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

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Cosmic inhomogeneities and accelerating expansion

Cosmic Inhomogeneities and Accelerating Expansion

Ho Le Tuan Anh

National University of Singapore

PAQFT 27-29 Nov 2008


Outline
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
Concordance model

  • Homogeneous

  • Isotropic

  • Nearly flat:

    Ωtotal ~ 1

  • Dark energy density:

    Ωλ ~ 70%

  • Use FLRW metric and Friedmann equations.


Concordance model1
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.


Concordance model2
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


Solutions of dark energy problems
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
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..


Model with a local void tomita s model
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


Sne and accelerating expansion
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
Distances in Tomita’s model

  • Angular Distance:

    • General definition:

      Where: λ: Affine parameter

      θ: Expansion parameter

  • Luminosity Distance:


Distances in tomita s model1
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


Boundary and initial conditions
Boundary and Initial conditions

  • Redshift at the shell are equal:

  • For :

  • For :

     Numerically solving equations (1), we can obtain angular and luminosity distance.


Method to check the model
Method to check the model

  • Theoretical distance modulus:

  • Observed distance modulus:

  • Best-fit values are determined by χ2 statistic:


Method to check the model1
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.


Supernova data and fitting
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:


Gold sample 182 sne
Gold Sample (182 SNe)

.

Dark Energy density - Matter density

Confidence contours with 68.3% & 95.4% CL (Profile A)


Gold sample
Gold Sample

.

  • R increases  Ω decreases and λ increases.

  • Best-fit values (profile A):

Lambda02

Omega02


Comments on results
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.


Comparison with riess 98 sne sample
Comparison with Riess 98 SNe sample

  • New confidence contours are much more compact than old ones  narrower constraints on parameters space.


Conclusion and discussion
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
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/.



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