Speaker
Description
"A central goal at the interface of quantum gravity and cosmology is to characterize spacetime in purely relational, coordinate-independent terms. In early-universe cosmology, observational access to spacetime geometry is mediated not through coordinates, but through the spectral modes of quantum fields and their higher-order correlators. However, the spectrum of a linear wave operator alone generally cannot distinguish isospectral, non-isometric geometries; one cannot, in general, “hear the shape” of spacetime.
We demonstrate that local nonlinear field interactions supply the missing information to reconstruct the underlying geometry in causal set theory, a Lorentz-invariant approach to quantum gravity in which spacetime is fundamentally discrete. Starting from the spectrum of a Hermitianized Benincasa-Dowker wave operator and a local λφ⁴ interaction in its spectral basis, we extract the unitary map to the local position basis and reconstruct the underlying finite causal set up to relabeling. Rather than requiring the full N⁴ vertex, a two-leg contraction leaving only N² components suffices, as we demonstrate explicitly on a 3+1D causal set with N = 20.
Because causal order and volume determine the underlying geometry, these nonlinearities render spacetime curvature audible. Furthermore, the continuum limit of the Benincasa-Dowker operator, □ − R/2 (where R is the Ricci scalar), suggests a direct extension of this construction to continuum spacetimes. More broadly, this raises the question of how much information about microscopic spacetime structure may be encoded in the nonlinear and higher-point field correlations accessible to cosmology."