Conformal invariant cosmological perturbations via the covariant approach:multicomponent universe

In recent years there has been a lot of interest in discussing frame dependences/independences of the cosmological perturbations under the conformal transformations. This problem has previously been investigated in terms of the covariant approach for a single component universe, and it was found that the covariant approach is very powerful to pick out the perturbative variables which are both gauge and conformal invariant. In this work, we extend the covariant approach to a universe with multicomponent fluids. We find that similar results can be derived,as expected. In addition, some other interesting perturbations are also identified to be conformal invariant, such as entropy perturbation between two different components.