  We consider the thermodynamical behavior of Banks-Zaks theory close to the
conformal point in a cosmological setting. Due to the anomalous dimension, the
resulting pressure and energy density deviate from that of radiation and result
in various interesting cosmological scenarios. Specifically, for a given range
of parameters one avoids the cosmological singularity. We provide a full "phase
diagram" of possible Universe evolution for the given parameters.
  For a certain range of parameters, the thermal averaged Banks-Zaks theory
alone results in an exponentially contracting universe followed by a
non-singular bounce and an exponentially expanding universe, i.e.
\textit{Inflation without a Big Bang singularity}, or shortly termed "dS
Bounce". The temperature of such a universe is bounded from above and below.
The result is a theory violating the classical Null Energy Condition (NEC).
  Considering the Banks-Zaks theory with an additional perfect fluid, yields an
even richer phase diagram that includes the standard Big Bang model, stable
single "normal" bounce, dS Bounce and stable cyclic solutions.
  The bouncing and cyclic solutions are with no singularities, and the
violation of the NEC happens only near the bounce. We also provide simple
analytical conditions for the existence of these non-singular solutions. Hence,
within effective field theory, we have a new alternative non-singular cosmology
based on the anomalous dimension of Bank-Zaks theory that may include inflation
and without resorting to scalar fields.
