1. Local Void vs Dark Energy Local Void vs Dark Energy Tirthabir Biswas IGC, Penn-State University with A Notari and R Mansouri, astro-ph/0606703 with A Notari, astro-ph/0702555 with A Notari, S Alexander & D Vaid, arXiv:0712.0370

2. Puzzles of Dark Energy Puzzles of Dark Energy Smallness Problem Smallness Problem Coincidence or Why now Problem Coincidence or Why now Problem These puzzles are not unique to ΛCDM… … we are still very much in the dark Is dark energy real? Is dark energy real?

3. Concordant ΛCDM Type Ia Supernovae Type Ia Supernovae WMAP (CMB) WMAP (CMB) SDSS (galaxy power spectrum) SDSS (galaxy power spectrum) LRG (Baryon acoustic peak, BAO) LRG (Baryon acoustic peak, BAO) ISW effect ISW effect … Success of ΛCDM, failure of EdS How can we even contemplate not having Λ? What could we have missed?

4. The Inhomogeneous Universe Is homogeneity a good assumption? Celerier ‘97 Back-reaction: “average expansion rate changes” [Brandenberger, Kolb…] Back-reaction: “average expansion rate changes” [Brandenberger, Kolb…] Perturbative approach… not clear whether we can trust the results Perturbative approach… not clear whether we can trust the results Exact Models: What do we really measure Exact Models: What do we really measure Redshift Redshift Luminosity Distance Luminosity Distance Evolution history of universe effects D L (z), but Evolution history of universe effects D L (z), but Inhomogeneities also effect light paths, or D L (z) Inhomogeneities also effect light paths, or D L (z) Additional symmetries may lead to under-estimation of effect Additional symmetries may lead to under-estimation of effect

5. Parameters governing the corrections Amplitude of perturbations Amplitude of perturbations Ratio between perturbation & cosmological length scale Ratio between perturbation & cosmological length scale small quantity, L ~ 10-20 Mpc/h, R H ~ 3000 Mpc/h small quantity, L ~ 10-20 Mpc/h, R H ~ 3000 Mpc/h How can it work? Scenario I, Average or integrated effect: Scenario I, Average or integrated effect: Light passes through hundreds of patches ~ 30 Mpc and pick up net correction Light passes through hundreds of patches ~ 30 Mpc and pick up net correction Does it adds coherrently? Yes. Does it adds coherrently? Yes. How does it depend on L/ R H,, How does it depend on L/ R H,, Doesn’t work, but could be a twist! Doesn’t work, but could be a twist! Scenario II, Local Effect: Scenario II, Local Effect: We are sitting inside a large ~ 300 Mpc void! We are sitting inside a large ~ 300 Mpc void! Locally effect goes like Locally effect goes like Hubble expansion rate different inside and outside the patch Hubble expansion rate different inside and outside the patch

6. Lemaitre Tolman Bondi Model Spherically symmetric metric Solution: Solution: Constraints: Constraints: Matching to FLRW at boundary: k’(L) = 0  same average density Matching to FLRW at boundary: k’(L) = 0  same average density Consistency at origin: k’(0) = 0 Consistency at origin: k’(0) = 0 Flat FLRW  k(L) = 0 Flat FLRW  k(L) = 0 Both Analytical & Numerical progress can be made

7. Swiss-Cheese toy Model Integrated Effect: Place observer and source at two opposite ends and source at two opposite ends Redshift Correction Redshift Correction Luminocity Distance correction Luminocity Distance correction Photon flux conservation should yield zero average effect? [Tetradis et.al.] Can we study non-spherical configuration?

8. Minimal Void Model We are sitting inside a large ~ O (100) Mpc/h void! Non-linear evolution  Why we can still be optimistic? We only need We only need We regularly observe voids ~ 50 Mpc/h, We regularly observe voids ~ 50 Mpc/h, & large structures, Great SLOAN wall ~ 400 Mpc/h & large structures, Great SLOAN wall ~ 400 Mpc/h huge “hole” spanning 150 Mpc/h, and 25% underdensity! [Frith et al] huge “hole” spanning 150 Mpc/h, and 25% underdensity! [Frith et al] Observational evidence of a hole explaining cold spot in CMB [Rudnick, Brown & Williams] Observational evidence of a hole explaining cold spot in CMB [Rudnick, Brown & Williams] How well do we understand nonlinear structure formation? How well do we understand nonlinear structure formation? Percolated voids ~ 100 Mpc/h [Shandarin, Sheth and Sahni] Percolated voids ~ 100 Mpc/h [Shandarin, Sheth and Sahni] Having a large local void may not be as unlikely

9. Size of patch? Distant supernovae has z ~ 0.5-1 ~ O(1000) Mpc/h Distant supernovae has z ~ 0.5-1 ~ O(1000) Mpc/h Extreamely unlikely Extreamely unlikely Would effect CMB fluctuations Would effect CMB fluctuations ruled out by distortion of black-body spectrum [Caldwell & Stebbins] ruled out by distortion of black-body spectrum [Caldwell & Stebbins] We only need to modify upto z ~ 0.08 ~ O(200) Mpc/h “Currently” acceleration inferred through a mismatch of between Nearby, z 0.4 supernovae data

10. H out H in H out H out H in H out z<0.1, nearby supernova’s inside the patch, experience faster local Hubble expansion faster local Hubble expansion z>0.1 outside the patch, see average expansion

13. Fitting WMAP Effect of void Central Observer+Spherical symmetry  only monopole Central Observer+Spherical symmetry  only monopole Off-center observer  dipole ~ 10 -3 Off-center observer  dipole ~ 10 -3  within 10% of void-radius [Alnes & Amarzguioui]  within 10% of void-radius [Alnes & Amarzguioui] Higher multipoles are much suppressed Higher multipoles are much suppressed Non-spherical voids: Interresting possibilities, Non-spherical voids: Interresting possibilities, low multipole anomalies in CMB [Silk & Inoue] ? low multipole anomalies in CMB [Silk & Inoue] ? Many large voids  interesting secondary effects to Many large voids  interesting secondary effects to CMB anisotropies ~ 10 -5, Implications for ISW CMB anisotropies ~ 10 -5, Implications for ISW Assume spherical symmetry, EdS good enough for WMAP

14. Can EdS fit the WMAP? Yes! Provided we give up near scale-invariance [Sarkar et.al.,Souradeep et.al.] Include running instead of Λ

15. Best fit WMAP parameters consistent with BBN consistent with BBN Bayons constitute 9% of matter, may be too low? Bayons constitute 9% of matter, may be too low? z rec ~ 13, broadly consistent z rec ~ 13, broadly consistent low spectral index & large running low spectral index & large running seemingly consistent with BAO [Eisenstein et al] seemingly consistent with BAO [Eisenstein et al] 0.43< h out <0.47 low Hubble parameter 0.43< h out <0.47 low Hubble parameter Along with the jump, local h ~ 0.59 possible! Along with the jump, local h ~ 0.59 possible! HKP: h=.72 .08 HKP: h=.72 .08 supernovae: h=.59 .04 supernovae: h=.59 .04 SZ effect: h=.54 .04 SZ effect: h=.54 .04

17. Baryon Acoustic Peak Galaxy power spectrum: Primodial Spectrum Primodial Spectrum Scale at Matter radiation equality Scale at Matter radiation equality Sound horizon at CMB: Sound horizon at CMB: Baryons can move in a spherical wave around a dark matter over-density giving a peak in the galaxy power spectrum Baryons can move in a spherical wave around a dark matter over-density giving a peak in the galaxy power spectrum Two constraints: [Eisenstein et.al.] To fix, we possibly need higher h out Include small curvature Include small curvature Look at other spectral modifications, a peak [Sarkar et.al.] Look at other spectral modifications, a peak [Sarkar et.al.] Enhances perturbations at the right scale! Enhances perturbations at the right scale!

18. Jobs to be done SN Ia, WMAP, local h, BBN can work SN Ia, WMAP, local h, BBN can work SDSS, LRG (BAO), ISW Lyman- , to be done [Zibin] SDSS, LRG (BAO), ISW Lyman- , to be done [Zibin] Try to fit WMAP with h ~.55 Try to fit WMAP with h ~.55 Origin of void? Origin of void? Can a peak in primordial spectrum help? Can a peak in primordial spectrum help? Study Non-linear aspects, such as percolation Study Non-linear aspects, such as percolation Non-standard structure formation scenarios: Interacting dark matter? Non-standard structure formation scenarios: Interacting dark matter?

19. Tests and Assessment Optimistic it can work, but Optimistic it can work, but Origin of void Origin of void Violation of Copernican principle, CMB dipole Violation of Copernican principle, CMB dipole Several tests: Several tests: D(z) curve differs from ΛCDM D(z) curve differs from ΛCDM direct observations of voids direct observations of voids correlated anisotropies in CMB and H measurements correlated anisotropies in CMB and H measurements Modifications in CMB black-body spectrum Modifications in CMB black-body spectrum Who knows in 5 years we may be talking mystery of the void mystery of the void