Now I fit out grid of 600 simulations using the \(P(k)\) covariance matrix from Boera et al., below are the posterior distributions comparing to the distributions when only the uncertainty in the data \(sigma\) is used for the likelihood. To check the implementation I also include the result of using a simplified matrix where only the diagonal elements are non-zero which should yield the same result as when using \(sigma\).

The distributions when using the covariance matrix suggest that a \(m_\mathrm{WDM}~4\) is preferred over \(CDM\) which is interesting

Below is the evolution of the temperature after marginalizing over the distributions obtained using the covariance matrix for the likelihood calculation