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  • Open Access

Fully relativistic evolution of vacuum tensor inhomogeneities during inflation

Ericka Florio* and E. Paul S. Shellard†

  • Centre for Theoretical Cosmology, Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom

  • *Contact author: eaf49@cam.ac.uk
  • †Contact author: eps1@cam.ac.uk
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Phys. Rev. D 113, 023534 – Published 21 January, 2026

DOI: https://doi.org/10.1103/l48w-z27g

Abstract

We present a complete method for the initialization and extraction of first-order inflationary tensor perturbations for fully relativistic simulations which incorporate gravitational backreaction. We outline a correspondence between the cosmological perturbation theory framework and the numerical relativity variables in the appropriate limit. We describe a generation method for stochastic tensoral initial conditions, inspired by the standard scalar initial condition used from inflation and implemented in lattice cosmology. We discuss the implementation of this procedure in the grchombo/grteclyn code, and demonstrate the detailed quantitative correspondence between the linearized and fully nonlinear solutions in the perturbative limit, through the evolution of the background and the tensor power spectrum. We also validate the methodology by showing that energy and momentum constraints are introduced and preserved to second-order or better. We provide some preliminary indicative results probing tensoral non-Gaussianity using the skewness and kurtosis. The computational pipeline presented here will be used to study the emergence of a primordial tensor bispectra and cross spectra that incorporate the effect of nonlinear gravitational couplings with the metric, which has potential applications for the analysis of next-generation cosmic microwave background observations.

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Phys. Rev. D 113, 023534– Published 21 January, 2026
  • Received 26 May 2025
  • Accepted 23 December 2025
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