Non-Hermitian Holographic Flows to Little Rip Cosmologies

This paper investigates the interior geometry of black holes in holographic models dual to non-Hermitian, PT-symmetric quantum field theories. Specifically, it explores whether violating the null energy condition (NEC) through non-Hermitian deformations allows for cosmological regimes that differ from the standard Belinski-Khalatnikov-Lifshitz (BKL) paradigm, which typically governs the approach to spacelike singularities.

The authors utilize a holographic model where a 3D Hermitian CFT is deformed by non-Hermitian sources for a charged scalar operator. By constructing a thermofield double (TFD) state—where both boundaries are governed by the same non-Hermitian Hamiltonian but with opposite time orientations—they effectively restore PT-symmetry at the level of the thermal state. They then analyze the bulk geometry of these black holes, focusing on the deep-interior dynamics and the behavior of two-sided heavy-operator correlators to probe the singularity.

The study uncovers a novel, non-Kasner regime within the PT-restored phase of the theory. Unlike standard BKL singularities, which are typically chaotic and Kasner-like, this interior describes an isotropic FLRW cosmology undergoing super-accelerated expansion, approaching a Little Rip. In this regime, curvature invariants diverge only asymptotically as proper time approaches infinity, rather than at a finite time. This geometry leaves a distinct signature on two-sided heavy-operator correlators: the renormalized geodesic length behaves non-algebraically in the large-energy limit, providing a clear observational distinction from standard Kasner interiors.

This work provides a concrete holographic realization of a Little Rip cosmology, offering a new laboratory to study cosmological singularities beyond the BKL paradigm. By establishing a potential Little Rip/CFT correspondence, the authors open a path to exploring complex cosmological dynamics through the lens of non-Hermitian quantum field theory, potentially bridging the gap between open quantum systems and gravitational physics.