Constant to the power of t in steady state I am wondering how to get the steady-state for the following Euler equation. I know that we can get rid of time in subscripts. However, here I have a constant (a) to the power of $t$. Does anyone know if there is a way to get rid of $t$ in power? Or can I just consider $a^t$ a new constant, say $\bar{a}$?
$$ \frac{1}{c_{t}}=a^t \beta E_t \Big[(1+r_{t+1})\dfrac{1}{c_{t+1}}\Big] $$
If the variables are constant, everything in the equation is time-invariant, while $a^t$ will still grow or fall over time (unless $a=1$). This is a contradiction and no steady state exists, unless $a=1$.