10 research outputs found
Optimising Boltzmann codes for the Planck era
High precision measurements of the Cosmic Microwave Background (CMB)
anisotropies, as can be expected from the Planck satellite, will require
high-accuracy theoretical predictions as well. One possible source of
theoretical uncertainty is the numerical error in the output of the Boltzmann
codes used to calculate angular power spectra. In this work, we carry out an
extensive study of the numerical accuracy of the public Boltzmann code CAMB,
and identify a set of parameters which determine the error of its output. We
show that at the current default settings, the cosmological parameters
extracted from data of future experiments like Planck can be biased by several
tenths of a standard deviation for the six parameters of the standard
Lambda-CDM model, and potentially more seriously for extended models. We
perform an optimisation procedure that leads the code to achieve sufficient
precision while at the same time keeping the computation time within reasonable
limits. Our conclusion is that the contribution of numerical errors to the
theoretical uncertainty of model predictions is well under control -- the main
challenges for more accurate calculations of CMB spectra will be of an
astrophysical nature instead.Comment: 13 pages, 4 figure
Caching and Interpolated Likelihoods: Accelerating Cosmological Monte Carlo Markov Chains
We describe a novel approach to accelerating Monte Carlo Markov Chains. Our
focus is cosmological parameter estimation, but the algorithm is applicable to
any problem for which the likelihood surface is a smooth function of the free
parameters and computationally expensive to evaluate. We generate a high-order
interpolating polynomial for the log-likelihood using the first points gathered
by the Markov chains as a training set. This polynomial then accurately
computes the majority of the likelihoods needed in the latter parts of the
chains. We implement a simple version of this algorithm as a patch (InterpMC)
to CosmoMC and show that it accelerates parameter estimatation by a factor of
between two and four for well-converged chains. The current code is primarily
intended as a "proof of concept", and we argue that there is considerable room
for further performance gains. Unlike other approaches to accelerating
parameter fits, we make no use of precomputed training sets or special choices
of variables, and InterpMC is almost entirely transparent to the user.Comment: v2 Trivial Latex change. Source code:
http://easther.physics.yale.edu/interpmc.htm
Single-field inflation constraints from CMB and SDSS data
We present constraints on canonical single-field inflation derived from WMAP
five year, ACBAR, QUAD, BICEP data combined with the halo power spectrum from
SDSS LRG7. Models with a non-scale-invariant spectrum and a red tilt n_s < 1
are now preferred over the Harrison-Zel'dovich model (n_s = 1, tensor-to-scalar
ratio r = 0) at high significance. Assuming no running of the spectral indices,
we derive constraints on the parameters (n_s, r) and compare our results with
the predictions of simple inflationary models. The marginalised credible
intervals read n_s = 0.962^{+0.028}_{-0.026} and r < 0.17 (at 95% confidence
level). Interestingly, the 68% c.l. contours favour mainly models with a convex
potential in the observable region, but the quadratic potential model remains
inside the 95% c.l. contours. We demonstrate that these results are robust to
changes in the datasets considered and in the theoretical assumptions made. We
then consider a non-vanishing running of the spectral indices by employing
different methods, non-parametric but approximate, or parametric but exact.
With our combination of CMB and LSS data, running models are preferred over
power-law models only by a Delta chi^2 ~ 5.8, allowing inflationary stages
producing a sizable negative running -0.063^{+0.061}_{-0.049} and larger
tensor-scalar ratio r < 0.33 at the 95% c.l. This requires large values of the
third derivative of the inflaton potential within the observable range. We
derive bounds on this derivative under the assumption that the inflaton
potential can be approximated as a third order polynomial within the observable
range.Comment: 32 pages, 7 figures. v2: additional references, some typos corrected,
passed to JCAP style. v3: minor changes, matches published versio