By Yoann Launay, DAMTP, University of Cambridge

In the past couple of years, we have planned and successfully executed theoretical and numerical pipelines to enable the study of inhomogeneous inflationary spacetimes with full dynamical degrees of freedom available in full general relativity. With respect to upcoming new generations of experiments, it is of great importance to probe highly non-linear and non-perturbative regimes which can emerge from simple Gaussian fluctuations sourced by the quantum vacuum energy. Most importantly, our studies are the first of their kind to provide a full spacetime numerical description of inflation from self-consistent initial conditions through nonlinear gravitational dynamics.

In our recent publication [arxiv:2502.06783, submitted to PRD] and displayed in the figure, we released our first numerical results highlighting excellent agreement with analytic predictions from  simple inflation models, while also offering new relativistic probes of previously unattainable regimes or scenarios. These simulations started from stochastic initial conditions and will benefit from an extension to stochastic sources at each time step [PhysRevD.109.123523]. This pioneering work solving stochastic partial differential equations for the inflationary universe will soon be offering new insights about nonlinear regimes producing non-Gaussian statistics.

As members of the DP002 group, these results were made possible by leveraging the computational resources provided by the DiRAC Data Intensive Service at Cambridge, together with the advanced capabilities of the public numerical relativity codes GRChombo and GRTeclyn, developed by the DiRAC-supported GRTL collaboration. 

Figure: Evolution (left to right) of boundary heatmaps and 3D rendering of volume isosrufaces of clustering energy density fluctuations. Before the inflaton decays, marking the birth of fundamental particles, fluctuations in spacetime and dark energy cluster, forming hotter, denser regions (orange to yellow) and colder regions (purple), thus initializing the cosmic web.