We study effects of inhomogeneities on distance measures in an exact relativistic Swiss-cheese mo... more We 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 LCDM background dynamics, and the `holes' are non-symmetric 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, and we explore a small additional effect due time evolution of the structures. We study the probability distributions of Δμ=μ_LCDM-μ_SC for sources at different redshifts in various Swiss-cheese constructions, where the light beams travel through a large number of randomly oriented holes with random impact parameters. We find fo...
Monthly Notices of the Royal Astronomical Society, 2012
The weak lensing signal (cosmic shear) has been shown to be strongly contaminated by the various ... more The 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 2-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 dependences of the IA correlations has also been proposed as a means to remove the 2-point IA contamination from the lensing signal. We explore here the redshift dependences of the IA and lensing bispectra in order to propose a self-calibration of the IA auto-correlations at the 3-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 |∆z P | 0.2. Using conservative estimates of photoz accuracy, we describe the 3-point self-calibration technique for the total IA signal, which can be accomplished through lensing tomography of photo-z bin size ∼ 0.01. We find that the 3-point self-calibration can function at the accuracy of the 2-point technique with modest constraints in redshift separation. This allows the 3-point IA auto-correlation self-calibration technique proposed here to significantly reduce the contamination of the IA contamination to the weak lensing bispectrum.
Monthly Notices of the Royal Astronomical Society, 2012
The intrinsic alignment (IA) of galaxies has been shown to be a significant barrier to precision ... more The intrinsic alignment (IA) of galaxies has been shown to be a significant barrier to precision cosmic shear measurements. (Zhang, 2010, ApJ, 720, 1090) proposed a selfcalibration 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-densitydensity 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 selfcalibration 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 percent level. The self-calibration is less accurate for adjacent bins, but still allows for a factor of three reduction in the IA contamination. The self-calibration thus promises to be an efficient technique to isolate both the 2-point and 3-point intrinsic alignment signals from weak lensing measurements.
Cosmic shear, or weak lensing by large-scale structure, has been used to constrain the matter pow... more Cosmic shear, or weak lensing by large-scale structure, has been used to constrain the matter power spectrum normalization around z ˜ 1, and future surveys are being planned to allow high signal-to-noise measurements of cosmic shear to constrain the equation of state of dark energy. One potential systematic error is the correlation between the intrinsic ellipticities of galaxies and the density field that causes gravitational lensing (GI correlation). We describe the original detection of GI correlations to 60/h Mpc scales using galaxies from the Main spectroscopic sample of the Sloan Digital Sky Survey (SDSS) around z ˜ 0.1, followed by a measurement of the scaling with luminosity and redshift for the red galaxies in the SDSS Luminous Red Galaxy sample around z ˜ 0.25. This highly statistically significant detection of GI correlations for galaxies brighter than L* has a sign predicted by theoretical models. The GI correlation could cause the existing lensing surveys at z ˜ 1 to underestimate the linear amplitude of fluctuations by as much as 20% depending on the source sample used. The GI contamination is dominated by the brightest galaxies, possibly due to anisotropic infall along filaments, although other sources of contamination cannot be excluded at this point. Unlike autocorrelations between galaxy intrinsic ellipticities (II correlations), the GI correlations cannot be eliminated by cross-correlating galaxy samples at different redshifts, and in fact are enhanced by this procedure. We discuss methods for eliminating GI contamination in current and future weak lensing surveys, particularly those with data in multiple passbands that allow for the exclusion of the brightest red galaxies, and show what fraction of a typical survey would need to be excluded to reduce the contamination to the sub-percent levels needed for precision cosmology.
One of the outstanding problems in general relativistic cosmology is that of the averaging. That ... more One of the outstanding problems in general relativistic cosmology is that of the averaging. That is, how the lumpy universe that we observe at small scales averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The root of the problem is that averaging does not commute with the Einstein equations that govern the dynamics of the model. This leads to the well-know question of backreaction in cosmology. In this work, we approach the problem using the covariant framework of Macroscopic Gravity (MG). We use its cosmological solution with a flat FLRW macroscopic background where the result of averaging cosmic inhomogeneities has been encapsulated into a backreaction density parameter denoted ΩA. We constrain this averaged universe using available cosmological data sets of expansion and growth including, for the first time, a full CMB analysis from Planck temperature anisotropy and polarization data, the supernovae data from Union 2.1, the galaxy power spectrum from WiggleZ, the weak lensing tomography shear-shear cross correlations from the CFHTLenS survey and the baryonic acoustic oscillation data from 6Df, SDSS DR7 and BOSS DR9. We find that −0.0155 ≤ ΩA ≤ 0 (at the 68% CL) thus providing a tight upper-bound on the backreaction term. We also find that the term is strongly correlated with cosmological parameters such ΩΛ, σ8 and H0. While small, a backreaction density parameter of a few percent should be kept in consideration along with other systematics for precision cosmology.
We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmologic... more We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmological models. The proposed cosmological construction is based on the observer past null cone. A known difficulty in using inhomogeneous models is that the null geodesic equation is not integrable in general. Our choice of null coordinates solves the radial ingoing null geodesic by construction. Furthermore, we use an approach where the velocity field is uniquely calculated from the metric rather than put in by hand. Conveniently, this allows us to explore models in a non-comoving frame of reference. In this frame, we find that the velocity field has shear, acceleration and expansion rate in general. We show that a comoving frame is not compatible with expanding perfect fluid models in the coordinates proposed and dust models are simply not possible. We describe the models in a non-comoving frame. We use the dust models in a non-comoving frame to outline a fitting procedure.
The contribution of the cosmological constant to the deflection angle and the time delays are der... more The contribution of the cosmological constant to the deflection angle and the time delays are derived from the integration of the gravitational potential as well as from Fermat's Principle. The findings are in agreement with recent results using exact solutions to Einstein's equations and reproduce precisely the new Λ-term in the bending angle and the lens equation. The consequences on time delay expressions are explored. While it is known that Λ contributes to the gravitational time delay, it is shown here that a new Λ-term appears in the geometrical time delay as well. Although these newly derived terms are perhaps small for current observations, they do not cancel out as previously claimed. Moreover, as shown before, at galaxy cluster scale, the Λ contribution can be larger than the second-order term in the Einstein deflection angle for several cluster lens systems. PACS numbers: 95.30.Sf,98.80.Es,98.62.Sb
Associated with the cosmic acceleration are the old and new cosmological constant problems, recen... more Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component while the new problem is related to this magnitude being of the same order of the matter energy density during the present epoch of cosmic evolution. Current plans to measure the equation of state or density parameters certainly constitute an important approach; however, as we discuss, this approach is faced with serious feasibility challenges and is limited in the type of conclusive answers it could provide. Therefore, is it really too early to seek actively for new tests and approaches to these problems? In view of the difficulty of this endeavor, we argue in this work that a good place to start is by questioning some of the assumptions underlying the formulation of these problems and finding new ways to put this questioning to the test. First, we calculate how much fine tuning the cosmic coincidence problem represents. Next, we discuss the potential of some cosmological probes such as weak gravitational lensing to identify novel tests to probe dark energy questions and assumptions and provide an example of consistency tests. Then, motivated by some theorems in General Relativity, we discuss if the full identification of the cosmological constant with vacuum energy is unquestionable. We discuss some implications of the simplest solution for the principles of General Relativity. Also, we point out the relevance of experiments at the interface of astrophysics and quantum field theory, such as the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions.
We expand previous work on an inverse approach to Einstein Field Equations where we include fluid... more We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of class B1. Although restricted, these spacetimes include many exact solutions of interest to compact object studies and to cosmological models studies. The question explored here is as follows: given a spacetime metric, what fluid flow (timelike congruence), if any, could generate the spacetime via Einstein's equations. We calculate the flow from the condition of a vanishing anisotropic stress tensor and give results in terms of the metric functions in the three canonical types of coordinates. A condition for perfect fluid sources is also provided. The framework developed is algorithmic and suited for the study and validation of exact solutions using computer algebra systems. The framework can be applied to solutions in comoving and non-comoving frames of reference, and examples in different types of coordinates are worked out.
We report new results on the effect of the cosmological constant Lambda on the bending of light b... more We report new results on the effect of the cosmological constant Lambda on the bending of light by a spherically symmetric mass. We show that when the Schwarzschild-de Sitter geometry is taken into account, Lambda does indeed contribute to the bending of light. We use this result to discuss an amended lens equation and new time delay expressions. Although the
We compare higher order gravity models to observational constraints from magnitude-redshift super... more We compare higher order gravity models to observational constraints from magnitude-redshift supernova data, distance to the last scattering surface of the CMB, and Baryon Acoustic Oscillations. We follow a recently proposed systematic approach to higher order gravity models based on minimal sets of curvature invariants, and select models that pass some physical acceptability conditions (free of ghost instabilities, real and
The question of whether or not the cosmological constant affects the bending of light around a co... more The question of whether or not the cosmological constant affects the bending of light around a concentrated mass has been the subject of some recent papers. We present here a simple, specific and transparent example where $\Lambda$ bending clearly takes place, and where it is clearly neither a coordinate effect nor an aberration effect. We then show that in some
We present new results on how well cosmic shear tomography can improve dark energy parameter cons... more We present new results on how well cosmic shear tomography can improve dark energy parameter constraints. In view of the parameterization dependence problems, we probe the dark energy using its density and also two variants of its equation of state. For the former, we model the density as a continuous function interpolated using 2 dimensionless amplitude parameters evaluated at equally spaced redshits. Unlike previous studies, we look here for combinations of experiments that will bring the 2 sigma errors on these parameters to a satisfactory level of precision, say 0.02. Many dark energy models occupy a very narrow range of this parameter sub-space, and only such precision will decisively settle the question. For CMB, we consider future constraints from one year of data from Planck, 8 years of data from WMAP, and one year of data from the Atacama Cosmology Telescope (ACT). We use two sets of 2000 supernovae with maximum redshifts 0.8 and 1.5 respectively, and consider two cosmic shear reference surveys: a wide survey with two tomographic bins and a deep survey with 10 bins. The 2-sigma constraints found from Planck, supernovae, and the wide lensing survey are impressive but not enough to close the question. When the deep survey with 10 bin tomography is used, the constraints reduce to the required level of precision. Thus, we find that after the combination of the three probes, cosmic shear tomography with many bins and several thousands square degrees can add the necessary improvement to the constraints on dark energy. However, the probes considered here are faced with serious systematic effects that need to be well understood and tightly controlled in order to match the statistical accuracy and make these constraints achievable.
We report new results on the effect of the cosmological constant Lambda on the bending of light b... more We report new results on the effect of the cosmological constant Lambda on the bending of light by a spherically symmetric mass. Contrarily to previous claims, we show that when the Schwarzschild-de Sitter geometry is taken into account, Lambda does indeed contribute to the bending of light. We use this result to derive an amended lens equation in which the contribution of Lambda to the Einstein deflection angle is taken into account. We apply the result to observations of Einstein radii around several systems where the lens is a distant galaxy or a cluster of galaxies. We find that the contribution of the Lambda-term to the bending angle is larger than the second-order term for many lens systems. Using these observations of bending angles, we derive new limits on the value of the cosmological constant. These limits constitute the best observational upper bound on Lambda after cosmological constraints and are only two orders of magnitude away from the value determined by those cosmological constraints. Next, we show that the result expands to the time delay expressions. While it is known that Lambda contributes to the gravitational time delay, it is shown here that a new Lambda-term appears in the geometrical time delay as well. Although these newly derived terms are perhaps small for current observations, they do not cancel out. We show that our results derive from various methods including the exact matching of solutions to Einstein's equations, approximations used in gravitational lensing, and Fermat's Principle.
We study effects of inhomogeneities on distance measures in an exact relativistic Swiss-cheese mo... more We 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 LCDM background dynamics, and the `holes' are non-symmetric 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, and we explore a small additional effect due time evolution of the structures. We study the probability distributions of Δμ=μ_LCDM-μ_SC for sources at different redshifts in various Swiss-cheese constructions, where the light beams travel through a large number of randomly oriented holes with random impact parameters. We find fo...
Monthly Notices of the Royal Astronomical Society, 2012
The weak lensing signal (cosmic shear) has been shown to be strongly contaminated by the various ... more The 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 2-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 dependences of the IA correlations has also been proposed as a means to remove the 2-point IA contamination from the lensing signal. We explore here the redshift dependences of the IA and lensing bispectra in order to propose a self-calibration of the IA auto-correlations at the 3-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 |∆z P | 0.2. Using conservative estimates of photoz accuracy, we describe the 3-point self-calibration technique for the total IA signal, which can be accomplished through lensing tomography of photo-z bin size ∼ 0.01. We find that the 3-point self-calibration can function at the accuracy of the 2-point technique with modest constraints in redshift separation. This allows the 3-point IA auto-correlation self-calibration technique proposed here to significantly reduce the contamination of the IA contamination to the weak lensing bispectrum.
Monthly Notices of the Royal Astronomical Society, 2012
The intrinsic alignment (IA) of galaxies has been shown to be a significant barrier to precision ... more The intrinsic alignment (IA) of galaxies has been shown to be a significant barrier to precision cosmic shear measurements. (Zhang, 2010, ApJ, 720, 1090) proposed a selfcalibration 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-densitydensity 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 selfcalibration 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 percent level. The self-calibration is less accurate for adjacent bins, but still allows for a factor of three reduction in the IA contamination. The self-calibration thus promises to be an efficient technique to isolate both the 2-point and 3-point intrinsic alignment signals from weak lensing measurements.
Cosmic shear, or weak lensing by large-scale structure, has been used to constrain the matter pow... more Cosmic shear, or weak lensing by large-scale structure, has been used to constrain the matter power spectrum normalization around z ˜ 1, and future surveys are being planned to allow high signal-to-noise measurements of cosmic shear to constrain the equation of state of dark energy. One potential systematic error is the correlation between the intrinsic ellipticities of galaxies and the density field that causes gravitational lensing (GI correlation). We describe the original detection of GI correlations to 60/h Mpc scales using galaxies from the Main spectroscopic sample of the Sloan Digital Sky Survey (SDSS) around z ˜ 0.1, followed by a measurement of the scaling with luminosity and redshift for the red galaxies in the SDSS Luminous Red Galaxy sample around z ˜ 0.25. This highly statistically significant detection of GI correlations for galaxies brighter than L* has a sign predicted by theoretical models. The GI correlation could cause the existing lensing surveys at z ˜ 1 to underestimate the linear amplitude of fluctuations by as much as 20% depending on the source sample used. The GI contamination is dominated by the brightest galaxies, possibly due to anisotropic infall along filaments, although other sources of contamination cannot be excluded at this point. Unlike autocorrelations between galaxy intrinsic ellipticities (II correlations), the GI correlations cannot be eliminated by cross-correlating galaxy samples at different redshifts, and in fact are enhanced by this procedure. We discuss methods for eliminating GI contamination in current and future weak lensing surveys, particularly those with data in multiple passbands that allow for the exclusion of the brightest red galaxies, and show what fraction of a typical survey would need to be excluded to reduce the contamination to the sub-percent levels needed for precision cosmology.
One of the outstanding problems in general relativistic cosmology is that of the averaging. That ... more One of the outstanding problems in general relativistic cosmology is that of the averaging. That is, how the lumpy universe that we observe at small scales averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The root of the problem is that averaging does not commute with the Einstein equations that govern the dynamics of the model. This leads to the well-know question of backreaction in cosmology. In this work, we approach the problem using the covariant framework of Macroscopic Gravity (MG). We use its cosmological solution with a flat FLRW macroscopic background where the result of averaging cosmic inhomogeneities has been encapsulated into a backreaction density parameter denoted ΩA. We constrain this averaged universe using available cosmological data sets of expansion and growth including, for the first time, a full CMB analysis from Planck temperature anisotropy and polarization data, the supernovae data from Union 2.1, the galaxy power spectrum from WiggleZ, the weak lensing tomography shear-shear cross correlations from the CFHTLenS survey and the baryonic acoustic oscillation data from 6Df, SDSS DR7 and BOSS DR9. We find that −0.0155 ≤ ΩA ≤ 0 (at the 68% CL) thus providing a tight upper-bound on the backreaction term. We also find that the term is strongly correlated with cosmological parameters such ΩΛ, σ8 and H0. While small, a backreaction density parameter of a few percent should be kept in consideration along with other systematics for precision cosmology.
We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmologic... more We use null spherical (observational) coordinates to describe a class of inhomogeneous cosmological models. The proposed cosmological construction is based on the observer past null cone. A known difficulty in using inhomogeneous models is that the null geodesic equation is not integrable in general. Our choice of null coordinates solves the radial ingoing null geodesic by construction. Furthermore, we use an approach where the velocity field is uniquely calculated from the metric rather than put in by hand. Conveniently, this allows us to explore models in a non-comoving frame of reference. In this frame, we find that the velocity field has shear, acceleration and expansion rate in general. We show that a comoving frame is not compatible with expanding perfect fluid models in the coordinates proposed and dust models are simply not possible. We describe the models in a non-comoving frame. We use the dust models in a non-comoving frame to outline a fitting procedure.
The contribution of the cosmological constant to the deflection angle and the time delays are der... more The contribution of the cosmological constant to the deflection angle and the time delays are derived from the integration of the gravitational potential as well as from Fermat's Principle. The findings are in agreement with recent results using exact solutions to Einstein's equations and reproduce precisely the new Λ-term in the bending angle and the lens equation. The consequences on time delay expressions are explored. While it is known that Λ contributes to the gravitational time delay, it is shown here that a new Λ-term appears in the geometrical time delay as well. Although these newly derived terms are perhaps small for current observations, they do not cancel out as previously claimed. Moreover, as shown before, at galaxy cluster scale, the Λ contribution can be larger than the second-order term in the Einstein deflection angle for several cluster lens systems. PACS numbers: 95.30.Sf,98.80.Es,98.62.Sb
Associated with the cosmic acceleration are the old and new cosmological constant problems, recen... more Associated with the cosmic acceleration are the old and new cosmological constant problems, recently put into the more general context of the dark energy problem. In broad terms, the old problem is related to an unexpected order of magnitude of this component while the new problem is related to this magnitude being of the same order of the matter energy density during the present epoch of cosmic evolution. Current plans to measure the equation of state or density parameters certainly constitute an important approach; however, as we discuss, this approach is faced with serious feasibility challenges and is limited in the type of conclusive answers it could provide. Therefore, is it really too early to seek actively for new tests and approaches to these problems? In view of the difficulty of this endeavor, we argue in this work that a good place to start is by questioning some of the assumptions underlying the formulation of these problems and finding new ways to put this questioning to the test. First, we calculate how much fine tuning the cosmic coincidence problem represents. Next, we discuss the potential of some cosmological probes such as weak gravitational lensing to identify novel tests to probe dark energy questions and assumptions and provide an example of consistency tests. Then, motivated by some theorems in General Relativity, we discuss if the full identification of the cosmological constant with vacuum energy is unquestionable. We discuss some implications of the simplest solution for the principles of General Relativity. Also, we point out the relevance of experiments at the interface of astrophysics and quantum field theory, such as the Casimir effect in gravitational and cosmological contexts. We conclude that challenging some of the assumptions underlying the cosmological constant problems and putting them to the test may prove useful and necessary to make progress on these questions.
We expand previous work on an inverse approach to Einstein Field Equations where we include fluid... more We expand previous work on an inverse approach to Einstein Field Equations where we include fluids with energy flux and consider the vanishing of the anisotropic stress tensor. We consider the approach using warped product spacetimes of class B1. Although restricted, these spacetimes include many exact solutions of interest to compact object studies and to cosmological models studies. The question explored here is as follows: given a spacetime metric, what fluid flow (timelike congruence), if any, could generate the spacetime via Einstein's equations. We calculate the flow from the condition of a vanishing anisotropic stress tensor and give results in terms of the metric functions in the three canonical types of coordinates. A condition for perfect fluid sources is also provided. The framework developed is algorithmic and suited for the study and validation of exact solutions using computer algebra systems. The framework can be applied to solutions in comoving and non-comoving frames of reference, and examples in different types of coordinates are worked out.
We report new results on the effect of the cosmological constant Lambda on the bending of light b... more We report new results on the effect of the cosmological constant Lambda on the bending of light by a spherically symmetric mass. We show that when the Schwarzschild-de Sitter geometry is taken into account, Lambda does indeed contribute to the bending of light. We use this result to discuss an amended lens equation and new time delay expressions. Although the
We compare higher order gravity models to observational constraints from magnitude-redshift super... more We compare higher order gravity models to observational constraints from magnitude-redshift supernova data, distance to the last scattering surface of the CMB, and Baryon Acoustic Oscillations. We follow a recently proposed systematic approach to higher order gravity models based on minimal sets of curvature invariants, and select models that pass some physical acceptability conditions (free of ghost instabilities, real and
The question of whether or not the cosmological constant affects the bending of light around a co... more The question of whether or not the cosmological constant affects the bending of light around a concentrated mass has been the subject of some recent papers. We present here a simple, specific and transparent example where $\Lambda$ bending clearly takes place, and where it is clearly neither a coordinate effect nor an aberration effect. We then show that in some
We present new results on how well cosmic shear tomography can improve dark energy parameter cons... more We present new results on how well cosmic shear tomography can improve dark energy parameter constraints. In view of the parameterization dependence problems, we probe the dark energy using its density and also two variants of its equation of state. For the former, we model the density as a continuous function interpolated using 2 dimensionless amplitude parameters evaluated at equally spaced redshits. Unlike previous studies, we look here for combinations of experiments that will bring the 2 sigma errors on these parameters to a satisfactory level of precision, say 0.02. Many dark energy models occupy a very narrow range of this parameter sub-space, and only such precision will decisively settle the question. For CMB, we consider future constraints from one year of data from Planck, 8 years of data from WMAP, and one year of data from the Atacama Cosmology Telescope (ACT). We use two sets of 2000 supernovae with maximum redshifts 0.8 and 1.5 respectively, and consider two cosmic shear reference surveys: a wide survey with two tomographic bins and a deep survey with 10 bins. The 2-sigma constraints found from Planck, supernovae, and the wide lensing survey are impressive but not enough to close the question. When the deep survey with 10 bin tomography is used, the constraints reduce to the required level of precision. Thus, we find that after the combination of the three probes, cosmic shear tomography with many bins and several thousands square degrees can add the necessary improvement to the constraints on dark energy. However, the probes considered here are faced with serious systematic effects that need to be well understood and tightly controlled in order to match the statistical accuracy and make these constraints achievable.
We report new results on the effect of the cosmological constant Lambda on the bending of light b... more We report new results on the effect of the cosmological constant Lambda on the bending of light by a spherically symmetric mass. Contrarily to previous claims, we show that when the Schwarzschild-de Sitter geometry is taken into account, Lambda does indeed contribute to the bending of light. We use this result to derive an amended lens equation in which the contribution of Lambda to the Einstein deflection angle is taken into account. We apply the result to observations of Einstein radii around several systems where the lens is a distant galaxy or a cluster of galaxies. We find that the contribution of the Lambda-term to the bending angle is larger than the second-order term for many lens systems. Using these observations of bending angles, we derive new limits on the value of the cosmological constant. These limits constitute the best observational upper bound on Lambda after cosmological constraints and are only two orders of magnitude away from the value determined by those cosmological constraints. Next, we show that the result expands to the time delay expressions. While it is known that Lambda contributes to the gravitational time delay, it is shown here that a new Lambda-term appears in the geometrical time delay as well. Although these newly derived terms are perhaps small for current observations, they do not cancel out. We show that our results derive from various methods including the exact matching of solutions to Einstein's equations, approximations used in gravitational lensing, and Fermat's Principle.
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Papers by Mustapha Ishak