Standard Model (ΛCDM): 1. Homogeneous - Isotropic Dark and Baryonic Matter.Alternatively: 2. Homogeneous-Isotropic-Constant Dark Energy Why Here? Inhomogeneous Dark Energy (Cosmological Constant) 3. General Relativity Consider Because: 1. New generic generalization of ΛCDM (breaks homogeneity of dark energy). Includes ΛCDM as special case. 2. Natural emergence of preferred axis (off – center observers) 3. Well defined physical mechanism (topological quintessence with Hubble scale global monopoles). J. Grande, L.P., Phys. Rev. D 84, 023514 (2011). 17 J. B. Sanchez, LP, in preparation.
  18. 18. Topological QuintessenceGlobal Monopole with Hubble scale Core (Topological Quintessence) Φ =η Φ=0 Energy-Momentum (asymptotic): V ( Φ) Evolution Equations: Φ Φ =η S2 18
  19. 19. Evolution of the MetricSpherically Symmetric Metric: Evolution: η = 0.6 m pl ρ rad ( ti ) = 0.1 ρ vac Rapid Expansion in the Monopole Core Preliminary Results J. B. Sanchez, LP, in preparation. 19
  20. 20. Toy Model: Generalized LTB (Inhomogeneous Dark Energy) Isotropic Inhomogeneius Fluid with anisotropic pressure 0 Cosmological Equation: Isocurvature Profiles (Flat): Ω M −out = 1 ΩM ( r )J. Grande, L.P., Phys. Rev. D 84, 023514 (2011).. ΩΜ ( r ) + Ω X ( r ) = 1 ΩX ( r) r0 Ω X −out = 0 20
  21. 21. Constraints for On-Center Observer ΛCDM limit Geodesics: χ 2 ; 541Luminosity Distance: χ 2 ( r0 , Ω Χ−in ) Union 2 χ2 contours Ruled out region at 3σ r0 <1.75 J. Grande, L.P., Phys. Rev. D 84, 023514 (2011). Ω M − in = 1 − Ω Χ − in 21
  22. 22. Off-Center Observer: Union2 ConstraintsMinimized with respect to (lc,bc) Minor improvement (if any) in quality of fit over ΛCDM, despite four additional parameters. Copernican Principle Respected (robs/r0 as large as 0.7). 22
  23. 23. ff-Center Observer: CMB multipoles alignmen 23
  24. 24. Summary Early hints for deviation from the cosmological principle and statistical isotropy are being accumulated. This appears to be one of the most likely directions which may lead to new fundamental physics in the coming years. The simplest mechanism that can give rise to a cosmological preferred axis is based on an off-center observer in a spherical energy inhomogeneity (dark matter of dark energy) Such a mechanism can give rise to aligned CMB multipoles and largescale velocity flows. If the inhomogeneity is attributed to a Hubble scale global monopole with a Hubble scale core other interesting effects may occur (direction dependent variation of fine structure constant, quasar polarization alignment etc). 24
  25. 25. Constraints for On-Center Observer ΛCDM limit Geodesics: Union 2 χ2 contoursLuminosity Distance: χ 2 ( r0 , Ω Χ−in ) Ruled out region at 3σ r0 < 1.75 25
  26. 26. Off-Center Observer ( l, b) Geodesics Luminosity Distance robs d L ( z , r0 , Ω Χ−in ; ξ , robs )ξ = ξ ( lc , bc ; l , b ) χ 2 ( r0 , Ω Χ−in ; robs , lc , bc ) 26
  27. 27. Off-Center Observer: Union2 ConstraintsMinimized with respect to (lc,bc) Minor improvement (if any) in quality of fit over ΛCDM, despite four additional parameters. Copernican Principle Respected (robs/r0 as large as 0.7). 27
  28. 28. Off-Center Observer: CMB dipole Constraints Last Scattering Surface Ω X −out = 0 zls ( ξ , robs ) Ω M −out = 1 r0 from geodesics (z to tdec) Ω M −in ᄁ 0.27 ξ robs H in ( z ) H out ( z ) Dipole a10(robs,r0) 28
  29. 29. Off-Center Observer: CMB dipole Constraints Problem with Copernican Principle ((robs/r0 )3< 10-5). Expected to be alleviated for r0~rls 29
  30. 30. Approaches in Cosmology Research A1: a. Focus on majority of data which are consistent with ΛCDM.b. Assume validity of ΛCDM and constrain standard model parameters with best possible accuracy A2:a. Focus on Theoretical Motivation and construct more general models. b. Use data to constrain the larger space of parameters. A3: a. Focus on minority of data that are inconsistent with ΛCDM at a level more than 2-3σ.b. Identify common features of these data and construct theoretical models consistent with these features. c. Make non-trivial predictions using these models. 30

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