Towards conformal cosmology

Approximate de Sitter symmetry of inflating Universe is responsible for the approximate flatness of the power spectrum of scalar perturbations. However, this is not the only option. Another symmetry that can explain nearly scale-invariant power spectrum is conformal invariance. We give a short review of models based on conformal symmetry that lead to the scale-invariant spectrum of the scalar perturbations. We discuss also potentially observable features of these models.