isocurvature perturbations yield: However, if the curvaton does not decay into the baryons or CDM at all, then ζ$_{i}$ = 0 and S i = − 3 ζ , the isocurvature mode becomes three times larger than the curvature perturbations, which is ruled out by the current CMB and LSS data [228–230], for axion isocurvature perturbations, see [231]. In terms of a constrainable parameter, √$_{α}$ ≡ S$_{i}$/ζ , the constrains on r read as: for α < 0 . 0037 at 95% c.l. [13, 274]. The fraction of energy densities, r = ρ$_{ϕ}$/ρ$_{r}$ , also governs the non-Gaussianity generated by the curvaton. Thus the constraint on non-Gaussianity parameter f$_{NL}$ yields S i = 3 ( 1 − r r ) ζ . (443) 0 . 98 < r ≈ 1 − √$_{α}$ 3 < 1 . 0 , (444) − 1 . 21 > f$_{NL}$ ≡ 5 4 r > − 1 . 25 , (445) which is 1 σ away from the central value of the quoted value from WMAP [13], which is − 9 < f$_{NL}$ < 111 (at 95% c.l.) In view of these bounds, it seems that the curvaton decay products cannot generate large CDM, or baryon isocurvature perturbations, or they must not decouple from the thermal plasma created before by that of the inflaton. This could be achieved simply if the curvaton and the inflaton decay products excite the relevant degrees of freedom required for BBN. Otherwise, the curvaton must dominate while decaying and create all the SM or MSSM degrees of freedom. There are mixed curvaton-inflaton scenarios, where the curvature perturbations are contributed by both inflaton and curvaton [832]. In such models larger f$_{NL}$ is expected. C. Curvaton candidates Only handful of the curvaton candidates exist which belong to the observable sector, i.e. charged under the SM gauge group [134–136, 823, 824, 833, 840, 841, 851, 854]. The SM Higgs can act as a potential curvaton, since Higgs is light compared to any high scale of inflation, it would induce fluctuations ∼ H$_{inf}$/ 2 π 〈 h 〉 ∼ 10 − $^{5}$, where 〈 h 〉 is the Higgs VEV during inflation. Validity of the SM Higgs potential beyond the electroweak scale makes it actually less attractive candidate, besides it cannot dominate the energy density of the 210