Quantum Complexity of Primordial Perturbations in Modified Gravity

A recent study has explored the quantum complexity of primordial curvature perturbations, fundamental for understanding the origin of cosmic structures, within the inflationary paradigm. The research compares the canonical scalar-field inflation model with a modified gravity model $f(\phi,R)$, focusing on the evolution of the two-mode squeezed state generated by the coupling between the $\vec{k}$ and $-\vec{k}$ momentum sectors. This work sheds new light on how modified gravity theories can influence the quantum properties of the early universe. The researchers started from the quadratic action for curvature perturbations and derived the evolution equations for the squeezed strength $r_k$ and squeezed angle $\phi_k$. Using these parameters, they evaluated both circuit complexity and Krylov-space diagnostics. Specifically, they computed Krylov complexity, Krylov entropy, Lanczos coefficients $b_n$, and an effective dissipative contribution $c_n$ within an open-system extension. Numerical analysis revealed that the $f(\phi,R)$ coupling in modified gravity enhances the squeezed strength relative to canonical scalar-field inflation. This enhancement in squeezed strength has direct implications for quantum complexity. Since the Krylov complexity of the two-mode squeezed state is directly controlled by the mean pair number ($K=\sinh^2 r_k$), the observed enhancement leads to a smaller growth in Krylov complexity and related Krylov-space quantities. Conversely, circuit complexity displayed a more pronounced evolution within the $f(\phi,R)$ framework, particularly after the horizon exit regime. These findings suggest that modifications to gravity can significantly alter how quantum information is processed and evolves in the primordial universe.

Relativistic Extended Thermodynamics for Polyatomic Gases in Curved Spacetime

Researchers have formulated a six-field Rational Extended Thermodynamics (RET$_6$) model for relativistic polyatomic gases in curved spacetime. This model, based on a polyatomic extension of the Boltzmann-Chernikov kinetic equation, incorporates dynamical pressure as the sole non-equilibrium variable. The one-particle distribution in this framework also depends on an internal-energy variable, and the closure of the associated relativistic moment hierarchy is achieved via the Maximum Entropy principle. The field equations, closure relations, and production term are directly derived from the underlying kinetic structure, rather than being phenomenologically postulated. The RET$_6$ model is extended from Minkowski spacetime to a general curved spacetime through minimal coupling and linked to Einstein's equations. A key structural result is a kinetic-theory no-go theorem stating that any stress-energy tensor induced by a non-negative relativistic one-particle distribution function satisfies the strong energy condition. When applied to a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime, it is observed that dynamical pressure modifies the expansion compared to the perfect-fluid Euler case, although the no-go theorem precludes acceleration driven solely by the RET$_6$ gas. Finally, by reintroducing a cosmological constant, the combined $\Lambda$RET$_6$ model demonstrates the existence and local stability of a de Sitter attractor at late times. Numerical simulations indicate that, for physically motivated post-recombination initial data and relaxation times, the expansion history rapidly approaches that of the $\Lambda$CDM model. The small non-equilibrium corrections observed are controlled by the relaxation time and the initial value of the dynamical pressure, suggesting this model may offer a more complete description of cosmological dynamics in certain phases.

Nonlinear Detectors Challenge Rindler Firewall Model

A recent study has investigated the response of nonlinear particle detectors to the so-called "Rindler firewall," a theoretical concept describing an extreme energy barrier at the event horizon of a black hole. Contrary to expectations for linear detectors, detectors coupled to composite observables of a quantum scalar field, such as quadratic field momentum or local energy density, exhibit irresolvable divergences. These results suggest a fundamental incompatibility between the standard Rindler firewall model and nonlinear detector interactions with local observables. The researchers developed a distributional framework to evaluate the response functions of these detectors. While derivative-coupling models recover a finite response, quadratic coupling to the field momentum leads to ill-defined products of distributions and formal δ(0)-type divergences. Since the local energy-density response is closely tied to the quadratic momentum response, these pathologies are consistent and point to an inherent problem with the firewall model. This finding is significant because the Rindler firewall is a theoretical construct used to explore information paradoxes in black holes. The emergence of these divergences suggests that the pathologies do not originate from the detector model itself, but rather from the discontinuous severing of correlations across the Rindler horizon, a central element of the firewall concept. This could imply a need to revise assumptions about the nature of spacetime near event horizons and how quantum information behaves in these extreme regions.