# Understanding Bose enhancement in reheating

I'm struggling to understand the Bose enhancement in reheating. I've read that:

• At the end of inflation, the inflaton field, $\phi$, is something like a condensate with excitations of a single momentum, say $p^\mu=(m_\phi,0)$ in the rest frame.
• The inflatons decay into pairs of bosons, say $bb$, with $q^{\mu}=(m_\phi/2,\pm\vec p)$, with $\vec p$ fixed by conservation of energy.
• The Fock space of the $b$ field is filled with states of momentum $\vec p$.
• This results in "Bose enhancement" of the decay $\phi\to bb$.

Why do the large occupation numbers for the final state $b$ enhance the decay rate $\phi\to bb$? Also, why can we assume that the inflaton field is like a condensate with excitations of the same momenta?

I've seen some arguments with matrix elements, $$|\langle n_\phi -1, n_k+1, n_{-k}+1 | a^\dagger_k a^\dagger_{-k} a_\phi | n_\phi, n_k, n_{-k} \rangle |^2 \propto n_k n_{-k}$$ but I find them surprising. Is there a physical/intuitive way to understand the enhancement? Is it reasonable to think of the $CPT$ process? I suppose I find it intuitive that $bb\to\phi$ with $\phi$ at threshold could be enhanced by high occupation numbers for the correct $b$ momenta.

• A comment on your last question: Mukhanov has a good discussion of this in his book Principles of Physical Cosmology, in chapter 5, I believe. – Danu Apr 6 '14 at 18:49
• @danu I didn't find Muhkanov that helpful. "...an oscillating homogenous field can be thought of as a condensate of massive scalar particles with zero momentum". That's not obvious to me :s – innisfree Apr 7 '14 at 5:40
• I remember reading it as well and being confused, only later understanding that he was referring back to something he derived earlier. I will try to take a look at it – Danu Apr 7 '14 at 5:51