# Ishak-Boushaki, Mustapha

Permanent URI for this collectionhttps://hdl.handle.net/10735.1/2489

Mustapha Ishak-Boushaki is an Associate Professor in the Department of Physics. He also serves on the faculty of the UT Dallas Cosmology, Relativity, and Astrophysics Group. Dr. Ishak-Boushaki's research interests include:

- Gravitational Lensing and applications to cosmology.
- The Acceleration of the expansion of the Universe: Cosmological Constant, Dark Energy.
- Constraining cosmological parameters and cosmological models using probes such as gravitational lensing, the cosmic microwave background (CMB), and supernova searches.
- General Relativity and Cosmological Exact Solutions to Einstein's Equations.
- Higher dimensional cosmological models.
- Projects at the intersection of modern cosmology and General Relativity.
- Junction conditions for matching space-times and constructing wormholes and spacetime thin-shells.
- Computer Algebra (symbolic computing) and application to cosmology and general relativity.

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# Browsing Ishak-Boushaki, Mustapha by Author "Peel, Austin"

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Item Effect of Inhomogeneities on High Precision Measurements of Cosmological Distances(American Physical Society, 2014-12-30) Peel, Austin; Troxel, Michael A.; Ishak-Boushaki, Mustapha; Peel, Austin; Troxel, Michael A.; Ishak-Boushaki, MustaphaWe study effects of inhomogeneities on distance measures in an exact relativistic Swiss-cheese model of the Universe, focusing on the distance modulus. The model has ΛCDM background dynamics, and the "holes" are nonsymmetric structures described by the Szekeres metric. The Szekeres exact solution of Einstein's equations, which is inhomogeneous and anisotropic, allows us to capture potentially relevant effects on light propagation due to nontrivial evolution of structures in an exact framework. Light beams traversing a single Szekeres structure in different ways can experience either magnification or demagnification, depending on the particular path. Consistent with expectations, we find a shift in the distance modulus μ to distant sources due to demagnification when the light beam travels primarily through the void regions of our model. Conversely, beams are magnified when they propagate mainly through the overdense regions of the structures, and we explore a small additional effect due to time evolution of the structures. We then study the probability distributions of Δμ = μ_{ΛCDM} – μ_{SC} for sources at different redshifts in various Swiss-cheese constructions, where the light beams travel through a large number of randomly oriented Szekeres holes with random impact parameters. We find for Δμ the dispersions 0.004 ≤ σ_{Δμ} ≤ 0.008 mag for sources with redshifts 1.0 ≤ ȥ ≤ 1.5, which are smaller than the intrinsic dispersion of, for example, magnitudes of type Ia supernovae. The shapes of the distributions we obtain for our Swiss-cheese constructions are peculiar in the sense that they are not consistently skewed toward the demagnification side, as they are in analyses of lensing in cosmological simulations. Depending on the source redshift, the distributions for our models can be skewed to either the demagnification or the magnification side, reflecting a limitation of these constructions. This could be the result of requiring the continuity of Einstein's equations throughout the overall spacetime patchwork, which imposes the condition that compensating overdense shells must accompany the underdense void regions in the holes. The possibility to explore other uses of these constructions that could circumvent this limitation and lead to different statistics remains open.Item Large-Scale Growth Evolution in the Szekeres Inhomogeneous Cosmological Models with Comparison to Growth Data(American Physical Society, 2012-12-06) Peel, Austin; Ishak-Boushaki, Mustapha; Troxel, Michael; 0000 0001 2874 3832 (Ishak-Boushaki, M)We use the Szekeres inhomogeneous cosmological models to study the growth of large-scale structure in the universe including nonzero spatial curvature and a cosmological constant. In particular, we use the Goode and Wainwright formulation of the solution, as in this form the models can be considered to represent exact nonlinear perturbations of an averaged background. We identify a density contrast in both classes I and II of the models, for which we derive growth evolution equations. By including Λ, the time evolution of the density contrast as well as kinematic quantities of interest can be tracked through the matter- and Λ-dominated cosmic eras up to the present and into the future. In class I, we consider a localized cosmic structure representing an overdensity neighboring a central void, surrounded by an almost Friedmann-Lemaître-Robertson-Walker background, while for class II, the exact perturbations exist globally. In various models of class I and class II, the growth rate is found to be stronger in the matter-dominated era than that of the standard lambda-cold dark matter (ΛCDM) cosmology, and it is suppressed at later times due to the presence of the cosmological constant. We find that there are Szekeres models able to provide a growth history similar to that of ΛCDM while requiring less matter content and nonzero spatial curvature, which speaks to the importance of including the effects of large-scale inhomogeneities in analyzing the growth of large-scale structure. Using data for the growth factor f from redshift space distortions and the Lyman-α forest, we obtain best fit parameters for class II models and compare their ability to match observations with ΛCDM. We find that there is negligible difference between best fit Szekeres models with no priors and those for ΛCDM, both including and excluding Lyman-α data. We also find that the standard growth index γ parametrization cannot be applied in a simple way to the growth in Szekeres models, so a direct comparison of the function f to the data is performed. We conclude that the Szekeres models can provide an exact framework for the analysis of large-scale growth data that includes inhomogeneities and allows for different interpretations of observations. © 2012 American Physical Society.Item Stringent Restriction from the Growth of Large-Scale Structure on Apparent Acceleration in Inhomogeneous Cosmological Models(2013-12-19) Ishak-Boushaki, Mustapha; Peel, Austin; Troxel, M. A.; 0000 0001 2874 3832 (Ishak-Boushaki, M); Ishak-Boushaki, Mustapha; Peel, Austin; Troxel, M. A.Probes of cosmic expansion constitute the main basis for arguments to support or refute a possible apparent acceleration due to different expansion rates in the Universe as described by inhomogeneous cosmological models. We present in this Letter a separate argument based on results from an analysis of the growth rate of large-scale structure in the Universe as modeled by the inhomogeneous cosmological models of Szekeres. We use the models with no assumptions of spherical or axial symmetries. We find that while the Szekeres models can fit very well the observed expansion history without a Λ, they fail to produce the observed late-time suppression in the growth unless Λ is added to the dynamics. A simultaneous fit to the supernova and growth factor data shows that the cold dark matter model with a cosmological constant (ΛCDM) provides consistency with the data at a confidence level of 99.65%, while the Szekeres model without Λ achieves only a 60.46% level. When the data sets are considered separately, the Szekeres with no Λ fits the supernova data as well as the ΛCDM does, but provides a very poor fit to the growth data with only 31.31% consistency level compared to 99.99% for the ΛCDM. This absence of late-time growth suppression in inhomogeneous models without a Λ is consolidated by a physical explanation.