Strong Gravitational Lensing and Dark Energy Complementarity

In the search for the nature of dark energy most cosmological probes measure simple functions of the expansion rate. While powerful, these all involve roughly the same dependence on the dark energy equation of state parameters, with anticorrelation between its present value w_0 and time variation w_a. Quantities that have instead positive correlation and so a sensitivity direction largely orthogonal to, e.g., distance probes offer the hope of achieving tight constraints through complementarity. Such quantities are found in strong gravitational lensing observations of image separations and time delays. While degeneracy between cosmological parameters prevents full complementarity, strong lensing measurements to 1% accuracy can improve equation of state characterization by 15-50%. Next generation surveys should provide data on roughly 10^5 lens systems, though systematic errors will remain challenging.Comment: 7 pages, 5 figure

Like vs. Like: Strategy and Improvements in Supernova Cosmology Systematics

Control of systematic uncertainties in the use of Type Ia supernovae as standardized distance indicators can be achieved through contrasting subsets of observationally-characterized, like supernovae. Essentially, like supernovae at different redshifts reveal the cosmology, and differing supernovae at the same redshift reveal systematics, including evolution not already corrected for by the standardization. Here we examine the strategy for use of empirically defined subsets to minimize the cosmological parameter risk, the quadratic sum of the parameter uncertainty and systematic bias. We investigate the optimal recognition of subsets within the sample and discuss some issues of observational requirements on accurately measuring subset properties. Neglecting like vs. like comparison (i.e. creating only a single Hubble diagram) can cause cosmological constraints on dark energy to be biased by 1\sigma or degraded by a factor 1.6 for a total drift of 0.02 mag. Recognition of subsets at the 0.016 mag level (relative differences) erases bias and reduces the degradation to 2%.Comment: 11 pages, 6 figure

Probing decisive answers to dark energy questions from cosmic complementarity and lensing tomography

We study future constraints on dark energy parameters determined from several combinations of CMB experiments, supernova data, and weak lensing surveys with and without tomography. In this analysis, we look in particular for combinations that will bring the uncertainties to a level of precision tight enough (a few percent) to answer decisively some of the dark energy questions. We probe the dark energy using two variants of its equation of state, and its energy density.We consider a set of 13 cosmological and systematic parameters, and assume reasonable priors on the lensing and supernova systematics. We consider various lensing surveys: a wide survey with f_{sky}=0.7, and with 2 (WLT2) and 5 (WLT5) tomographic bins; a deep survey with 10 bins (WLT10). The constraints found from Planck, 2000 supernovae with z_max=0.8, and WLT2 are: {sigma(w_0)=0.086, sigma(w_1)=0.069}, {sigma(w_0)=0.088, sigma(w_a)=0.11}, and {sigma(E_1)=0.029, sigma(E_2)=0.065}. With 5 bins, we find {sigma(w_0)=0.04, sigma(w_1)=0.034}, {sigma(w_0)=0.041, sigma(w_a)=0.056}, and {sigma(E_1)=0.012, sigma(E_2)=0.049}. Finally, we find from Planck, 2000 supernovae with z_max=1.5, and WLT10 with f_{sky}=0.1: {sigma(w_0)=0.032, sigma(w_1)=0.027}, {sigma(w_0)=0.033, sigma(w_a)=0.040}, and {sigma(E_1)=0.01, sigma(E_2)=0.04}. Although some worries remain about other systematics, our study shows that after the combination of the 3 probes, lensing tomography with many redshift bins and large coverages of the sky has the potential to add key improvements to the dark energy parameter constraints. However, the requirement for very ambitious and sophisticated surveys in order to achieve some of the constraints or to improve them suggests the need for new tests to probe the nature of dark energy in addition to constraining its equation of state. (Abriged)Comment: 14 pages, 5 figures; matches MNRAS accepted versio

Systematic Errors in Future Weak Lensing Surveys: Requirements and Prospects for Self-Calibration

We study the impact of systematic errors on planned weak lensing surveys and compute the requirements on their contributions so that they are not a dominant source of the cosmological parameter error budget. The generic types of error we consider are multiplicative and additive errors in measurements of shear, as well as photometric redshift errors. In general, more powerful surveys have stronger systematic requirements. For example, for a SNAP-type survey the multiplicative error in shear needs to be smaller than 1%(fsky/0.025)^{-1/2} of the mean shear in any given redshift bin, while the centroids of photometric redshift bins need to be known to better than 0.003(fsky/0.025)^{-1/2}. With about a factor of two degradation in cosmological parameter errors, future surveys can enter a self-calibration regime, where the mean systematic biases are self-consistently determined from the survey and only higher-order moments of the systematics contribute. Interestingly, once the power spectrum measurements are combined with the bispectrum, the self-calibration regime in the variation of the equation of state of dark energy w_a is attained with only a 20-30% error degradation.Comment: 20 pages, 9 figures, to be submitted to MNRAS. Comments are welcom

Strongly anharmonic current-phase relation in ballistic graphene Josephson junctions

Motivated by a recent experiment directly measuring the current-phase relation (CPR) in graphene under the influence of a superconducting proximity effect, we here study the temperature dependence of the CPR in ballistic graphene SNS Josephson junctions within the the self-consistent tight-binding Bogoliubov-de Gennes (BdG) formalism. By comparing these results with the standard Dirac-BdG method, where rigid boundary conditions are assumed at the SN interfaces, we show on a crucial importance of both proximity effect and depairing by current for the CPR. The proximity effect grows with temperature and reduces the skewness of the CPR towards the harmonic result. In short junctions ($L<\xi$) current depairing is also important and gives rise to a critical phase $\phi_c<\pi/2$ over a wide range of temperatures and doping levels.Comment: 7 pages, 4 figures. v2 contains very minor change