On model selection forecasting, Dark Energy and modified gravity

ABSTRACT The Fisher matrix approach (Fisher (1935)) allows one to calculate in advance howwell a given experiment will be able to estimate model parameters, and has been aninvaluable tool in experimental design. In the same spirit, we present here a methodto predict how well a given experiment can distinguish between different models, re-gardless of their parameters. From a Bayesian viewpoint, this involves computation ofthe Bayesian evidence. In this paper, we generalise the Fisher matrix approach fromthe context of parameter fitting to that of model testing, and show how the expectedevidence can be computed under the same simplifying assumption of a gaussian like-lihood as the Fisher matrix approach for parameter estimation. With this ‘Laplaceapproximation’ all that is needed to compute the expected evidence is the Fisher ma-trix itself. We illustrate the method with a study of how well upcoming and plannedexperiments should perform at distinguishing between Dark Energy models and mod-ified gravity theories. In particular we consider the combination of 3D weak lensing,for which planned and proposed wide-field multi-band imaging surveys will providesuitable data, and probes of the expansion history of the Universe, such as proposedsupernova and baryonic acoustic oscillations surveys. We find that proposed large-scale weak lensing surveys from space should be able readily to distinguish GeneralRelativity from modified gravity models.Key words: methods: statistical, cosmological parameters, dark energy

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