MSSM flat direction can remain long lived [410, 411]. However, if the curvaton does not dominate while decaying, and the curvaton decay products do not thermalize with the inflaton decay products, then this will lead to potentially large isocurvature fluctuations [131, 834–837]. Note that the non-Gaussianity parameter, f$_{NL}$ , is also constrained by the allowed isocurvature perturbations [133, 838, 839]. The curvaton can easily dominate the energy density if the inflaton decay products are dumped outside our own Hubble patch, which may be realizable in certain brane-world models with warped extra dimensions [840–842]. 

• Thermalization: 

When the curvaton energy density does not dominate while decaying, then the curva- ton decay products must thermalize with that of the inflaton decay products, other- wise, there will be large remnant isocurvature perturbations. It is desirable that both inflaton and curvaton excites solely the SM and/or MSSM degrees of freedom, which requires non-trivial construction on both the sectors [136]. 

Curvaton paradigm with more than 2 light fields were also constructed in [843, 844], but they bear more uncertainties, especially when the curvatons belong to the hidden sector. There are various challenges to the curvaton paradigm, which we discuss below. 

• An absolute gauge singlet or a hidden sector curvaton: 

An absolute gauge singlet curvaton’s origin might lie within string theory [129, 130], or from a hidden sector [316, 826, 828, 842, 845–850]. The modulus will generically couple to all other sectors presumably with a universal coupling , i.e. gravitationally suppressed interaction. Note that dumping entropy into non-SM-like sectors from the curvaton decay would lead to large isocurvature perturbations, if the curvaton is subdominant, and these non-SM like degrees of freedom do not thermalize with that of the inflaton decay products before BBN [834]. 

If the inflaton is also a modulus or a hidden sector field, then it is important to make sure that the inflaton and the curvaton are extremely weakly coupled, otherwise, inflaton decay into curvaton can destroy the curvaton condensate prematurely before its dominance. 

