We study the propagation of super-horizon cosmological perturbations in a non-singular bounce spacetime. The model we consider combines a ghost condensate with a Galileon term in order to induce a ghost-free bounce. Our calculation is performed in harmonic gauge, which ensures that the linearized equations of motion remain well-defined and nonsingular throughout. We find that, despite the fact that near the bounce the speed of sound becomes imaginary, super-horizon curvature perturbations remain essentially constant across the bounce. In fact, we show that there is a time close to the bounce where curvature perturbations of all wavelengths are required to be momentarily exactly constant. We relate our calculations to those performed in other gauges, and comment on the relation to previous results in the literature. a lorenzo.battarra@aei.mpg.de b

The no-boundary proposal provides a compelling theory for the initial conditions of our universe. We study the implications of such initial conditions for ekpyrotic and cyclic cosmologies. These cosmologies allow for the existence of a new type of "ekpyrotic instanton", which describes the creation of a universe in the ekpyrotic contraction phase. Remarkably, we find that the ekpyrotic attractor can explain how the universe became classical. In a cyclic context, in addition to the ekpyrotic instantons there exist de Sitter-like instantons describing the emergence of the universe in the dark energy phase. Our results show that typically the ekpyrotic instantons yield a higher probability. In fact, in a potential energy landscape allowing both inflationary and cyclic cosmologies, the no-boundary proposal implies that the probability for ekpyrotic and cyclic initial conditions is vastly higher than that for inflationary ones.

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We investigate in detail the properties of oscillating instanton solutions discussed recently in the literature. We find that the solutions with N nodes contain exactly N homogeneous negative modes in their spectrum of linear perturbations. The existence of extra negative modes for the N > 1 solutions suggest that they are not final state physical objects resulting from tunneling, but rather unstable intermediate thermal configurations. By contrast, the single negative mode for the N ¼ 1 instanton confirms its interpretation as mediating the curved-space tunneling between vacua with equal energy densities.

We examine the processes of quantum squeezing and decoherence of density perturbations produced during a slowly contracting ekpyrotic phase in which entropic perturbations are converted to curvature perturbations before the bounce to an expanding phase. During the generation phase, the entropic fluctuations evolve into a highly squeezed quantum state, analogous to the evolution of inflationary perturbations. Subsequently, during the conversion phase, quantum coherence is lost very efficiently due to the interactions of entropy and adiabatic modes. Moreover, while decoherence occurs, the adiabatic curvature perturbations inherit their semiclassicality from the entropic perturbations. Our results confirm that, just as for inflation, an ekpyrotic phase can generate nearly scale-invariant curvature perturbations which may be treated as a statistical ensemble of classical density perturbations, in agreement with observations of the cosmic background radiation.

We perform a detailed study of the existence and the properties of O(4)-invariant instanton solutions in Einstein-scalar theory in the presence of flat potential barriers, i.e. barriers where the second derivative of the potential is small at the top of the barrier. We find a whole zoo of solutions: Hawking-Moss, Coleman-De Luccia (CdL), oscillating instantons, asymmetric CdL as well as other non-standard CdL-like solutions with additional negative modes in their spectrum of fluctuations. Our work shows how these different branches of solutions are connected to each other via "critical" instantons possessing an extra zero mode fluctuation. Overall, the space of finite action euclidean solutions to these theories with flat barriers is surprisingly rich and intricate

We study the process of quantum tunnelling in scalar-tensor theories in which the scalar field is non-minimally coupled to gravity. In these theories gravitational instantons can deviate substantially from sphericity and can in fact develop a neck - a feature prohibited in theories with minimal coupling. Such instantons with necks lead to the materialisation of bubble geometries containing a wormhole region. We clarify the relationship of neck geometries to violations of the null energy condition, and also derive a bound on the size of the neck relative to that of the instanton

We numerically study the dual field theory evolution of five-dimensional asymptotically anti-de Sitter solutions of supergravity that develop cosmological singularities. The dual theory is an unstable deformation of the N = 4 gauge theory on R × S 3 , and the big crunch singularity in the bulk occurs when a boundary scalar field runs to infinity. Consistent quantum evolution requires one imposes boundary conditions at infinity. Modeling these by a steep regularization of the scalar potential, we find that when an initially nearly homogeneous wavepacket rolls down the potential, most of the potential energy of the initial configuration is converted into gradient energy during the first oscillation of the field. This indicates there is no transition from a big crunch to a big bang in the bulk for dual boundary conditions of this kind.