Cosmic Inhomogeneities and Accelerating Expansion Ho Le Tuan Anh National University of Singapore PAQFT Nov 2008

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

Concordance model Homogeneous Isotropic Nearly flat: Ω total ~ 1 Dark energy density: Ω λ ~ 70% Use FLRW metric and Friedmann equations.

 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. Concordance model

 Weak points: Cosmological constant problem: λ extremely small. Cosmic coincidence problem: Ω λ + Ω m ≈ 1 Mysterious nature of dark energy:  What dark energy consists of ?  Whether it is constant or not?  Its equation of state ?  Due to Appearance of Cosmological Constant λ Concordance model

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…

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..

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. Ω 0 I H 0 II Model with a local void (Tomita’s model)

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.

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

Applying to the model: –Where: j: 1, 2 (inner and outer region) Ω 0 : Present matter density parameter λ 0 : Present dark energy density parameter Distances in Tomita’s model

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

Method to check the model Theoretical distance modulus: Observed distance modulus: Best-fit values are determined by χ 2 statistic:

Method to check the model Relation between σ mz and σ z : Probability distribution function: Eliminate nuisance parameters by taking integral: –y: nuisance parameters set. –μ 0 : the set of distance moduli used.

Supernova data and fitting Apply the model with Riess 2007 Gold sample Consider several cases with specific values of to avoid over-complication. –z 1 =0.067, 0.08, 0.1 – = 0.70, 0.082, 0.085, 0.90 –Different matter density profiles: Profile A B C D

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

Gold Sample R increases  Ω decreases and λ increases. Best-fit values (profile A): Rz1z1 H0H Lambda 02 Omega 02.

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. Rz1z1 H0H

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

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…

References 1.Alexander, S. a. B., Tirthabir and Notari, Alessio and Vaid, Deepak. 2007, arxiv: astro-ph/ Alnes, H., Amarzguioui, M., & Gron, O. 2006, Physical Review D, 73 3.Celerier, M.-N. 2007, arxiv: astro-ph/ Celerier, M. N. 2000, Astronomy and Astrophysics, 353, 63 5.Liddle, A. 2003, An introduction to modern cosmology (Wiley) 6.Moffat, J. W. 2006, Journal of Cosmology and Astroparticle Physics, arxiv: astro-ph/ Peebles, P. J. E. 1993, Principles of physical cosmology (Princeton University Press) 8.Riess, A. G., et al. 1998, Astronomical Journal, 116, , Astrophysical Journal, 659, , Astrophysical Journal, 607, Roos, M. 2003, Introduction to cosmology (Wiley) 12.Tomita, K. 2000, Astrophysical Journal, 529, , Astrophysical Journal, 529, , Progress of Theoretical Physics, 106, , Monthly Notices of the Royal Astronomical Society, 326, Tomita, K., Asada, H., & Hamana, T in Workshop on Gravitational Lens Phenomena and High-Redshift Universe, Distances in inhomogeneous cosmological models (Kyoto, Japan: Progress Theoretical Physics Publication Office), Wood-Vasey, W. M., et al. 2007, Astrophysical Journal, 666,

Thank you for your attention