We show that the most general scalar-tensor theory of gravity up to four derivatives in $3+1$ dimensions is well-posed in a modified version of the CCZ4 formulation of the Einstein equations in singularity-avoiding coordinates. We demonstrate the robustness of our new formulation in practice by studying equal mass black hole binary mergers for different values of the coupling constants. Although our analysis of well-posedness is restricted to cases in which the couplings are small, we find that in simulations we are able to push the couplings to larger values, so that a certain weak coupling condition is order one, without instabilities developing. Our Letter provides the means for such simulations to be undertaken by the many numerical relativity codes that rely on the moving puncture gauge to evolve black hole singularities.

Some of the most important quintessential inflation scenarios, such as the Peebles–Vilenkin model, are described in detail. These models are able to explain the early- and late-time accelerated expansions of our universe, and the phase transition from the end of inflation to the beginning of kination where the adiabatic evolution of the universe was broken in order to produce enough particles to reheat the universe with a viable temperature, thereby aligning with the Hot Big Bang universe. In addition, while considering the reheating to be due to the gravitational production of superheavy particles conformally coupled to gravity, we checked that the considered scenarios do not suffer problems due to the overproduction of gravitational waves at the end of inflation, and thus the validity of Big Bang nucleosynthesis is preserved.

The dynamics of interacting dark matter-dark energy models is characterized through an interaction rate function quantifying the energy flow between these dark sectors. In most of the interaction functions, the expansion rate Hubble function is considered and sometimes it is argued that, as the interaction function is a local property, the inclusion of the Hubble function may influence the overall dynamics. This is the starting point of the present article where we consider a very simple interacting cosmic scenario between vacuum energy and the cold dark matter characterized by various interaction functions originated from a general interaction function: $Q=\mathrm{\Gamma }{\rho }_c^{\alpha }{\rho }_x^{1-\alpha -\beta }({\rho }_c+{\rho }_x{)}^{\beta }$, where ${\rho }_c$, ${\rho }_x$ are respectively the cold dark matter density and vacuum energy density; $\alpha$, $\beta$ are real numbers and $\mathrm{\Gamma }$ is the coupling parameter with dimension equal to the dimension of the Hubble rate. We investigate four distinct interacting cosmic scenarios and constrain them both theoretically and observationally. Our analyses clearly reveal that the interaction models should be carefully handled.

We develop a modified CCZ4 formulation of the Einstein equations in $d+1$ spacetime dimensions for general relativity plus a Gauss-Bonnet term, as well as for the most general parity-invariant scalar-tensor theory of gravity up to four derivatives. We demonstrate well-posedness for both theories and provide full expressions for their implementation in numerical relativity codes. As a proof of concept, we study the so-called “stealth scalarization” induced by the spin of the remnant black hole after the merger. As in previous studies using alternative gauges, we find that the scalarization occurs too late after the merger to impact the tensor waveform, unless the parameters are finely tuned. Naively increasing the coupling to accelerate the growth of the scalar field risks a breakdown of the effective field theory, and therefore well-posedness, as the evolution is pushed into the strongly coupled regime. Observation of such an effect would therefore rely on the detection of the scalar radiation that is produced during scalarization. This work provides a basis on which further studies can be undertaken using codes that employ a moving-punctures approach to managing singularities in the numerical domain. It is therefore an important step forward in our ability to analyze modifications of general relativity in gravitational wave observations.

We study the consequences of reheating in quintessential inflation. From simple inflationary quintessential models introduced by de Haro, Amorós, and Pan in [ Phys. Rev. D 93, 084018 (2016)] and [ Phys. Rev. D 94, 064060 (2016)], we show that when the reheating is due to the production of heavy massive particles conformally coupled with gravity, a viable model which matches with the current observational data is only possible for reheating temperatures that range between 1 GeV and $10^4\mathrm{GeV}$. On the other hand, when the Universe reheats via the production of massless particles, viability of the model is only possible when those particles are nearly conformally coupled with gravity, leading to a reheating temperature between 1 MeV and $10^4\mathrm{GeV}$.