Amplitude of dark energy perturbations

We propose a model which produces dark energy perturbations large enough to explain the lack of power seen at the quadrupole scale in the cosmic microwave background. If the dark energy is frozen from horizon exit during inflation until dark energy domination, then it is not possible to have perturbations in the dark energy which are large enough. We propose using a tachyonic amplification mechanism to overcome this. The dark energy is taken to be a complex scalar field, where the radial field has a Mexican hat potential. During inflation, the radial component is trapped near the maximum of its potential. At the end of inflation, it rolls down to the minimum. The dark energy today is taken to be a pseudo-Nambu-Goldstone boson. The perturbations generated during inflation are amplified by the rolling of the radial field. We also examine the use of the variable decay mechanism in order to generate an anticorrelation between the dark energy perturbations and the curvature perturbation. We show that using this mechanism then constrains the properties of the dark energy and its evolution from redshift one until today.

Figure 1

This figure shows how the amplification of $\delta Q$ takes place. The Mexican hat potential, whose radial form is given in Eq. (37), is displayed. The large scale perturbation, $\delta Q$, can be thought of as the difference, in the circumference direction, between two separate homogeneous Universes [9], whose trajectories in field space (thick black lines) are labeled by “A“ and “B“. The initial ($\delta Q_i$) and final ($\delta Q_f$) perturbations are drawn with thick gray lines.

Figure 2

The evolution of the equation of state of the quintessence ($w_Q$), with redshift $z$, when the potential is of the form Eq. (55) and the initial condition is given in Eq. (62). The quintessence is taken to make up $73\%$ of the energy density today.