Correspondence of F(R) gravity singularities in Jordan and Einstein frames

We study the finite time singularity correspondence between the Jordan and Einstein frames for various F(R) gravity theories. Particularly we investigate the ordinary pure F(R) gravity case and the unimodular F(R) gravity cases, in the absence of any matter fluids. In the ordinary F(R) gravity cases, by using specific illustrative examples, we show that it is possible to have various correspondences of finite time singularities, and in some cases it is possible a singular cosmology in one frame might be non-singular in the other frame. In the unimodular F(R) gravity case, the unimodular constraint is affected by the conformal transformation, so this has an effect on the metric we choose. Moreover, we study the Einstein frame counterpart theory of the unimodular F(R) gravity case, and we investigate the correspondences of the singularities in the two theories by considering specific illustrative examples. Finally, a brief dynamical system analysis is performed for the vacuum unimodular F(R) gravity and we demonstrate how the dynamical system behaves near the future Big Rip singularity

Nonminimal Couplings in the Early Universe: Multifield Models of Inflation and the Latest Observations

Models of cosmic inflation suggest that our universe underwent an early phase of accelerated expansion, driven by the dynamics of one or more scalar fields. Inflationary models make specific, quantitative predictions for several observable quantities, including particular patterns of temperature anistropies in the cosmic microwave background radiation. Realistic models of high-energy physics include many scalar fields at high energies. Moreover, we may expect these fields to have nonminimal couplings to the spacetime curvature. Such couplings are quite generic, arising as renormalization counterterms when quantizing scalar fields in curved spacetime. In this chapter I review recent research on a general class of multifield inflationary models with nonminimal couplings. Models in this class exhibit a strong attractor behavior: across a wide range of couplings and initial conditions, the fields evolve along a single-field trajectory for most of inflation. Across large regions of phase space and parameter space, therefore, models in this general class yield robust predictions for observable quantities that fall squarely within the "sweet spot" of recent observations.Comment: 17pp, 2 figs. References added to match the published version. Published in {\it At the Frontier of Spacetime: Scalar-Tensor Theory, Bell's Inequality, Mach's Principle, Exotic Smoothness}, ed. T. Asselmeyer-Maluga (Springer, 2016), pp. 41-57, in honor of Carl Brans's 80th birthda

Gravitational effective action at second order in curvature and gravitational waves

We consider the full effective theory for quantum gravity at second order in curvature including non-local terms. We show that the theory contains two new degrees of freedom beyond the massless graviton: namely a massive spin-2 ghost and a massive scalar field. Furthermore, we show that it is impossible to fine-tune the parameters of the effective action to eliminate completely the classical spin-2 ghost because of the non-local terms in the effective action. Being a classical field, it is not clear anyway that this ghost is problematic. It simply implies a repulsive contribution to Newton’s potential. We then consider how to extract the parameters of the effective action and show that it is possible to measure, at least in principle, the parameters of the local terms independently of each other using a combination of observations of gravitational waves and measurements performed by pendulum type experiments searching for deviations of Newton’s potential

Gravitons in Flatland

We review some features of three-dimensional (3D) massive gravity theories. In particular, we stress the role of the Schouten tensor. explore an analogy with Lovelock gravity and discuss renormalizabilty