Theories where the Planck scale is dynamically generated from dimensionless interactions provide predictive inflationary potentials and super-Planckian field variations. We first study the minimal single field realisation in the low-energy effective field theory limit, finding the predictions n s ≈ 0.96 for the spectral index and r ≈ 0.13 for the tensor-toscalar ratio, which can be reduced down to ≈ 0.04 in presence of large couplings. Next we consider agravity as a dimensionless quantum gravity theory finding a multifield inflation that converges towards an attractor trajectory and predicts n s ≈ 0.96 and 0.003 < r < 0.13, interpolating between the quadratic and Starobinsky inflation. These theories relate the smallness of the weak scale to the smallness of inflationary perturbations: both arise naturally because of small couplings, implying a reheating temperature of 10 7−9 GeV. A measurement of r by Keck/Bicep3 would give us information on quantum gravity in the dimensionless scenario.

f (R)-theories of gravity are reviewed in the framework of the matter-antimatter asymmetry in the Universe. The asymmetry is generated by the gravitational coupling of heavy (Majorana) neutrinos with the Ricci scalar curvature. In order that the mechanism works, a time varying nonzero Ricci curvature is necessary. The latter is provided by f (R) cosmology, whose Lagrangian density is of the form L(R) ∼ f (R). In particular we study the cases f (R) ∼ R + αR n and f (R) ∼ R 1+ǫ . 98.80.Cq

By considering f (R) gravity models, the cosmic evolution is modified with respect to the standard ΛCDM scenario. In particular, the thermal history of particles results modified. In this paper, we derive the evolution of relics particles (WIMPs) assuming a reliable f (R) cosmological solution and taking into account observational constraints. The connection to the PAMELA experiment is also discussed. Results are consistent with constraints coming from BICEP2 and PLANCK experiments.