Biblio.bib

@article{Energy-MomentumTensor,
	title = {Noether and {H}ilbert (metric) energy-momentum tensors are not, in general, equivalent},
	journal = {Nuclear Physics B},
	volume = {962},
	pages = {115240},
	year = {2021},
	issn = {0550-3213},
	doi = {https://doi.org/10.1016/j.nuclphysb.2020.115240},
	url = {https://www.sciencedirect.com/science/article/pii/S0550321320303254},
	author = {Mark Robert Baker and Natalia Kiriushcheva and Sergei Kuzmin},
	abstract = {Multiple methods for deriving the energy-momentum tensor for a physical theory exist in the literature. The most common methods are to use Noether's first theorem with the 4-parameter Poincaré translation, or to write the action in a curved spacetime and perform variation with respect to the metric tensor, then return to a Minkowski spacetime. These are referred to as the Noether and Hilbert (metric/ curved space/ variational) energy-momentum tensors, respectively. In electrodynamics and other simple models, the Noether and Hilbert methods yield the same result. Due to this fact, it is often asserted that these methods are generally equivalent for any theory considered, and that this gives physicists a freedom in using either method to derive an energy-momentum tensor depending on the problem at hand. The ambiguity in selecting one of these two different methods has gained attention in the literature, but the best attempted proofs of equivalence of the two methods require restrictions on the order of derivatives and rank of fields; general equivalence of the Noether and Hilbert methods has not been established. For spin-2, the ideal candidate to check this equivalence for a more complicated model, there exist many energy-momentum tensors in the literature, none of which are gauge invariant, so it is not clear which expression one hopes to obtain from the Noether and Hilbert approaches unlike in the case of e.g. electrodynamics. It has been shown, however, that the linearized Gauss-Bonnet gravity model (second order derivatives, second rank tensor potential) has an energy-momentum tensor that is unique, gauge invariant, symmetric, conserved, and trace-free when derived from Noether's first theorem (all the same properties of the physical energy-momentum tensor of electrodynamics). This makes it the ideal candidate to check if the Noether and Hilbert methods coincide for a more complicated model. It is proven here using this model as a counterexample, by direct calculation, that the Noether and Hilbert energy-momentum tensors are not, in general, equivalent.}
}
@article{NoetherVsHilbert,
	author = {Itin, Yakov},
	title = {Energy–momentum tensor: Noether vs {H}ilbert},
	journal = {International Journal of Geometric Methods in Modern Physics},
	volume = {0},
	number = {0},
	pages = {2350208},
	year = {0},
	doi = {10.1142/S0219887823502080},
	URL = {https://doi.org/10.1142/S0219887823502080},
	eprint = { https://doi.org/10.1142/S0219887823502080},
	abstract = { Several definitions of the energy–momentum tensor in classical field models on differential manifolds are examined in this work. We specifically talk about the connection between - Hilbert’s symmetric and Noether’s asymmetric energy–momentum tensors. We consider a matter field Lagrangian on a manifold endowed with a teleparallel (coframe) structure. The associated 3-form of coframe conserved current can be viewed as a link between Noether’s and Hilbert’s energy–momentum tensors. In these circumstances, we are able to show the complete equivalence of Hilbert’s and Noether’s currents for the matter field. }
}



@article{Bunch_Renorm,
	doi = {10.1088/0305-4470/13/3/022},
	url = {https://dx.doi.org/10.1088/0305-4470/13/3/022},
	year = {1980},
	month = {mar},
	publisher = {},
	volume = {13},
	number = {3},
	pages = {901},
	author = {T S Bunch and  P Panangaden and  L Parker},
	title = {On renormalisation of $\lambda\phi^4$ field theory in curved space-time.},
	journal = {Journal of Physics A: Mathematical and General},
	abstract = {Renormalisation of lambda phi 4 theory in curved space-time is considered in the interaction picture. A generalisation of normal ordering to curved space-time is introduced, based on the construction of adiabatic particle states in Robertson-Walker space-time. Dimensional regularisation is used to define uniquely the divergent quantities which are removed by normal ordering. It is shown that this normal ordering is sufficient to make finite all physical processes including vacuum polarisation to first order in lambda . An alternative and equivalent procedure is given which requires renormalisation of the mass and of the constant which couples the field to the Ricci scalar. The stress tensor is found to be finite to first order in lambda and it is shown that if the free-field theory in a Robertson-Walker universe predicts that particles are created by the gravitational field with a black-body spectrum then this spectrum is maintained when first-order self-interactions are taken into account. Finally, some aspects of the renormalisation of second-order physical processes are discussed.}
}

@book{BirrelDavies, place={Cambridge}, series={Cambridge Monographs on Mathematical Physics}, title={Quantum Fields in Curved Space}, DOI={10.1017/CBO9780511622632}, publisher={Cambridge University Press}, author={Birrell, N. D. and Davies, P. C. W.}, year={1982}, collection={Cambridge Monographs on Mathematical Physics}}

@article{BesselComplex,
	title={Bessel functions of purely imaginary order, with an application to second-order linear differential equations having a large parameter}, volume={21}, DOI={10.1137/0521055}, number={4}, journal={SIAM Journal on Mathematical Analysis}, author={Dunster, T. M.}, year={1990}, pages={995–1018},
} 

@misc{DLMF,
	title = "{NIST Digital Library of Mathematical Functions}",
	howpublished = "\url{https://dlmf.nist.gov/}, Release 1.1.11 of 2023-09-15",
	url = "https://dlmf.nist.gov/",
	note = "F.~W.~J. Olver, A.~B. {Olde Daalhuis}, D.~W. Lozier, B.~I. Schneider,
	R.~F. Boisvert, C.~W. Clark, B.~R. Miller, B.~V. Saunders,
	H.~S. Cohl, and M.~A. McClain, eds."}

@article{VacuumdeSitter,
	title = {Vacuum states in de {S}itter space},
	author = {Allen, Bruce},
	journal = {Phys. Rev. D},
	volume = {32},
	issue = {12},
	pages = {3136--3149},
	numpages = {0},
	year = {1985},
	month = {Dec},
	publisher = {American Physical Society},
	doi = {10.1103/PhysRevD.32.3136},
	url = {https://link.aps.org/doi/10.1103/PhysRevD.32.3136}
}


@article{CanoJones,
	author        = "A. Cano and E. Follana",
	title         = "{\href{https://deposita.unizar.es/record/69150?ln=es}{Geodésicas tipo tiempo en agujeros negros de
	Schwarzchild y Kerr}}",
	year          = "2022",
	note          = "Bachelor thesis in spanish.",
}

@book{QuantumEffects, place={Cambridge}, title={Introduction to Quantum Effects in Gravity}, DOI={10.1017/CBO9780511809149}, publisher={Cambridge University Press}, author={Mukhanov, Viatcheslav and Winitzki, Sergei}, year={2007}}

@misc{QFTCurved,
	author        = "M. Mariño",
	title = "{\href{https://www.marcosmarino.net/uploads/1/3/3/5/133535336/polycopie-qfcs.pdf}{QFT in curved space}}",
	note = "\textit{preliminary} and \textit{unfinished}  set of notes, last checked Nov. 13th 2023."}

@book{UCHBINDER_ODINCOV_SHAPIRO_1992, place={Bristol}, title={Effective action in quantum gravity}, publisher={Institute of Physics}, author={Buchbinder, I.L and Odintsov, S.D and Shapiro, I.L}, year={1992}} 

@article{HOLLANDS20151,
	title = {Quantum fields in curved spacetime},
	journal = {Physics Reports},
	volume = {574},
	pages = {1-35},
	year = {2015},
	note = {Quantum fields in curved spacetime},
	issn = {0370-1573},
	doi = {https://doi.org/10.1016/j.physrep.2015.02.001},
	url = {https://www.sciencedirect.com/science/article/pii/S0370157315001416},
	author = {Stefan Hollands and Robert M. Wald},
	abstract = {We review the theory of quantum fields propagating in an arbitrary, classical, globally hyperbolic spacetime. Our review emphasizes the conceptual issues arising in the formulation of the theory and presents known results in a mathematically precise way. Particular attention is paid to the distributional nature of quantum fields, to their local and covariant character, and to microlocal spectrum conditions satisfied by physically reasonable states. We review the Unruh and Hawking effects for free fields, as well as the behavior of free fields in deSitter spacetime and FLRW spacetimes with an exponential phase of expansion. We review how nonlinear observables of a free field, such as the stress–energy tensor, are defined, as well as time-ordered-products. The “renormalization ambiguities” involved in the definition of time-ordered products are fully characterized. Interacting fields are then perturbatively constructed. Our main focus is on the theory of a scalar field, but a brief discussion of gauge fields is included. We conclude with a brief discussion of a possible approach towards a nonperturbative formulation of quantum field theory in curved spacetime and some remarks on the formulation of quantum gravity.}
}

@book{QFT_&_BlackHoleThermo,
	author = "Wald, Robert M.",
	title = "{Quantum Field Theory in Curved Space-Time and Black Hole Thermodynamics}",
	isbn = "978-0-226-87027-4",
	publisher = "University of Chicago Press",
	address = "Chicago, IL",
	series = "Chicago Lectures in Physics",
	year = "1995"
}

@book{Parker:2009uva,
	author = "Parker, Leonard E. and Toms, D.",
	title = "{Quantum Field Theory in Curved Spacetime}: {Quantized Field and Gravity}",
	doi = "10.1017/CBO9780511813924",
	isbn = "978-0-521-87787-9, 978-0-521-87787-9, 978-0-511-60155-2",
	publisher = "Cambridge University Press",
	series = "Cambridge Monographs on Mathematical Physics",
	month = "8",
	year = "2009"
}

@article{DeWitt,
	title = {Feynman propagator in curved spacetime: {A} momentum-space representation},
	author = {Bunch, T. S. and Parker, Leonard},
	journal = {Phys. Rev. D},
	volume = {20},
	issue = {10},
	pages = {2499--2510},
	numpages = {0},
	year = {1979},
	month = {Nov},
	publisher = {American Physical Society},
	doi = {10.1103/PhysRevD.20.2499},
	url = {https://link.aps.org/doi/10.1103/PhysRevD.20.2499}
}

@article{TFG_Miguel,
	author        = "Pardina, M. and Asorey, M.",
	title         = "\href{https://deposita.unizar.es/record/62852?ln=es}{Agujeros negros en teorías de gravitación con altas
	derivadas}",
	year          = "2022",
}
@article{Duff77,
	title = {Observations on conformal anomalies},
	journal = {Nuclear Physics B},
	volume = {125},
	number = {2},
	pages = {334-348},
	year = {1977},
	issn = {0550-3213},
	doi = {https://doi.org/10.1016/0550-3213(77)90410-2},
	url = {https://www.sciencedirect.com/science/article/pii/0550321377904102},
	author = {M.J. Duff},
	abstract = {Conformal anomalies are re-examined in the light of their possible applications to the Hawking effect, to gravitational instantons, to asymptotic freedom and Weinberg's “asymptotic safety” programme. A general formula is derived which relates the numerical coefficients appearing in the anomalous trace of the stress tensor.}
}

@book{BiblioQFT,
	added-at = {2010-06-06T21:01:27.000+0200},
	author = {Peskin, Michael Edward and Schroeder, Daniel V.},
	biburl = {https://www.bibsonomy.org/bibtex/26a68f04983505fac8d80bd21e00a1d6f/wc},
	description = {SPIRES-HEP: FIND KEY 3485960},
	interhash = {e839db5bd06e66a35503aa936e299a0d},
	intrahash = {6a68f04983505fac8d80bd21e00a1d6f},
	keywords = {diplom field peskin qft quantum schroeder theory},
	note = {Reading, USA: Addison-Wesley (1995) 842},
	publisher = {Westview Press},
	timestamp = {2010-11-17T12:34:45.000+0100},
	title = {{An Introduction to Quantum Field Theory}},
	year = 1995
}

@book{BiblioGR,
	author = "Weinberg, Steven",
	title = "{Gravitation and Cosmology}: {Principles and Applications of the General Theory of Relativity}",
	isbn = "978-0-471-92567-5, 978-0-471-92567-5",
	publisher = "John Wiley and Sons",
	address = "New York",
	year = "1972"
}

@article{UnruhExperiment, title={Observation of thermal {H}awking radiation and its temperature in an analogue black hole}, volume={569}, DOI={10.1038/s41586-019-1241-0}, number={7758}, journal={Nature}, author={Muñoz de Nova, J.R. and Golubkov, K. and Kolobov, V.I. and Steinhauer, J.}, year={2019}, month={May}, pages={688–691}} 

@article{QGpheno_Report,
	title = {Quantum gravity phenomenology at the dawn of the multi-messenger era—A review},
	journal = {Progress in Particle and Nuclear Physics},
	volume = {125},
	pages = {103948},
	year = {2022},
	issn = {0146-6410},
	doi = {https://doi.org/10.1016/j.ppnp.2022.103948},
	url = {https://www.sciencedirect.com/science/article/pii/S0146641022000096},
	author = {A. Addazi and others},
	keywords = {Lorentz invariance violation and deformation, Gamma-ray astronomy, Cosmic neutrinos, Ultra-high-energy cosmic rays, Gravitational waves},
	abstract = {The exploration of the universe has recently entered a new era thanks to the multi-messenger paradigm, characterized by a continuous increase in the quantity and quality of experimental data that is obtained by the detection of the various cosmic messengers (photons, neutrinos, cosmic rays and gravitational waves) from numerous origins. They give us information about their sources in the universe and the properties of the intergalactic medium. Moreover, multi-messenger astronomy opens up the possibility to search for phenomenological signatures of quantum gravity. On the one hand, the most energetic events allow us to test our physical theories at energy regimes which are not directly accessible in accelerators; on the other hand, tiny effects in the propagation of very high energy particles could be amplified by cosmological distances. After decades of merely theoretical investigations, the possibility of obtaining phenomenological indications of Planck-scale effects is a revolutionary step in the quest for a quantum theory of gravity, but it requires cooperation between different communities of physicists (both theoretical and experimental). This review, prepared within the COST Action CA18108 “Quantum gravity phenomenology in the multi-messenger approach”, is aimed at promoting this cooperation by giving a state-of-the art account of the interdisciplinary expertise that is needed in the effective search of quantum gravity footprints in the production, propagation and detection of cosmic messengers.}
}

@article{Stelle_1978, title={Classical gravity with higher derivatives}, volume={9}, DOI={10.1007/bf00760427}, number={4}, journal={General Relativity and Gravitation}, author={Stelle, K. S.}, year={1978}, pages={353–371}} 

@article{a2Ambig,
	title = {An overview of the anomaly-induced inflation},
	journal = {Nuclear Physics B - Proceedings Supplements},
	volume = {127},
	pages = {196-200},
	year = {2004},
	issn = {0920-5632},
	doi = {https://doi.org/10.1016/S0920-5632(03)02431-9},
	url = {https://www.sciencedirect.com/science/article/pii/S0920563203024319},
	author = {Ilya L. Shapiro},
	abstract = {The anomaly-induced inflation (modified Starobinsky model) is based on the application of the effective quantum field theory approach to the Early Universe. We present a brief general review of this model with a special attention to the existing difficulties and unsolved problems.}
}

@article{ASOREY,
	doi = {10.1088/0264-9381/21/1/011},
	url = {https://dx.doi.org/10.1088/0264-9381/21/1/011},
	year = {2003},
	month = {nov},
	publisher = {},
	volume = {21},
	number = {1},
	pages = {163},
	author = {M Asorey and  E V Gorbar and  I L Shapiro},
	title = {Universality and ambiguities of the conformal anomaly},
	journal = {Classical and Quantum Gravity},
	abstract = {The one-loop structure of the trace anomaly is investigated using different regularizations and renormalization schemes: dimensional, proper time and Pauli–Villars. The universality of this anomaly is analysed from a very general perspective. The Euler and Weyl terms of the anomalous trace of the stress tensor are absolutely universal. The pure derivative □R term is shown to be universal only if the regularization breaks conformal symmetry softly. If the breaking of conformal symmetry by the regularization method is hard the coefficient of this term might become arbitrary which points out the presence of an ambiguous  term in the effective quantum action. These ambiguities arise in some prescriptions of dimensional and Pauli–Villars regularizations. We discuss the implications of these results for anomaly-induced inflationary scenarios and AdS/CFT correspondence.}
}