Ekpyrotic cosmology with a zero-shear S-brane

In a recent paper [R. Brandenberger and Z. Wang, Phys. Rev. D 101, 063522 (2020)] we proposed a mechanism for a continuous transition between a contracting ekpyrotic phase and the standard big bang phase of expansion: the bounce is generated by an S-brane which represents the effects of higher-mass string states in the low-energy effective field theory. We showed that gravitational waves on cosmological scales obtain a nearly scale-invariant spectrum. Here, we study the cosmological fluctuations in this setup, assuming that the S-brane has zero shear. We find a nearly scale-invariant spectrum of cosmological perturbations with a slight red tilt. The scenario yields two consistency relations for cosmological observations: one relating the tensor-to-scalar ratio with the scalar spectral tilt, and one relating the tensor tilt to the scalar tilt. The predicted tensor-to-scalar ratio is within the reach of upcoming cosmic microwave background observations. The tensor tilt is blue.