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I have a puzzle when I study the hybrid inflation model.
Suppose we have two scalar fields, [itex]\phi_1 and \phi_2[/itex]
first, let's consider the situation where they are in their independent potentials
[itex]V(\phi_i)=m_i^2\phi_i^2, i = 1,2[/itex]
with initial value
[itex]\phi_i^{ini}[/itex]
We can solve the scalar dynamic equations for them. And they are both in harmonic oscillation. This is Okay.
But when a 'mixing term' [itex]\lambda^2 \phi_1\phi_2[/itex] is introduced, [itex]\phi_1[/itex] and [itex]\phi_2[/itex] get infinite values, if \lambda is large. This can be showed numerically. What I thought is the large mixing term would lead to [itex]\phi_1 = \phi_2[/itex]. So why it goes to infinite?
And we can rotate [itex]\phi_1[/itex] and [itex]\phi_2[/itex] to a basis where there is no mixing term. In this basis, we would not get infinite values for [itex]\phi_1[/itex] or [itex]\phi_2[/itex]. So it seems I get a different result working in different basis. What is the problem
Suppose we have two scalar fields, [itex]\phi_1 and \phi_2[/itex]
first, let's consider the situation where they are in their independent potentials
[itex]V(\phi_i)=m_i^2\phi_i^2, i = 1,2[/itex]
with initial value
[itex]\phi_i^{ini}[/itex]
We can solve the scalar dynamic equations for them. And they are both in harmonic oscillation. This is Okay.
But when a 'mixing term' [itex]\lambda^2 \phi_1\phi_2[/itex] is introduced, [itex]\phi_1[/itex] and [itex]\phi_2[/itex] get infinite values, if \lambda is large. This can be showed numerically. What I thought is the large mixing term would lead to [itex]\phi_1 = \phi_2[/itex]. So why it goes to infinite?
And we can rotate [itex]\phi_1[/itex] and [itex]\phi_2[/itex] to a basis where there is no mixing term. In this basis, we would not get infinite values for [itex]\phi_1[/itex] or [itex]\phi_2[/itex]. So it seems I get a different result working in different basis. What is the problem