72,874 research outputs found

    The Cosmic Linear Anisotropy Solving System (CLASS) III: Comparision with CAMB for LambdaCDM

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    By confronting the two independent Boltzmann codes CLASS and CAMB, we establish that for concordance cosmology and for a given recombination history, lensed CMB and matter power spectra can be computed by current codes with an accuracy of 0.01%. We list a few tiny changes in CAMB which are necessary in order to reach such a level. Using the common limit of the two codes as a set of reference spectra, we derive precision settings corresponding to fixed levels of error in the computation of a CMB likelihood. We find that for a given precision level, CLASS is about 2.5 times faster than CAMB for computing the lensed CMB spectra of a LambdaCDM model. The nature of the main improvements in CLASS (which may each contribute to these performances) is discussed in companion papers.Comment: 16 pages, 4 figures, 1 table. Typos corrected, comparison extended to lower precision settings. Code available at http://class-code.ne

    CMB power spectrum parameter degeneracies in the era of precision cosmology

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    Cosmological parameter constraints from the CMB power spectra alone suffer several well-known degeneracies. These degeneracies can be broken by numerical artefacts and also a variety of physical effects that become quantitatively important with high-accuracy data e.g. from the Planck satellite. We study degeneracies in models with flat and non-flat spatial sections, non-trivial dark energy and massive neutrinos, and investigate the importance of various physical degeneracy-breaking effects. We test the CAMB power spectrum code for numerical accuracy, and demonstrate that the numerical calculations are accurate enough for degeneracies to be broken mainly by true physical effects (the integrated Sachs-Wolfe effect, CMB lensing and geometrical and other effects through recombination) rather than numerical artefacts. We quantify the impact of CMB lensing on the power spectra, which inevitably provides degeneracy-breaking information even without using information in the non-Gaussianity. Finally we check the numerical accuracy of sample-based parameter constraints using CAMB and CosmoMC. In an appendix we document recent changes to CAMB's numerical treatment of massive neutrino perturbations, which are tested along with other recent improvements by our degeneracy exploration results.Comment: 27 pages, 28 figures. Latest CAMB version available from http://camb.info/. Reduced number of figures, plot legend corrected and minor edits to match published versio

    Motivic invariant of real polynomial functions and Newton polyhedron

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    We propose a computation of real motivic zeta functions for real polynomial functions, using Newton polyhedron. As a consequence we show that the weights are blow-Nash invariants of convenient weighted homogeneous polynomials in three variables.Comment: 22 pages in Math. Proc. Camb. Phil. Soc, 201

    CMB Tensor Anisotropies in Metric f(R) Gravity

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    We present a description of CMB anisotropies generated by tensor perturbations in f(R) theories of gravity. The temperature power spectrum in the special case of f(R)=Rnf(R)=R^n is computed using a modified version of CAMB package.Comment: 4 pages, 1 figure. Contribution submitted to the proceedings of the Spanish Relativity Meeting ERE2011, September 2011, Madrid, Spai
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