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Cosmic Inhomogeneities and Accelerating ExpansionPowerPoint Presentation

Cosmic Inhomogeneities and Accelerating Expansion

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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

- Conclusion and Discussion

Concordance model

- Homogeneous
- Isotropic
- Nearly flat:
Ωtotal ~ 1

- Dark energy density:
Ωλ ~ 70%

- Use FLRW metric and Friedmann equations.

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 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

- 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..

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

- 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

- General definition:
- Luminosity Distance:

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

- Where:

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

- Theoretical distance modulus:
- Observed distance modulus:
- Best-fit values are determined by χ2 statistic:

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

- 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)

.

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):

Lambda02

Omega02

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

- 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

- 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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