Cosmic Inhomogeneities and Accelerating Expansion

1. Cosmic Inhomogeneities and Accelerating Expansion Ho Le Tuan Anh National University of Singapore PAQFT 27-29 Nov 2008

2. Outline • Concordance model • Model with a local void • Motivation for suggesting model • Model • Method to check the model • Results with Riess 2007 SNe Gold sample • Conclusion and Discussion

3. Concordance model • Homogeneous • Isotropic • Nearly flat: Ωtotal ~ 1 • Dark energy density: Ωλ ~ 70% • Use FLRW metric and Friedmann equations.

4. Concordance model • Successes in explaining: • Existence and thermal form of the CMB radiation. • Relative abundance of light elements. • Age of the Universe. • SNe Ia data with accelerating expansion of the universe.

5. Concordance model • Weak points: • Cosmological constant problem: λ extremely small. • Cosmic coincidence problem: Ωλ + Ωm ≈ 1 • Mysterious nature of dark energy: • What dark energy consists of ? • Whether it is constant or not? • Its equation of state ?  Due toAppearance of Cosmological Constant λ

6. Solutions of Dark Energy Problems • Modifying General Relativity Theory at large distances scales • Considering systematic uncertainties: • Intergalactic dust. • Gravitational lensing. • Sn progenitors’ evolution. • Etc… • Proposals of inhomogeneous models: LTB models, Stephani models, Swiss-cheese models…

7. Models with a local void • Motivation for suggesting: • Evidences of local void and the shell (Sloan Great Wall) from galaxy redshift survey, SDSS, 2dF redshift survey… • Systematic deviation of clusters’ motions from the global Hubble flow. • Cold spot in the CMB may be associated with a Big Void in the large-scale structure. • Etc..

8. Model with a local void (Tomita’s model) • Consist of 2 homogeneous and isotropic regions (inner and outer), separated by a single,spherical singular shell. • Each is FLRW cosmology with different parameters set. • Ω0I < Ω0II ; H0I > H0II

9. SNe and Accelerating expansion • The homogeneous and isotropic model can not fit SNe data without dark energy term accelerating expansion appears. • Therefore, if dark energy term disappears, accelerating expansion disappears, too. This happens in inhomogeneous model.

10. Distances in Tomita’s model • Angular Distance: • General definition: Where: λ: Affine parameter θ: Expansion parameter • Luminosity Distance:

11. Distances in Tomita’s model • Applying to the model: • Where: j: 1, 2 (inner and outer region) Ω0: Present matter density parameter λ0: Present dark energy density parameter

12. Boundary and Initial conditions • Redshift at the shell are equal: • For : • For :  Numerically solving equations (1), we can obtain angular and luminosity distance.

13. Method to check the model • Theoretical distance modulus: • Observed distance modulus: • Best-fit values are determined by χ2 statistic:

14. Method to check the model • Relation between σmz and σz : • Probability distribution function: • Eliminate nuisance parameters by taking integral: • y: nuisance parameters set. • μ0: the set of distance moduli used.

15. Supernova data and fitting • Apply the model with Riess 2007 Gold sample • Consider several cases with specific values of to avoid over-complication. • z1=0.067, 0.08, 0.1 • = 0.70, 0.082, 0.085, 0.90 • Different matter density profiles:

16. Gold Sample (182 SNe) . Dark Energy density - Matter density Confidence contours with 68.3% & 95.4% CL (Profile A)

17. Gold Sample . • R increases  Ω decreases and λ increases. • Best-fit values (profile A): Lambda02 Omega02

18. Comments on results • The model can fit the SNe data without dark energy. • Best-fit values are consistent with other measurements on Hubble constant, local matter density. • A slightly better fit to the SNe data than ΛCDM model. • Testing with different matter density profiles A, B, C, D  Confidence contours and are very insensitive with matter density profiles.

19. Comparison with Riess 98 SNe sample • New confidence contours are much more compact than old ones  narrower constraints on parameters space.

20. Conclusion and Discussion • Dark Energy problems can be solved with inhomogeous models. • Local void model can consistently account for SNe data as well as constraints cosmological parameters values. • Off-center observer should be considered in the future. • Investigating the model with other recent observations such as WMAP, BAO, ESSENCE…

21. References • Alexander, S. a. B., Tirthabir and Notari, Alessio and Vaid, Deepak. 2007, arxiv: astro-ph/0712.0370 • Alnes, H., Amarzguioui, M., & Gron, O. 2006, Physical Review D, 73 • Celerier, M.-N. 2007, arxiv: astro-ph/0702416 • Celerier, M. N. 2000, Astronomy and Astrophysics, 353, 63 • Liddle, A. 2003, An introduction to modern cosmology (Wiley) • Moffat, J. W. 2006, Journal of Cosmology and Astroparticle Physics, arxiv: astro-ph/0505326 • Peebles, P. J. E. 1993, Principles of physical cosmology (Princeton University Press) • Riess, A. G., et al. 1998, Astronomical Journal, 116, 1009 • ---. 2007, Astrophysical Journal, 659, 98 • ---. 2004, Astrophysical Journal, 607, 665 • Roos, M. 2003, Introduction to cosmology (Wiley) • Tomita, K. 2000, Astrophysical Journal, 529, 26 • ---. 2000, Astrophysical Journal, 529, 38 • ---. 2001, Progress of Theoretical Physics, 106, 929 • ---. 2001, Monthly Notices of the Royal Astronomical Society, 326, 287 • Tomita, K., Asada, H., & Hamana, T. 1998. in Workshop on Gravitational Lens Phenomena and High-Redshift Universe, Distances in inhomogeneous cosmological models (Kyoto, Japan: Progress Theoretical Physics Publication Office), 155 • Wood-Vasey, W. M., et al. 2007, Astrophysical Journal, 666, 694 • http://www.wikipedia.org. • http://braeburn.pha.jhu.edu/~ariess/R06/.

22. Thank you for your attention