( (q_1 - q_2 - 1) (q_1 + q_2 - 2) \epsilon^{1 - 2 q_1}
  ) + a_{21} (q_1 - q_2 + 1) (q_1 + q_2) \epsilon^{2 q_1 - 1} \right],
\label{c51}
\\ c_{52}&=&\frac{c_{11}}{(1-2q_2)(1-2q_1)2k(1-2q_1)} \left[ 2 a_{11}
  (1 + q_1 - q_2) (-2 + q_1 + q_2) \epsilon^{1 - 2 q_2} \right.
  \nonumber \\ &+& \left. a_{12} (-2 + q_1 + q_2)^2 \epsilon^{-2 (-1 +
    q_1 + q_2)} + a_{21} (1 + q_1 - q_2)^2 \epsilon^{2 (q_1 -
    q_2)}\right],
\label{c52}\end{aligned}$$

and $$\begin{aligned}
\label{a11}
a_{11} & = \frac{2\left[k^2\delta^2+(q_1-1)q_1\right]\sin
  (2k\Delta)}{\delta} - 2 k \cos (2 k \Delta), \\
\label{a12}
a_{12} & = \delta^{2q_1-2}
\left[-4kq_1\delta\cos(2k\Delta)-2(q_1-k\delta)(q_1+k\delta)
  \sin(2k\Delta)\right],
\\
\label{a21}
a_{21} & =
\delta^{-2q_1}\left[2(q_1-k\delta-1)(q_1+k\delta-1)\sin(2k\Delta)-
  4k(q_1-1)\delta\cos(2k\Delta)\right]
.\end{aligned}$$ Note that these coefficients oscillate as a function of $k$. These oscillations are important, however, only for small wavelength fluctuations. For these we will obtain oscillations in the power spectrum. The final general result for the power spectrum is given by $$\begin{aligned}
P_{\zeta} & = \zeta^2 k^{3}  \sim \left( \frac{v}{z} \right)^2 k^{3}
\nonumber  \\ & = \left[
  \frac{c_{51}(\tau-\tau_B)^{1-q_2}+c_{52}(\tau-\tau_B)^{q_2}}{(\tau-\tau_B)^{q_2}}
  \right]^2 k^{3}    \nonumber \\  &= \left[ c_{51}
  (\tau-\tau_B)^{1-2q_2} + c_{52} \right]^2 k^{3} \, .
\label{finalPzeta}\end{aligned}$$ Below we will analyze some of the specific cases given by our two models when applying 