# Exploring parameter space of inflation models

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Rafid Mahbub
I have been studying primordial black hole formation through inflation for a while and I was curious to know how the parameters in an inflation model are determined such that they are consistent with CMB constraints. In my literature reviews, there are quite a few models that exhibit an inflection point in the inflaton potentials, but with quite a few parameters that need to be tuned. Is some kind of Markov Chain Monte Carlo method used to do this?

## Answers and Replies

Science Advisor
Gold Member
I have been studying primordial black hole formation through inflation for a while and I was curious to know how the parameters in an inflation model are determined such that they are consistent with CMB constraints. In my literature reviews, there are quite a few models that exhibit an inflection point in the inflaton potentials, but with quite a few parameters that need to be tuned. Is some kind of Markov Chain Monte Carlo method used to do this?
Typically, yes. One of a variety of software packages are used to compute the power spectrum given the set of cosmological parameters (many are listed here under the "CMB Tools" sub-header, confusingly the same as the header).

Then, some form of Monte Carlo chain is used to determine the probability distribution given a likelihood function (which stems from one or more experiments). Both Planck and WMAP supply software which can be used to calculate the likelihood that a given power spectrum matches their CMB data.