content_image/329349.jpg content_image/329350.jpg
VEVs also lead to automatically successful inflation similarly to chaotic inflation. In the inflationary valley, 〈 ψ 〉 = 0, the effective potential is given by: 4 

<img src='content_image/329349.jpg'>

whose phenomenology has been studied around Eq. (168), using p = 2, V$_{0}$ = λM $^{4}$/ 4, and V$_{0}$/M 2 P = m $^{2}$/ 2. Therefore, the predictions are disfavored by the data because of a blue tilt in the spectrum, i.e. n$_{s}$ > 1, in the small field regime, φ$_{Q}$ < M$_{P}$ . Note however that if its end is accompanied by the formation of cosmic strings, a slightly blue spectrum is found in agreement with the data, if these cosmic strings contribute to the CMB anisotropies around 10% [263]. It was also suggeste in [510] that loop corrections to the hybrid tree level potential due to a Yukawa coupling to the right handed neutrino can render the spectral index of the model below 1, like for the chaotic model. This was confirmed recently in [539], where a red spectral tilt was found, even in the small field regime. These Yukawa couplings were also found suitable for a successful reheating phase and the generation of lepton/baryon asymmetry after inflation. 

Note that a more realistic version of the model would include a quartic term for φ allowed by symmetries and generated by the Feynman diagrams involving loops of ψ fields. If this term dominates over the quadratic term in the inflationary valley, it was found that the spectral index would then be very close to unity [206]. Note that the coupling to a Higgs-type waterfall field has potentially important cosmological consequences [540, 541], as topological defects generically form during this symmetry breaking after inflation. This will be discussed in Sec. IV E 2. 

## 2. Mutated and smooth hybrid inflation 

Two variations of the hybrid inflation idea were proposed soon after the original model, both assuming that the term φ 2 is negligible. 

The two-field scalar potentials are of the form: 

<img src='content_image/329350.jpg'>

They share the common feature of having an inflationary trajectory during which 〈 ψ 〉 is varying and not vanishing. They also both reduce, in the one-field approximation to the form of Eq. (175). 

