Evidence for Cosmological Acceleration
Yes, the evidence for periodic cosmological acceleration events is still quite strong, but we are much less sure of what causes this.
For example, there are inhomogeneous cosmological models that can cause acceleration like that observed with Dark Energy or a Cosmological Constant. Moreover, Prof. Paul Steinhardt (Princeton), who was one of the founders of the Inflationary Cosmology, argues that inflation and the whole LambdaCDM Cosmological Model have largely failed to explain the newer empirical evidence and need to be superseded.
Cosmology may be on the threshold of paradigm change. Stay tuned and keep an open, unbiased mind. Demand evidence-based modeling.
RLO