Cosmological condensation of scalar fields: Making a dark energy

Our Universe is ruled by quantum mechanics and its extension quantum field theory. However, the explanations for a number of cosmological phenomena such as inflation, dark energy, symmetry breakings, and phase transitions need the presence of classical scalar fields. Although the process of condensation of scalar fields in the lab is fairly well understood, the extension of results to a cosmological context is not trivial. Here we investigate the formation of a condensate—a classical scalar field—after reheating of the Universe. We assume a light quantum scalar field produced by the decay of a heavy particle, which for simplicity is assumed to be another scalar. We show that during the radiation domination epoch under certain conditions, the decay of the heavy particle alone is sufficient for the production of a condensate. This process is very similar to preheating—the exponential particle production at the end of inflation. During the matter domination epoch when the expansion of the Universe is faster, the decay alone cannot keep the growing trend of the field and the amplitude of the condensate decreases rapidly, unless there is a self-interaction. This issue is particularly important for dark energy. We show that quantum corrections of the self-interaction play a crucial role in this process. Notably, they induce an effective action which includes inverse power-law terms, and therefore can lead to a tracking behavior even when the classical self-interaction is a simple power-law of order 3 or 4. This removes the necessity of having nonrenormalizable terms in the Lagrangian. If dark energy is the condensate of a quantum scalar field, these results show that its presence is deeply related to the action of quantum physics at the largest observable scales.

Figure 1

Real, imaginary, and absolute values of one of the terms, respectively, in $U_k$ and $V_k$. We used $\alpha =0$ and $\beta =100$. The general aspects of these functions are not very sensitive to $\alpha$ and are very similar for large $\beta \gtrsim 10$. Note that although there are resonant jumps in the value of $U$ and $V$, due to the complexity of the interaction term, they are not regular like in preheating case.