In my Masters thesis, I analyzed one of the most important results in Cosmology, the Reciprocity Theorem, illustrating several proofs and reviewing astrophysical observations. In terms of luminosity distance and angular diameter distance, the Reciprocity Theorem is also known as Cosmic Distance Duality Relation (CDDR).
Several proofs of this theorem were found, using independent methodologies. However, all these proofs are in the framework of geometrical optics approximation and are based on the same two assumptions: photons travel along null geodesics; the photon number is conserved along their path. In my thesis I reviewed five different proofs of this theorem: three of them analyze bundles on light rays, the others obtain the same result in statistical mechanics.
This relation and its consequences were tested, in particular studying deviations of the CDDR in galaxy clusters. The astrophysical observations that I presented use various methodologies, each having advantages as well as problems, such as the choice of the mass distribution function for gas in galaxy clusters and the SNe Ia light curve fitter. However, they are all consistent with CDDR within 2σ. The choice of analyzing these relations in galaxy cluster observations is motivated by the need for testing deviations which cannot be observed at small scales.
My PhD research addressed aspects of Quantum Gravity Phenomenology. This branch of physics is critically important since it aims to test effects of theories of Quantum Gravity (QG). Among several aspects of Quantum Gravity Phenomenology, the Generalized Uncertainty Principle (GUP) is a modification of Heisenberg's Uncertainty Principle (HUP) with the purpose of describing a minimal measurable length. GUP and its implications can be one of the rare opportunities to test quantum gravitational regimes at accessible energy scales, even though the Planck energy scale is several orders of magnitude away. My research was motivated by two critically important questions: are there any observable effects of this proposed fundamental modification of the HUP? And if so, in which quantum system?
As part of this program:
I investigated formal aspects and issues related to models of quantum mechanics with a minimal measurable length. In particular, I analyzed the concept of position, the role of conjugate variables, as well as aspects concerning space and time transformations.
I proposed to apply GUP to the theory of quantum angular momentum and to spectroscopy. Indeed, since theories of QG predict the existence of a minimal measurable length, the same theories also predict a minimal angular resolution. Working on this project I found several new, testable results and effects driven by the GUP. I also found modifications to the hydrogen atom and the theoretical description of spectroscopic lines.
I studied a practical realization of an experiment to test the GUP in Quantum Optics. I showed how it may be possible to enhance the Planck scale effects to any desired level, while reducing unwanted deleterious effects.
I investigated the influence of GUP on the harmonic oscillator, especially its coherent and squeezed states. In particular, using a perturbative approach, I defined a new set of annihilation, creation, and number operators. This allowed me to study Planck scale corrected coherent and squeezed states for the modified Hamiltonian.
Extending the perturbative approach in the previous point, I found a general method to define perturbed ladder operators for a harmonic oscillator with a generic potential.
Using these studies on the harmonic oscillator with a minimal length, an extension of Quantum Optics with a similar realization has been proposed and the study of quantum noises in Michelson-Morley interferometers has been performed. This resulted in the identification of signatures of Planck-scale effects in LIGO experiments.
The harmonic oscillator has been considered again in a non-perturbative analysis with a minimal length, obtaining new ladder operators and a toy model for QFT with a minimal length.
Assuming the equivalence between Hamilton's equations of classical mechanics and Heisenberg's equations of quantum mechanics, I was able to find a consistent description of classical systems inspired by GUP. This led to a rigorous study of a new mechanical theory with modified Poisson brackets. Minimal coupling, harmonic oscillator, and the Kepler problem has been studied.
I collaborated in a project addressing relativistic quantum mechanical theories with a minimal observable length. Although few attempts have been made in the past, to my knowledge no systematic study of Relativistic Quantum Mechanics or of Quantum Field Theory exists. In particular, the Klein-Gordon, Dirac, the electromagnetic field, and some applications are studied. We expect this study to open new possibilities of testing quantum gravitational effects in relativistic systems.
My current research activities are in theoretical modelizations and experimental realizations of multimode sources for non-classical radiation. Using quadratic interaction between light fields and LiNbO3, amplitude-squeezed twin beams can be generated. This protocol can have significant impact on future communication technologies.
Why I’ve removed journal titles from the papers on my CV, by Adrian Barnett
33 P. Bosso, F. Illuminati, L. Petruzziello, F. Wagner, Spin couplings as witnesses of Planck scale phenomenology (2024).
32 P. Bosso, Minimal-length quantum field theory: a first-principle approach (2024).
31. P. Bosso, O. Obregón, S. Rastgoo, W. Yupanqui, Black hole interior quantization: a minimal uncertainty approach (2024).
30. P. Bosso, G. Fabiano, D. Frattulillo, F. Wagner, The fate of Galilean relativity in minimal-length theories (2023).
29. P. Bosso, G. G. Luciano, L. Petruzziello, F. Wagner, 30 years in: Quo vadis generalized uncertainty principle?, in Focus Issue Focus on Quantum Gravity Phenomenology in the Multi-Messenger Era: Challenges and Perspectives (2023).
28. P. Bosso, F. Illuminati, L. Petruzziello, F. Wagner, Bell nonlocality in maximal-length quantum mechanics” (2023).
27. P. Bosso, L. Petruzziello, F. Wagner, The minimal length: a cut-off in disguise? (2023).
26. P. Bosso, L. Petruzziello, F. Wagner, F. Illuminati, Bell nonlocality in quantum-gravity induced minimal-length quantum mechanics (2022).
25. P. Bosso, Space and time transformations with a minimal length (2023).
24. (Proceedings) V.N. Todorinov, S. Das, P. Bosso, Effective field theory from relativistic Generalized Uncertainty Principle, (2023).
23. P. Bosso, L. Petruzziello, F. Wagner, The minimal length is physical (2022).
22. P. Bosso, J.M. López Vega, Minimal Length Phenomenology and the Black Body Radiation (2022).
21. P. Bosso, M. Fridman, G.G. Luciano, Dark Matter as an effect of a minimal length, in Special Issue Generalized Uncertainty Relations: Existing Paradigms and New Approaches (2022).
20. A. Addazi et al., Quantum gravity phenomenology at the dawn of the multi-messenger era – A review, arXiv:2111.05659 [hep-ph] (2022).
I contributed to Section 2.2.4.
19. P. Bosso, Position in Minimal Length Quantum Mechanics, in Special Issue The Quantum & The Gravity (2022).
18. P. Bosso, G. G. Luciano, Generalized Uncertainty Principle: from the harmonic oscillator to a QFT toy model, arXiv:2109.15259 [hep-th] (2021).
17. P. Bosso, O. Obregón, S. Rastgoo and W. Yupanqui, Deformed algebra and the effective dynamics of the interior of black holes, arXiv:2012.04795 [gr-qc] (2021).
16. P. Bosso, On the quasi-position representation in theories with a minimal length, arXiv:2005.12258 [gr-qc] (2021).
15. (Proceedings) P. Bosso, Position in models of quantum mechanics with a minimal length (2021).
14. P. Bosso, A. Huber, V. Todorinov, Experimental test of fair three-sided coins (2021).
13. P. Bosso, S. Das, V. Todorinov, Quantum field theory with the generalized uncertainty principle II: Quantum electrodynamics, arXiv:2005.03772 [gr-qc] (2021).
12. P. Bosso, S. Das, V. Todorinov, Quantum field theory with the generalized uncertainty principle I: scalar electrodynamics, arXiv:2005.03771 [gr-qc] (2020).
11. P. Bosso, S. Das, V. Todorinov, Response to Comments on the paper "Relativistic generalized uncertainty principle" (2020).
10. P. Bosso, O. Obregón, Minimal Length Effects on Quantum Cosmology and Quantum Black Hole Models, arXiv:1904.06343 [gr-qc] (2020).
9. V. Todorinov, P. Bosso, S. Das, Relativistic Generalized Uncertainty Principle, arXiv:1810.11761 [gr-qc] (2019).
8. P. Bosso, S. Das, On Lorentz invariant mass and length scales, arXiv:1812.05595 [gr-qc] (2019).
7. P. Bosso, S. Das, Comments on 'Schwinger's Model of Angular Momentum with GUP' by H. Verma et al., arXiv:1809.02605 [quant-ph] (2019).
6. P. Bosso, S. Das, R. Mann, Potential tests of the generalized uncertainty principle in the advanced LIGO experiment, arXiv:1804.03620 [gr-qc] (2018).
5. P. Bosso, S. Das, Generalized ladder operators for the perturbed harmonic oscillator, arXiv:1807.05436 [quant-ph] (2018).
4. P. Bosso, Rigorous Hamiltonian and Lagrangian analysis of classical and quantum theories with minimal length, arXiv:1804.08202 [gr-qc] (2018)
3. P. Bosso, S. Das, R. Mann, Planck scale Corrections to the Harmonic Oscillator, Coherent and Squeezed States, arXiv:1704.08198 [gr-qc] (2017)
2. P. Bosso, S. Das I. Pikovski, M. Vanner, Amplified transduction of Planck-scale effects using quantum optics, arXiv:1610.06796 [gr-qc] (2017)
1. P. Bosso, S. Das, Generalized Uncertainty Principle and Angular Momentum, arXiv:1607.01083 [gr-qc] (2017)
Generalized Uncertainty Principle and Quantum Gravity Phenomenology