Jing Liu, Zong-Kuan Guo, Rong-Gen Cai, Gary Shiu

We study the production of gravitational waves during oscillations of the inflaton around the minimum of a cuspy potential after inflation. We find that a cusp in the potential can trigger copious oscillon formation, which sources a characteristic energy spectrum of gravitational waves with double peaks. The discovery of such a double-peak spectrum could test the underlying inflationary physics.

Abhay Ashtekar, Béatrice Bonga

Somewhat surprisingly, in many of the widely used monographs and review articles the term \emph{Transverse-Traceless modes} of linearized gravitational waves is used to denote two entirely different notions. These treatments generally begin with a decomposition of the metric perturbation that is \emph{local in the momentum space} (and hence non-local in physical space), and denote the resulting transverse traceless modes by $h_{ab}^{\TT}$. However, while discussing gravitational waves emitted by an isolated system --typically in a later section-- the relevant modes are extracted using a `projection operator' that is \emph{local in physical space}. These modes are also called transverse-traceless and again labeled $h_{ab}^{\TT}$, implying that this is just a reformulation of the previous notion. But the two notions are conceptually distinct and the difference persists even in the asymptotic region. We show that this confusion arises already in Maxwell theory that is often discussed as a prelude to the gravitational case. Finally, we discuss why the distinction has nonetheless remained largely unnoticed, and also point out that there are some important physical effects where only one of the notions gives the correct answer.

Abhay Ashtekar, Béatrice Bonga

In much of the literature on linearized gravitational waves two completely different notions are called transverse traceless modes and labelled $h_{ab}^{TT}$, often in different sections of the same reference, without realizing the underlying inconsistency. We compare and contrast the two notions and find that the difference persists even at leading asymptotic order near future null infinity $\mathit{I}^+$. We discuss why the distinction has nonetheless remained largely unnoticed, and also point out that there are some important physical effects where only one of the notions gives the correct answer.

Michael Dumbser, Federico Guercilena, Sven Koeppel, Luciano Rezzolla, Olindo Zanotti

We present a strongly hyperbolic first-order formulation of the Einstein equations based on the conformal and covariant Z4 system (CCZ4) with constraint-violation damping, which we refer to as FO-CCZ4. As CCZ4, this formulation combines the advantages of a conformal and traceless formulation, with the suppression of constraint violations given by the damping terms, but being first order in time and space, it is particularly suited for a discontinuous Galerkin (DG) implementation. The strongly hyperbolic first-order formulation has been obtained by making careful use of first and second-order ordering constraints. A proof of strong hyperbolicity is given for a selected choice of gauges via an analytical computation of the entire eigenstructure of the FO-CCZ4 system. The resulting governing partial differential equations system is written in non-conservative form and requires the evolution of 58 unknowns. A key feature of our formulation is that the first-order CCZ4 system decouples into a set of pure ordinary differential equations and a reduced hyperbolic system of partial differential equations that contains only linearly degenerate fields. We implement FO-CCZ4 in a high-order path-conservative arbitrary-high-order-method-using-derivatives (ADER)-DG scheme with adaptive mesh refinement and local time-stepping, supplemented with a third-order ADER-WENO subcell finite-volume limiter in order to deal with singularities arising with black holes. We validate the correctness of the formulation through a series of standard tests in vacuum, performed in one, two and three spatial dimensions, and also present preliminary results on the evolution of binary black-hole systems. To the best of our knowledge, these are the first successful three-dimensional simulations of moving punctures carried out with high-order DG schemes using a first-order formulation of the Einstein equations.

S. W. Hawking, Thomas Hertog

The usual theory of inflation breaks down in eternal inflation. We derive a dual description of eternal inflation in terms of a deformed IR CFT located at the threshold of eternal inflation. The partition function gives the amplitude of different geometries of the threshold surface in the Hartle-Hawking state. Its local and global behavior in dual toy models shows that the amplitude is low for surfaces which are not nearly conformal to the round three-sphere, and essentially zero for surfaces with negative curvature. Based on this we conjecture that the exit from eternal inflation does not produce an infinite fractal-like multiverse, but is finite and reasonably smooth.