My past and current research activity sits in Quantum Field Theory in Curved Spacetimes and Semiclassical Gravity in the realm of Algebraic Quantum Field Theory, with main applications in Inflationary Cosmology and Black Hole Physics. In the semiclassical approach, the interplay between quantum matter and gravity is described by the modification of the spacetime geometry induced by quantum fields, i.e., the backreaction. To this avail, algebraic methods provide a precise mathematical formulation of the phenomena ruling the propagation of quantum fields on globally hyperbolic Lorentzian manifolds. The fundamental equations in Semiclassical Gravity incorporating backreaction are the Semiclassical Einstein Equations, in which the classical Einstein tensor is equated to the expectation value of the renormalized quantum stress-energy tensor.
My research in this context has offered new important insights about the existence of local and global solutions of the Semiclassical Einstein Equations, and their properties of stability under small perturbations. Furthermore, new semiclassical results have been obtained in cosmological models and black hole spacetimes, concerning the backreaction effects in horizon mechanics and thermodynamics, and in the framework of the theory of cosmological perturbations.
More recently, my research activity has also focused on the study of Fermionic Cellular Automata (FCA) in the framework of Operator Algebra and its applications to Quantum Information Theory. FCA constitute the fermionic counterpart of Quantum Cellular Automata, which represent the most general discrete-time, finite-range unitary dynamics of a lattice of countably many quantum systems. In the algebraic framework FCA are homogeneous automorphisms of superalgebras which model local and causal discrete evolutions in time of a grid of Fermionic modes located at each quantum cell.
[1] M. B. Fröb, D. Glavan, P. Meda, and I. Sawicki, “One-loop correction to primordial tensor modes during radiation era”, arXiv preprint (2025) [2504.02609].
In a joint collaboration with Dr. M. B. Fröb (Institut für Theoretische Physik, Universität Leipzig), Dr. D. Glavan, and Dr. I. Sawicki (CEICO, FZU - Institute of Physics of the Czech Academy of Sciences), superhorizon perturbations driving the radiation dominated Universe were studied in the framework of Cosmological Perturbation Theory. We evaluate the one-loop correction to the power spectrum of primordial tensor perturbations interacting with a plasma of free photons in a thermal state. It turns out to be a growing logarithmic secular correction to the power spectrum, thus indicating the breakdown of the one-loop expansion and/or of the linear evolution of tensor perturbations on superhorizon scales.
[2] E. D’Angelo, M. B. Fröb, S. Galanda, P.Meda, A. Much, and K. Papadopoulos, “Entropy-area law and temperature of de Sitter horizons from modular theory”, Progress of Theoretical and Experimental Physics, Volume 2024 (2024). [10.1093/ptep/ptae003].
In a joint collaboration with Dr. E. D'Angelo (University of Genoa), Dr. M. B. Fröb (Institut für Theoretische Physik, Universität Leipzig), Mr. S. Galanda (University of Genoa), Dr. A. Much (Institut für Theoretische Physik, Universität Leipzig), and K. Papadopoulos (Kuwait University), a new semiclassical derivation of an entropy-area law is given for the future horizon of an observer living in a de Sitter diamond in the static patch, using Tomita–Takesaki modular theory and coherent states. Moreover, the local temperature measured by an observer at rest is evaluated, and it exhibits subleading quantum corrections with respect to the well-known cosmological horizon temperature.
[3] P. Meda, N. Pinamonti, and D. Siemssen, “Existence and uniqueness of solutions of the semiclassical Einstein equation in cosmological models”, Ann. Henri Poincaré 22 (2021) [10.1007/s00023- 021-01067-8].
The initial-value formulation of the Semiclassical Einstein Equations in cosmological spacetimes is addressed for massive, arbitrary coupled scalar fields. In this case, both fourth-order derivatives of the metric and the term with the highest derivative appear in a non local form. It was proved the existence and uniqueness of solutions for short intervals of time by applying the Banach fixed point theorem, after rewriting the semiclassical equation in a new, non-standard form. The work was a joint collaboration with Prof. N. Pinamonti (University of Genoa) and Dr. D. Siemssen (University of Wuppertal).
[1] P. Meda, N. Pinamonti, S. Roncallo, and N. Zanghì, “Evaporation of four-dimensional dynamical black holes sourced by the quantum trace anomaly”, Class. Quant. Grav. 38 (2021) [10.1088/1361-6382/ac1fd2].
Black hole evaporation was originally shown by S. Hawking, who proved that a static black hole can emit thermal radiation at late times, hence losing mass in time, in absence of backreaction. In a joint work with Prof. N. Pinamonti, Dr. S. Roncallo, and Prof. N. Zanghì (University of Genova), the evaporation of a four dimensional spherical black hole was studied by analyzing the local dynamics of the dynamical horizon. Taking into account the backreaction of a massless, conformally coupled scalar field, it was proved that the trace anomaly of the quantum stress-energy tensor can be source of evaporation, after assuming vacuum-like initial conditions in the past and an auxiliary averaged quantum energy condition outside the horizon.
[1] P. Meda, and N. Pinamonti, “Linear Stability of Semiclassical Theories of Gravity”, Ann. Henri Poincaré 24 (2023) [10.1007/s00023-022-01246-1].
In collaboration with Prof. N. Pinamonti (University of Genoa), the issue of linear stability of semiclassical theories in the weak field limit was investigating in a toy model, consisting of a quantum scalar field in interaction with a classical scalar field. This model also mimics the dynamics of the Semiclassical Einstein Equations in cosmological spacetimes. It was shown that, if the quantum field which drives the backreaction is massive, then a well-posed initial-value problem can be formulated for several choices of the renormalization parameters. This result proves the absence of exponentially growing solutions in time ("runaway solutions") and the stability of the underlying semiclassical solution.
[1] L. S. Trezzini, M. Lugli, P. Meda, A. Bisio, P. Perinotti, and A. Tosini, “Fermionic cellular automata in one dimension”, arXiv preprint (2025) [2501.05349].
In a joint work with Mr. L. S. Trezzini, Dr. M. Lugli, Prof. A. Bisio, Prof. P. Perinotti, and Dr. A. Tosini (University of Pavia), we strengthen the classification of FQCA in terms of an index modulo circuits by removing the ancilla degrees of freedom in defining the equivalence classes. Moreover, we provide a complete characterization of one-dimensional, nearest-neighbours FQCA consisting of a single local Fermionic mode per site. In this classification, we find a class of FQCA which is unique to the Fermionic theory and cannot be expressed in terms of single mode and controlled-phase gates composed with shifts, as is the case for qubit cellular automata.