Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2305.12215

Introduction to Loop Quantum Gravity: Rovelli's lectures on LQG

Pietropaolo Frisoni
View original source ↗Read source document ↗Export metadata ↓

Abstract

These notes are a transcript of Carlo Rovelli's lectures on Loop Quantum Gravity, given in Marseille in 2018, which (at present) can be entirely found on YouTube. I transcribed them in LaTeX in early 2020 as an exercise to get ready for my Ph.D. in LQG at Western University. This transcript is meant to be a (hopefully helpful) integration for the video version. I reported the order of the topics and the chronological structure exactly as presented by Rovelli throughout the course, primarily to facilitate the comparison. Each Section corresponds to a different Lecture. The parts written in textit are my additions. Sometimes in the text, I report references, which specify precisely the minute and the second of the corresponding video on YouTube, to very short historical digressions or excursus made during the lectures by Rovelli that I have not explicitly transcribed in these notes. Where appropriate, I took some figures from the book "Covariant Loop Quantum Gravity - An elementary introduction to Quantum Gravity and Spinfoam Theory" by Carlo Rovelli and Francesca Vidotto, to which I always refer by the term "the book" in the following. For what concerns the equations, where possible, I tried to write down the "correct" versions present within the book. Finally, I thank Carlo Rovelli himself for reviewing these notes. I apologize in advance for any errors, and I wish everyone a lot of fun!

Explore related subjects

gr-qcmath-phmath.MPquant-ph

Keep this discovery

BibTeXRIS

Pietropaolo Frisoni. 2023-05-20. Introduction to Loop Quantum Gravity: Rovelli's lectures on LQG. https://arxiv.org/abs/2305.12215

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Electrovacuum Black Hole Uniqueness

We prove the black hole uniqueness conjecture in the axially symmetric, stationary, electrovacuum setting, subject to the refined asymptotic analysis of the associated singular harmonic maps, which includes an analyticity hypothesis at the axes. More precisely, it is shown that any asymptotically flat solution of the Einstein--Maxwell equations in this class, with more than one black hole horizon component is either: Majumdar--Papapetrou, up to a duality rotation, in which case all logarithmic angle defects vanish, or every finite axis rod logarithmic angle defect is strictly negative and hence every interaction force is strictly attractive. The proof extends the singular harmonic map method used for vacuum Kerr uniqueness in [18].

gr-qc↗
arXiv2026

Constraining Modified Mass-to-Horizon Cosmology Through Primordial Inflationary Observables

We investigate slow-roll inflation in a modified cosmological framework inspired by a generalized mass-to-horizon relation (MHR), $M=\gamma {c^2 L^n}/{G}$, where $n$ is a real parameter and $\gamma$ a dimensional constant. Using Padmanabhan's emergence paradigm, we derive the modified Friedmann equations for a flat FRW universe and analyze the dynamics of a canonical scalar field (inflaton) under the slow-roll approximation. We study the resulting inflationary phenomenology for power-law and Starobinsky potentials. For power-law potentials, the MHR modification fails to reconcile these models with current CMB constraints on $r$ and $n_s$. In contrast, Starobinsky inflation exhibits significant sensitivity to deviations from $n=1$. A perturbative analysis ($n=1+\Delta$) yields corrections to inflationary observables. We observe that the scalar power-spectrum normalization, under a fixed-Starobinsky prescription, imposes the stringent constraint $0.960 \lesssim n \lesssim 1.040$ for $N=60$ efolds. This is considerably tighter than spectral-index bounds. Our results establish inflation, particularly Starobinsky-like models, as a sensitive probe of generalized horizon thermodynamics and departures from standard MHR scaling.

gr-qc↗
arXiv2026

Improving the Sensitivity of Gravitational Wave Detection with Weighted Conformal Prediction

In the last decade, kilometre-scale interferometric gravitational-wave detectors have observed hundreds of compact binary mergers, the majority of which are binary black holes. However, the data are noise-dominated, and multiple independent search algorithms (pipelines) are used to enhance sensitivity and improve robustness. Rather than the standard approach of selecting the most significant pipeline output, we combine the outputs from all pipelines using a conformal prediction-based framework to provide statistically rigorous confidence estimates for candidate events. While combining pipelines improves sensitivity and ranking robustness, it requires a principled statistical framework that remains valid as data properties evolve across observing runs. A key challenge is distribution shifts between simulated datasets used for training and calibration and the real, unlabelled, observations used for testing, which can invalidate coverage guarantees and bias confidence estimates. In this work, we address this challenge by incorporating likelihood-ratio reweighting into our conformal prediction framework to account for covariate shift. Using mock datasets containing simulated signals, we demonstrate that weighted conformal prediction restores well-calibrated coverage under covariate shift and increases the confidence of events near the detection threshold, recovering true signals that would otherwise be missed.

gr-qc↗