Cosmological Systematics Beyond Nuisance Parameters : Form Filling Functions

In the absence of any compelling physical model, cosmological systematics are often misrepresented as statistical effects and the approach of marginalising over extra nuisance systematic parameters is used to gauge the effect of the systematic. In this article we argue that such an approach is risky at best since the key choice of function can have a large effect on the resultant cosmological errors. As an alternative we present a functional form filling technique in which an unknown, residual, systematic is treated as such. Since the underlying function is unknown we evaluate the effect of every functional form allowed by the information available (either a hard boundary or some data). Using a simple toy model we introduce the formalism of functional form filling. We show that parameter errors can be dramatically affected by the choice of function in the case of marginalising over a systematic, but that in contrast the functional form filling approach is independent of the choice of basis set. We then apply the technique to cosmic shear shape measurement systematics and show that a shear calibration bias of |m(z)|< 0.001(1+z)^0.7 is required for a future all-sky photometric survey to yield unbiased cosmological parameter constraints to percent accuracy. A module associated with the work in this paper is available through the open source iCosmo code available at http://www.icosmo.org .Comment: 24 pages, 18 figures, accepted to MNRA

Constraining Scale-Dependent Non-Gaussianity with Future Large-Scale Structure and the CMB

We forecast combined future constraints from the cosmic microwave background and large-scale structure on the models of primordial non-Gaussianity. We study the generalized local model of non-Gaussianity, where the parameter f_NL is promoted to a function of scale, and present the principal component analysis applicable to an arbitrary form of f_NL(k). We emphasize the complementarity between the CMB and LSS by using Planck, DES and BigBOSS surveys as examples, forecast constraints on the power-law f_NL(k) model, and introduce the figure of merit for measurements of scale-dependent non-Gaussianity.Comment: 28 pages, 8 figures, 2 tables; v2: references update

Growth Rate of Large Scale Structure as a Powerful Probe of Dark Energy

The redshift evolution of the growth rate of the gravitational potential, d(D/a)/dz, is an excellent discriminator of dark energy parameters and, in principle, more powerful than standard classical tests of cosmology. This evolution is directly observable through the integrated Sachs-Wolfe effect in cosmic microwave background (CMB) anisotropies. We consider the prospects of measuring the growth rate via a novel method employed through measurements of CMB polarization towards galaxy clusters. The potentially achievable errors on dark energy parameters are comparable and fully complementary to those expected from other upcoming tests of dark energy, making this test a highly promising tool of precision cosmology.Comment: 4 pages, 2 figures, submitted to Phys. Rev. Let

Weak lensing, dark matter and dark energy

Weak gravitational lensing is rapidly becoming one of the principal probes of dark matter and dark energy in the universe. In this brief review we outline how weak lensing helps determine the structure of dark matter halos, measure the expansion rate of the universe, and distinguish between modified gravity and dark energy explanations for the acceleration of the universe. We also discuss requirements on the control of systematic errors so that the systematics do not appreciably degrade the power of weak lensing as a cosmological probe.Comment: Invited review article for the GRG special issue on gravitational lensing (P. Jetzer, Y. Mellier and V. Perlick Eds.). V3: subsection on three-point function and some references added. Matches the published versio

Systematic effects on dark energy from 3D weak shear

We present an investigation into the potential effect of systematics inherent in multi-band wide field surveys on the dark energy equation of state determination for two 3D weak lensing methods. The weak lensing methods are a geometric shear-ratio method and 3D cosmic shear. The analysis here uses an extension of the Fisher matrix framework to jointly include photometric redshift systematics, shear distortion systematics and intrinsic alignments. We present results for DUNE and Pan-STARRS surveys. We show that assuming systematic parameters are fixed, but possibly biased, results in potentially large biases in dark energy parameters. We quantify any potential bias by defining a Bias Figure of Merit. We also show the effect on the dark energy Figure of Merit of marginalising over each systematic parameter individually. We find that the largest effect on the Figure of Merit comes from uncertainty in the photometric redshift systematic parameters. These can reduce the Figure of Merit by up to a factor of 2 to 4 in both 3D weak lensing methods, if no informative prior on the systematic parameters is applied. Shear distortion systematics have a smaller overall effect. Intrinsic alignment effects can reduce the Figure of Merit by up to a further factor of 2. This, however, is a worst case scenario. By including prior information on systematic parameters the Figure of Merit can be recovered to a large extent. We conclude that, as a rule of thumb, given a realistic current understanding of intrinsic alignments and photometric redshifts, then including all three primary systematic effects reduces the Figure of Merit by at most a factor of 2, but that in reality this factor should be much less. [abridged]Comment: 20 pages, 11 figures, submitted to MNRA

Could dark energy be vector-like?

In this paper I explore whether a vector field can be the origin of the present stage of cosmic acceleration. In order to avoid violations of isotropy, the vector has be part of a ``cosmic triad'', that is, a set of three identical vectors pointing in mutually orthogonal spatial directions. A triad is indeed able to drive a stage of late accelerated expansion in the universe, and there exist tracking attractors that render cosmic evolution insensitive to initial conditions. However, as in most other models, the onset of cosmic acceleration is determined by a parameter that has to be tuned to reproduce current observations. The triad equation of state can be sufficiently close to minus one today, and for tachyonic models it might be even less than that. I briefly analyze linear cosmological perturbation theory in the presence of a triad. It turns out that the existence of non-vanishing spatial vectors invalidates the decomposition theorem, i.e. scalar, vector and tensor perturbations do not decouple from each other. In a simplified case it is possible to analytically study the stability of the triad along the different cosmological attractors. The triad is classically stable during inflation, radiation and matter domination, but it is unstable during (late-time) cosmic acceleration. I argue that this instability is not likely to have a significant impact at present.Comment: 28 pages, 6 figures. Uses RevTeX4. v2: Discussion about relation to phantoms added and additional references cite

New Constraints from High Redshift Supernovae and Lensing Statistics upon Scalar Field Cosmologies

We explore the implications of gravitationally lensed QSOs and high-redshift SNe Ia observations for spatially flat cosmological models in which a classically evolving scalar field currently dominates the energy density of the Universe. We consider two representative scalar field potentials that give rise to effective decaying $\Lambda$ (``quintessence'') models: pseudo-Nambu-Goldstone bosons ($V(\phi)=M^4(1+\cos (\phi /f))$) and an inverse power-law potential ($V(\phi)=M^{4+\alpha}\phi ^{-\alpha}$). We show that a large region of parameter space is consistent with current data if $\Omega_{m0} > 0.15$. On the other hand, a higher lower bound for the matter density parameter suggested by large-scale galaxy flows, $\Omega_{m0} > 0.3$, considerably reduces the allowed parameter space, forcing the scalar field behavior to approach that of a cosmological constant.Comment: 6 pages, 2 figures, submitted to PR

ALMA observations of lensed Herschel sources: testing the dark matter halo paradigm

With the advent of wide-area submillimetre surveys, a large number of high-redshift gravitationally lensed dusty star-forming galaxies have been revealed. Because of the simplicity of the selection criteria for candidate lensed sources in such surveys, identified as those with S500 μm > 100 mJy, uncertainties associated with the modelling of the selection function are expunged. The combination of these attributes makes submillimetre surveys ideal for the study of strong lens statistics. We carried out a pilot study of the lensing statistics of submillimetre-selected sources by making observations with the Atacama Large Millimeter Array (ALMA) of a sample of strongly lensed sources selected from surveys carried out with the Herschel Space Observatory. We attempted to reproduce the distribution of image separations for the lensed sources using a halo mass function taken from a numerical simulation that contains both dark matter and baryons. We used three different density distributions, one based on analytical fits to the haloes formed in the EAGLE simulation and two density distributions [Singular Isothermal Sphere (SIS) and SISSA] that have been used before in lensing studies. We found that we could reproduce the observed distribution with all three density distributions, as long as we imposed an upper mass transition of ∼1013 M⊙ for the SIS and SISSA models, above which we assumed that the density distribution could be represented by a Navarro–Frenk–White profile. We show that we would need a sample of ∼500 lensed sources to distinguish between the density distributions, which is practical given the predicted number of lensed sources in the Herschel surveys

Dark Energy and Neutrino Masses from Future Measurements of the Expansion History and Growth of Structure

We forecast the expected cosmological constraints from a combination of probes of both the universal expansion rate and matter perturbation growth, in the form of weak lensing tomography, galaxy tomography, supernovae, and the cosmic microwave background incorporating all cross-correlations between the observables for an extensive cosmological parameter set. We allow for non-zero curvature and parameterize our ignorance of the early universe by allowing for a non-negligible fraction of dark energy (DE) at high redshifts. We find that early DE density can be constrained to 0.2% of the critical density of the universe with Planck combined with a ground-based LSST-like survey, while curvature can be constrained to 0.06%. However, these additional degrees of freedom degrade our ability to measure late-time dark energy and the sum of neutrino masses. We find that the combination of cosmological probes can break degeneracies and constrain the sum of neutrino masses to 0.04 eV, present DE density also to 0.2% of the critical density, and the equation of state to 0.01 - roughly a factor of two degradation in the constraints overall compared to the case without allowing for early DE. The constraints for a space-based mission are similar. Even a modest 1% dark energy fraction of the critical density at high redshift, if not accounted for in future analyses, biases the cosmological parameters by up to 2 sigma. Our analysis suggests that throwing out nonlinear scales (multipoles > 1000) may not result in significant degradation in future parameter measurements when multiple cosmological probes are combined. We find that including cross-correlations between the different probes can result in improved constraints by up to a factor of 2 for the sum of neutrino masses and early dark energy density.Comment: 25 pages, 12 figures. Added new figure, discussion of intrinsic alignments, and references. Matches version accepted for publication in PR