  We present a generalised calculation for the spectrum of primordial tensor
perturbations in a cyclic Universe, making no assumptions about the vacuum
state of the theory and accounting for the contribution of tensor modes
produced in the dark energy phase of the previous cycle. We show that these
modes have minimal impact on the spectrum observed in the current cycle, except
for corrections on scales as large as the comoving Hubble radius today. These
corrections are due to sub-horizon modes produced towards the end of the dark
energy phase, persisting into the ekpyrotic phase of the next cycle as
additional quanta. In relation to the vacuum state, we argue that
non-Bunch-Davies quanta can easily overwhelm the energy density driving the
dark energy phase, potentially compromising the model. Therefore, avoiding
backreaction effects sets restrictive constraints on deviations away from the
Bunch-Davies vacuum during this phase, limiting the overall freedom to consider
alternative vacua in the cyclic Universe.
