Abstract: We present a method to minimize, or even cancel out, the nuisance parameters affecting a measurement. Our approach is general and can be applied to any experiment or observation where systematic errors are a concern e.g. are larger than statistical errors. We compare it with the Bayesian technique used to deal with nuisance parameters: marginalization, and show how the method compares and improves by avoiding biases. We illustrate the method with several examples taken from the astrophysics and cosmology world: baryonic acoustic oscillations (BAOs), cosmic clocks, Type Ia supernova (SNIa) luminosity distance, neutrino oscillations and dark matter detection. By applying the method we not only recover some known results but also find some interesting new ones. For BAO experiments we show how to combine radial and angular BAO measurements in order to completely eliminate the dependence on the sound horizon at radiation drag. In the case of exploiting SNIa as standard candles we show how the uncertainty in the luminosity distance by a second parameter modelled as a metallicity dependence can be eliminated or greatly reduced. When using cosmic clocks to measure the expansion rate of the universe, we demonstrate how a particular combination of observables nearly removes the metallicity dependence of the galaxy on determining differential ages, thus removing the agemetallicity degeneracy in stellar populations. We hope that these findings will be useful in future surveys to obtain robust constraints on the dark energy equation of state.

Abstract: We compute a new generation of standard solar models (SSMs) that includes recent updates on some important nuclear reaction rates and a more consistent treatment of the equation of state. Models also include a novel and flexible treatment of opacity uncertainties based on opacity kernels, required in. light of recent theoretical and experimental works on radiative opacity. Two large sets of SSMs, each based on a different canonical set of solar abundances with high and low metallicity (Z), are computed to determine model uncertainties and correlations among different observables. We present detailed comparisons of high-and low-Z models against different ensembles of solar observables,. including solar neutrinos, surface helium abundance, depth of the. convective envelope, and sound speed profile. A global comparison, including all observables, yields a p-value of 2.7 sigma for the high-Z model and 4.7 sigma for the low-Z one. When the sound speed differences in the narrow region of 0.65 < r/R-circle dot < 0.70 are excluded from the analysis, results are 0.9 sigma and 3.0 sigma for high-and low-Z models respectively. These results show that. high-Z models agree well with solar data but have a systematic problem right below the bottom of the convective envelope linked to steepness of molecular weight and temperature gradients, and that low-Z models lead to a much more general disagreement with solar data. We also show that, while simple parametrizations of opacity uncertainties can strongly alleviate the solar abundance problem, they are insufficient to substantially improve the agreement of SSMs with helioseismic data beyond that obtained for high-Z models due to the intrinsic correlations of theoretical predictions.