**6. Conclusions**

In this article, we have clarified some general properties of the primordial cosmological tensor power spectrum in emergen<sup>t</sup> models. Following a purely phenomenological approach, we have studied how different features in the behavior of the scale factor around the transition time (or before) can affect the spectrum. The main results are the following:


This work establishes that non-trivial features occurring at the transition time in an emergen<sup>t</sup> universe might be detectable in the primordial tensor spectrum. The detection of the CMB B-modes is a very active field involving big collaborations. On the ground, progress is expected from the BICEPor POLARBEAR(now grouped into Stage 4) experiments and, in space, potentially from LiteBIRD. At this stage, trying to detect those modes is probably the best path toward finding traces of quantum gravity effects in the CMB. The features studied in this work may therefore be observable in the not so distant future, if the duration and energy scale of inflation are favorable.

It would clearly be interesting to go beyond the tensor spectrum and to investigate scalar perturbations that are currently observed. This, however, requires an explicit specific model as the evolution of the scale factor is no longer enough to compute the evolution of perturbations.

**Author Contributions:** conceptualization, K.M. and A.B.; methodology, K.M. and A.B.; software, K.M.; validation, K.M.; formal analysis, K.M. and A.B.; investigation, K.M. and A.B.; resources, A.B.; writing—original draft preparation, K.M. and A.B.; writing—review and editing, K.M. and A.B.; project administration, A.B.

**Funding:** This research received no external funding.

**Acknowledgments:** K.M. is supported by a gran<sup>t</sup> from the CFM foundation.

**Conflicts of Interest:** The authors declare no conflict of interest.
