Slow roll solutions to inflationary potentials have been widely believed to be the only universal attractor. Over the last few years there has been growing interest in a new class of inflationary models known as Constant-Roll Inflation. Constant roll solutions are a generalization of "ultra-slow roll" dynamics, where the first slow roll parameter is small, but the second slow roll parameter η is larger than unity. In Ultra-slow Roll Inflation, the large-η solution is a dynamical transient, relaxing exponentially to the attractor de Sitter solution. In the constant roll generalization, recent papers have concluded that Constant-Roll Inflation represents a new class of non-slow roll attractor solutions. In this paper we show that these attractor solutions are actually the usual slow roll attractor, disguised by a parameter duality, and that the large-η solutions, as in the case of ultraslow roll, represent a dynamical transient.

There has been considerable recent interest in a new class of non-slow roll inflationary solutions known as constant roll inflation. Constant roll solutions are a generalization of the ultra-slow roll (USR) solution, where the first Hubble slow roll parameter is small, but the second Hubble slow roll parameter η is not. While it is known that the USR solutions represent dynamical transients, there has been some disagreement in literature about whether or not large-η constant roll solutions are attractors or are also a class of transient solutions. In this paper we show that the large-η constant roll solutions do in fact represent transient solutions by performing stability analysis on the exact analytic (large-η) constant roll solutions. *

Motivated by the apparent discrepancy between Cosmic Microwave Background measurements of the Hubble constant and measurements from Type-Ia supernovae, we construct a model for Dark Energy with equation of state w = p/ρ < −1, violating the Null Energy Condition. Naive canonical models of so-called "Phantom" Dark Energy require a negative scalar kinetic term, resulting in a Hamiltonian unbounded from below and associated vacuum instability. We construct a scalar field model for Dark Energy with w < −1, which nonetheless has a Hamiltonian bounded from below in the comoving reference frame, i.e. in the rest frame of the fluid. We demonstrate that the solution is a cosmological attractor, and find that early-time cosmological boundary conditions consist of a "frozen" scalar field, which relaxes to the attractor solution once the Dark Energy component dominates the cosmological energy density. We consider the model in an arbitrary choice of gauge, and find that, unlike the case of comoving gauge, the fluid Hamiltonian is in fact unbounded from below in the reference frame of a highly boosted observer, corresponding to a nonlinear gradient instability. We discuss this in the context of general NEC-violating perfect fluids, for which this instability is a general property.

Inspired the low cosmic variance we present a study on the statistical variance expected in observing Bell's inequality violation by primordial quantum states violation. We consider the statistical variance inherent to three sets of pseudo-spin operators used to construct Bell's inequality.We find that for a highly squeezed state, such as the relevant CMB states, the statistical variation will vanish and does not contribute to theoretical uncertainties.