eprintid: 36791
rev_number: 15
eprint_status: archive
userid: 9110
dir: disk0/00/03/67/91
datestamp: 2025-07-09 07:47:37
lastmod: 2025-07-10 18:16:44
status_changed: 2025-07-09 07:47:37
type: doctoralThesis
metadata_visibility: show
creators_name: Hemmatyar, Shayan
title: Theoretical and Machine Learning Approaches to Beyond General Relativity: Stability of Generalized Proca Theories and Multi-Method Classification of Gravitational Wave Observables
subjects: ddc-500
subjects: ddc-530
divisions: i-130300
adv_faculty: af-13
cterms_swd: Quantum Stability
cterms_swd: Gravitational waves
cterms_swd: machine learning
cterms_swd: neural network
cterms_swd: generalized Proca theories
cterms_swd: quantum field theory
cterms_swd: classification
cterms_swd: modified gravity
cterms_swd: beyond general relativity
cterms_swd: 1-loop computation
cterms_swd: curved spacetime
cterms_swd: power counting
cterms_swd: UV-divergent
cterms_swd: decoupling limit
cterms_swd: stuckelberg transformation
abstract: This thesis explores two complementary approaches to testing and understanding grav- ity beyond General Relativity (GR). The first part focuses on Generalized Proca theo- ries—vector-tensor models that extend the Proca action through derivative self-interactions and non-minimal couplings, while maintaining second-order equations of motion and avoid- ing ghost instabilities. We analyze the quantum consistency of these theories in both flat Minkowski spacetime and weakly curved backgrounds. In flat space, we compute one-loop corrections and observe the emergence of gauge-invariant structures, suggesting a form of radiative stability. In curved spacetime, we develop a scalar-vector-tensor (SVT) decom- position to isolate physical modes and consistently integrate out non-dynamical fields. Our results show that the theories remain well-behaved under quantum corrections, supporting their viability as effective field theories.
The second part leverages gravitational wave (GW) observations as precision probes of strong-field gravity. Using convolutional neural networks (CNNs), we construct a ma- chine learning framework to classify GW signals as either consistent with GR or exhibiting beyond-GR (BGR) deviations. The dataset includes both artificial phase deformations and physically motivated waveforms derived using the parameterized post-Einsteinian (ppE) formalism. A key tool is the response function, which captures the sensitivity of the wave- form to small deformations. We show that training neural networks on response functions significantly improves classification accuracy and lowers detection thresholds. Applied to massive graviton models, this approach allows us to estimate the smallest graviton mass distinguishable from GR predictions.
Together, these investigations form a coherent program to study modified gravity from both theoretical and observational perspectives, contributing to the broader effort of devel- oping consistent and testable alternatives to Einstein’s theory.
date: 2025
id_scheme: DOI
id_number: 10.11588/heidok.00036791
ppn_swb: 1930290098
own_urn: urn:nbn:de:bsz:16-heidok-367910
date_accepted: 2025-06-25
advisor: HASH(0x5608d3e23ba0)
language: eng
bibsort: HEMMATYARSTHEORETICA2025
full_text_status: public
place_of_pub: Heidelberg
citation:   Hemmatyar, Shayan  (2025) Theoretical and Machine Learning Approaches to Beyond General Relativity: Stability of Generalized Proca Theories and Multi-Method Classification of Gravitational Wave Observables.  [Dissertation]     
document_url: https://archiv.ub.uni-heidelberg.de/volltextserver/36791/1/PhD_Thesis_Shayan_Hemmatyar.pdf