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Extra info for Physics Reports vol.314
As a simple example, consider Eq. m # . It has the same Z symmetry as the original potential, corresponding to invariance under P! But as shown in Fig. 3, the minimum at the origin is replaced by minima at "$(m/( ). (m/( ). Then, if the constant < is chosen appropriately, one has near the minimum (141) <"mJ I #A I #B I , where mJ "(2m and we are not interested in the precise values of A and B. The minima represent possible vacuum expectation values (vevs) of the "eld. Each of them represents a possible vacuum of the theory, around which are small oscillations corresponding (after quantization) to particles.
S, where S is evaluated on the last-scattering surface. ect coming from the curvature perturbation we just calculated, and the "rst term is the anisotropy / just after last scattering (on a comoving P P hypersurface). ect, so for a given large-scale density perturbation the isocurvature perturbation gives an anisotropy six times bigger. As a result an isocurvature perturbation with a #at spectrum cannot be the dominant contribution to the cmb, though one could contemplate a small contribution .
133) I The use of a complex "eld is particularly appropriate if the potential depends only on " ". Then Eq. (127) is replaced by (134) <( )"< #m" "# " " . Complex "elds are, in any case, part of the language of supersymmetry. With two or more real "elds, it is no longer true that the most general Lorentz-invariant Lagrangian density L can be reduced to the above form, Eq. (129), by a "eld rede"nition. For several real "elds , the most general kinetic term involving derivatives is L L " H R RI , (135) KL I K L KL where H is an arbitrary function of the "elds.