# 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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### Recent Submissions

Item First Detection of the GI-Type of Intrinsic Alignments of Galaxies Using the Selfcalibration Method in a Photometric Galaxy Survey(Institute of Physics, 2020-08-05) Pedersen, Eske M.; Yao, Ji; Ishak-Boushaki, Mustapha; 0000-0002-6024-466X (Ishak-Boushaki, M); 0000-0002-7336-2796 (Yao, J); Pedersen, Eske M.; Yao, Ji; Ishak-Boushaki, MustaphaWeak gravitational lensing is one of the most promising cosmological probes to constrain dark matter, dark energy, and the nature of gravity at cosmic scales. Intrinsic alignments (IAs) of galaxies have been recognized as one of the most serious systematic effects facing gravitational lensing. Such alignments must be isolated and removed to obtain a pure lensing signal. Furthermore, the alignments are related to the processes of galaxy formation, so their extracted signal can help in understanding such formation processes and improving their theoretical modeling. We report in this Letter the first detection of the gravitational shear–intrinsic shape (GI) correlation and the intrinsic shape–galaxy density (Ig) correlation using the self-calibration method in a photometric redshift survey. These direct measurements are made from the KiDS-450 photometric galaxy survey with a significance of 3.65σ in the third bin for the Ig correlation, and 3.51σ for the GI cross-correlation between the third and fourth bins. The self-calibration method uses the information available from photometric surveys without needing to specify an IA model and will play an important role in validating IA models and IA mitigation in future surveys such as the Rubin Observatory Legacy Survey of Space and Time, Euclid, and WFIRST.Item Testing Gravity Theories Using Tensor Perturbations(American Physical Society, 2016-12-21) Lin, Weikang; Ishak-Boushaki, Mustapha; 0000 0001 2874 3832 (Ishak-Boushaki, M); Lin, Weikang; Ishak-Boushaki, MustaphaPrimordial gravitational waves constitute a promising probe of the very early Universe and the laws of gravity. We study in this work changes to tensor-mode perturbations that can arise in various proposed modified gravity theories. These include additional friction effects, nonstandard dispersion relations involving a massive graviton, a modified speed, and a small-scale modification. We introduce a physically motivated parametrization of these effects and use current available data to obtain exclusion regions in the parameter spaces. Taking into account the foreground subtraction, we then perform a forecast analysis focusing on the tensor-mode modified-gravity parameters as constrained by the future experiments COrE, Stage-IV and PIXIE. For a fiducial value of the tensor-to-scalar ratio r = 0.01, we find that an additional friction of 3.5-4.5% compared to GR will be detected at 3-σ by these experiments, while a decrease in friction will be more difficult to detect. The speed of gravitational waves needs to be by 5-15% different from the speed of light for detection. We find that the minimum detectable graviton mass is about 7.8 - 9.7 × 10⁻³³ eV, which is of the same order of magnitude as the graviton mass that allows massive gravity theories to produce late-time cosmic acceleration. Finally, we study the tensor-mode perturbations in modified gravity during inflation using our parametrization. We find that, in addition to being related to r, the tensor spectral index would be related to the friction parameter ν₀ by nT = -3ν₀ - r/8. Assuming that the friction parameter is unchanged throughout the history of the Universe, and that ν₀ is much larger than r, the future experiments considered here will be able to distinguish this modified-gravity consistency relation from the standard inflation consistency relation, and thus can be used as a further test of modified gravity. In summary, tensor-mode perturbations and cosmic-microwave-background B-mode polarization provide a complementary avenue to test gravity theories. © 2016 American Physical Society.Item Expansion and Growth of Structure Observables in a Macroscopic Gravity Averaged Universe(American Physical Society, 2015-03-30) Wijenayake, Tharake; Ishak-Boushaki, Mustapha; 0000 0001 2874 3832 (Ishak-Boushaki, M); Wijenayake, Tharake; Ishak-Boushaki, MustaphaWe investigate the effect of averaging inhomogeneities on expansion and large-scale structure growth observables using the exact and covariant framework of macroscopic gravity (MG). It is well known that applying the Einstein's equations and spatial averaging do not commute and lead to the averaging problem and backreaction terms. For the MG formalism applied to the Friedman-Lemaitre-Robertson-Walker (FLRW) metric, the extra term can be encapsulated as an averaging density parameter denoted Ω(A). An exact isotropic cosmological solution of MG for the flat FLRW metric is already known in the literature; we derive here an anisotropic exact solution. Using the isotropic solution, we compare the expansion history to current available data of distances to supernovae, baryon acoustic oscillations, cosmic microwave background last scattering surface data, and Hubble constant measurements, and find -0.05 ≤ Ω_A ≤ 0.07 (at the 95% confidence level). For the flat metric case this reduces to -0.03 ≤ Ω_A ≤ 0.05. The positive part of the intervals can be rejected if a mathematical (and physical) prior is taken into account. We also find that the inclusion of this term in the fits can shift the values of the usual cosmological parameters by a few to several percents. Next, we derive an equation for the growth rate of large-scale structure in MG that includes a term due to the averaging and assess its effect on the evolution of the growth compared to that of the Lambda cold dark matter (Λ CDM) concordance model. We find that an Ω_A term of an amplitude range of [-0.04; -0.02] lead to a relative deviation of the growth from that of the Λ CDM of up to 2%-4% at late times. Thus, the shift in the growth could be of comparable amplitude to that caused by similar changes in cosmological parameters like the dark energy density parameter or its equation of state. The effect could also be comparable in amplitude to some systematic effects considered for future surveys. This indicates that the averaging term and its possible effect need to be tightly constrained in future precision cosmological studies.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 Cross-Correlation between Cosmic Microwave Background Lensing and Galaxy Intrinsic Alignment as a Contaminant to Gravitational Lensing Cross-Correlated Probes of the Universe(American Physical Society, 2014-03-25) Troxel, M. A.; Ishak-Boushaki, Mustapha; 0000 0001 2874 3832 (Ishak-Boushaki, M); Troxel, M. A.; Ishak-Boushaki, MustaphaWe introduce here a cross-correlation term between CMB lensing and galaxy intrinsic alignment, noted here as φl. This effect acts as a contaminant to the cross correlation between CMB lensing and galaxy lensing. The latter cross correlation has recently been detected for the first time, and measurements will greatly improve as the area of overlap between galaxy and CMB surveys increases and measurements of the CMB polarization become more significant. This will constitute a powerful probe for studying the structure and evolution of the universe. The magnitude of the φl term is found to be about 15% of the pure CMB lensing- galaxy lensing component and acts to reduce the magnitude of its measured spectrum. This offset in the spectrum will strongly impact its use for precision cosmological study if left unmitigated. We also propose here a method to calibrate this φl contamination through the use of a scaling relation that allows one to reduce the impact of φl by a factor of 20 or more in all redshift bins, which would reduce its magnitude down to detection limits in almost all cases. This will allow the full use of this probe for precision cosmology.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.Item Growth of Structure in the Szekeres Class-II Inhomogeneous Cosmological Models and the Matter-Dominated Era(2012-04-03) Ishak-Boushaki, Mustapha; Peel, Austin; 0000 0001 2874 3832 (Ishak-Boushaki, M); Ishak-Boushaki, Mustapha; Peel, AustinThis study belongs to a series devoted to using the Szekeres inhomogeneous models in order to develop a theoretical framework where cosmological observations can be investigated with a wider range of possible interpretations. While our previous work addressed the question of cosmological distances versus redshift in these models, the current study is a start at looking into the growth rate of large-scale structure. The Szekeres models are exact solutions to Einstein's equations that were originally derived with no symmetries. We use here a formulation of the Szekeres models that is due to Goode and Wainwright, who considered the models as exact perturbations of a Friedmann-Lemaître- Robertson-Walker (FLRW) background. Using the Raychaudhuri equation we write, for the two classes of the models, exact growth equations in terms of the under/overdensity and measurable cosmological parameters. The new equations in the overdensity split into two informative parts. The first part, while exact, is identical to the growth equation in the usual linearly perturbed FLRW models, while the second part constitutes exact nonlinear perturbations. We integrate numerically the full exact growth rate equations for the flat and curved cases. We find that for the matter-dominated cosmic era, the Szekeres growth rate is up to a factor of three to five stronger than the usual linearly perturbed FLRW cases, reflecting the effect of exact Szekeres nonlinear perturbations. We also find that the Szekeres growth rate with an Einstein-de Sitter background is stronger than that of the well-known nonlinear spherical collapse model, and the difference between the two increases with time. This highlights the distinction when we use general inhomogeneous models where shear and a tidal gravitational field are present and contribute to the gravitational clustering. Additionally, it is worth observing that the enhancement of the growth found in the Szekeres models during the matter-dominated era could suggest a substitute to the argument that dark matter is needed when using FLRW models to explain the enhanced growth and resulting large-scale structures that we observe today.Item Self-Calibration Technique for Three-Point Intrinsic Alignment Correlations in Weak Lensing Surveys(2011-11-15) Troxel, Michael A.; Ishak-Boushaki, Mustapha; 0000 0001 2874 3832 (Ishak-Boushaki, M); Troxel, Michael A.; Ishak-Boushaki, MustaphaThe intrinsic alignment (IA) of galaxies has been shown to be a significant barrier to precision cosmic shear measurements. Recently, Zhang proposed a self-calibration technique for the power spectrum to calculate the induced gravitational shear-galaxy intrinsic ellipticity correlation (GI) in weak lensing surveys with photo-z measurements, which is expected to reduce the IA contamination by at least a factor of 10 for currently proposed surveys. We confirm this using an independent analysis and propose an expansion to the self-calibration technique for the bispectrum in order to calculate the dominant IA gravitational shear-gravitational shear-intrinsic ellipticity correlation (GGI) contamination. We first establish an estimator to extract the galaxy density-density-intrinsic ellipticity (ggI) correlation from the galaxy ellipticity-density-density measurement for a photo-z galaxy sample. We then develop a relation between the GGI and ggI bispectra, which allows for the estimation and removal of the GGI correlation from the cosmic shear signal. We explore the performance of these two methods, compare to other possible sources of error, and show that the GGI self-calibration technique can potentially reduce the IA contamination by up to a factor of 5-10 for all but a few bin choices, thus reducing the contamination to the per cent level. The self-calibration is less accurate for adjacent bins, but still allows for a factor of 3 reduction in the IA contamination. The self-calibration thus promises to be an efficient technique to isolate both the two-point and three-point intrinsic alignment signals from weak lensing measurements. © 2011 The Authors Monthly Notices of the Royal Astronomical Society © 2011 RAS.Item Self-Calibration for Three-Point Intrinsic Alignment Autocorrelations in Weak Lensing Surveys(2012-06-08) Troxel, Michael A. .; Ishak-Boushaki, Mustapha; 0000 0001 2874 3832 (Ishak-Boushaki, M); Troxel, Michael A. .; Ishak-Boushaki, MustaphaThe weak lensing signal (cosmic shear) has been shown to be strongly contaminated by the various types of galaxy intrinsic alignment (IA) correlations, which poses a barrier to precision weak lensing measurements. The redshift dependence of the IA signal has been used at the two-point level to reduce this contamination by only measuring cross-correlations between large redshift bins, which significantly reduces the galaxy intrinsic ellipticity-intrinsic ellipticity (II) correlation. A self-calibration technique based on the redshift dependencies of the IA correlations has also been proposed as a means to remove the two-point IA contamination from the lensing signal. We explore here the redshift dependencies of the IA and lensing bispectra in order to propose a self-calibration of the IA autocorrelations at the three-point level (i.e. GGI, GII and III), which can be well understood without the assumption of any particular IA model. We find that future weak lensing surveys will be able to measure the distinctive IA redshift dependence over ranges of |Δ_ȥ^P| ≤ 0.2. Using conservative estimates of photo-ȥ accuracy, we describe the three-point self-calibration technique for the total IA signal, which can be accomplished through lensing tomography of photo-ȥ bin size ∼0.01. We find that the three-point self-calibration can function at the accuracy of the two-point technique with modest constraints in redshift separation. This allows the three-point IA autocorrelation self-calibration technique proposed here to significantly reduce the contamination of the IA contamination to the weak lensing bispectrum.Item Self-Calibrating the Gravitational Shear-Intrinsic Ellipticity-Intrinsic Ellipticity Cross-Correlation(2012-06-01) Troxel, Michael A.; Ishak-Boushaki, Mustapha; Troxel, Michael A.; Ishak-Boushaki, MustaphaWe extend the 3-point intrinsic alignment self-calibration technique to the gravitational shear-intrinsic ellipticity-intrinsic ellipticity (GII) bispectrum. While significantly decreased from using cross-correlations instead of autocorrelation in a single photo-z bin, the GII contamination persists in adjacent photo-z bins and must be accounted for and removed from the lensing signal. The proposed technique will allow the measurement and removal of the GII intrinsic alignment contamination from the cross-correlation weak lensing signal. We relate the GII and galaxy density-intrinsic ellipticity-intrinsic ellipticity (gII) bispectra through use of the galaxy bias, and develop the estimator necessary to isolate the gII bispectrum from observations. We find that the GII self-calibration technique performs at a level comparable to that of the gravitational shear-gravitational shear-intrinsic ellipticity correlation (GGI) self-calibration technique, with measurement error introduced through the gII estimator generally negligible when compared to minimum survey error. The accuracy of the relationship between the GII and gII bispectra typically allows the GII self-calibration to reduce the GII contamination by a factor of 10 or more for all adjacent photo-z bin combinations at ℓ > 300. For larger scales, we find that the GII contamination can be reduced by a factor of 3-5 or more. The GII self-calibration technique is complementary to the existing GGI self-calibration technique, which together will allow the total intrinsic alignment cross-correlation signal in 3-point weak lensing to be measured and removed.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 Spatial Curvature and Cosmological Tests of General Relativity(American Physical Society, 2012-03-23) Ishak-Boushaki, Mustapha; Dossett, Jason N.; 0000 0001 2874 3832 (Ishak-Boushaki, M); Ishak-Boushaki, Mustapha; Dossett, Jason N.It is well-known that allowing for spatial curvature affects constraints on cosmological parameters such as the dark energy equation of state parameters. Here we study the effect of curvature on constraints on parameters used to test general relativity (GR) at cosmological scales, commonly known as modified growth (MG) parameters. While current data taken in the context of the ΛCDM model points to a universe that is spatially flat, this constraint does not necessarily hold in modified gravity theories or even in relativistic inhomogeneous cosmological models. Using the latest cosmological data sets we find that MG parameters are correlated with the curvature parameter Ω_k and the constraints on the MG parameters are weakened compared to when Ω_k is not included in the parameter analysis. We next use various future simulated data sets, including cosmic microwave background, weak lensing, and Integrated Sachs-Wolfegalaxy cross-correlations, where the fiducial model is spatially curved but we assume a flat model when fitting the MG parameters. We find the assumption of a spatially flat model on a spatially curved universe does indeed cause an artificial shift in the constraints on the MG parameters, in some cases even producing an apparent deviation from GR in the MG parameter space. For our simulated data, tension with GR begins to manifest itself for fiducial models with |Ω k| ≥ 0:02 and apparent deviations appear for |Ω_k| ≥ 0:05. We find that for negatively curved models the apparent deviation is more significant. The manifestation of this apparent deviation from GR due to the assumption of spatial flatness above leads one to conclude that, when using future high-precision data to perform these tests, spatial curvature must be included in the parameter analysis along with the other core cosmological parameters and the MG parameters.