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Gravitational Physics: From Quantum to Waves | SpringerLink

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Gravitational Physics: From Quantum to Waves

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Multiple Messengers and Challenges in Astroparticle Physics

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Abstract

Gravitational interaction is widely considered one of the most challenging topics of physics. Despite of the undoubtful successes of General Relativity, the lack of a self-consistent theory, capable of encompassing gravitational aspects of quantum phenomena, local scales, galactic and extragalactic astrophysics up to cosmology, it is one of the most frustrating aspects of this long ranging interaction. Here, with no claim to completeness, we review some of these aspects considering the issues of foundation of General Relativity, quantum gravity, strong and weak field regimes, alternative theories of gravity, gravitational waves and multimessanger astronomy. The goal is to provide a quick summary and guideline for these open issues. Particular emphasis is given to the theory and the discovery gravitational waves that have been the experimentum crucis to confirm General Relativity and definitely opened the era of the so called gravitational astronomy.

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Notes

  1. 1.

    This fact does not imply, of course, that imprints of Quantum Gravity phenomenology cannot be found in lower energy experiments.

  2. 2.

    Higher order terms in the perturbative series imply an infinite number of free parameters. At the one-loop level it is sufficient to renormalize only the effective constants \(G_{eff}\) and \(\Lambda _{eff}\) which, at low energy, reduce to Newton’s constant \(G_N\) and the cosmological constant \(\Lambda \).

  3. 3.

    String theory contains only one fundamental dimensionfull parameter, the string length. The connection to low energies may nonetheless be non-unique due to the existence of many different possible “vacua”.

  4. 4.

    In order to avoid the inhomogeneities.

  5. 5.

    The components of the 4-vector \(A_\mu =(A^0, \mathbf {A})\) and \(A^\mu =(A_0, \mathbf {A})\) with \(A^0=-A_0\). Vector components with upper and lower indices are related by \(x_\mu =g_{\mu \nu }x^\nu \), where \(g_{\mu \nu }\) is the metric tensor which appears in the definition of the invariant space-time interval \(ds^2=g_{\mu \nu }dx^\mu dx^\nu \). The components of \(g_{\mu \nu }\) are \(g_{11}=g_{22}=g_{33}=1\), \(g_{00}=-1\) and all other components are zero.

  6. 6.

    Technically, the SU(2) group is different from the group of 3-dimensional rotations, O(3); the SU(2) group is the “covering group” of O(3).

  7. 7.

    We will deduce below these some equations in the framework of GR.

  8. 8.

    Hereafter, scalar fields and potentials are understood as their effective values, obtained averaging over quantum states. In this sense, classical fields and potentials are the expectation values of quantum fields and potentials.

  9. 9.

    Equations (306) and (307) can include terms containing derivatives of the metric of order higher than fourth (fourth order corresponding to the \(R^{2}\) term) if all possible Feynman diagrams are included. For example, corrections such as \(R\Box R\) or \(R^{2}\Box R\) can be present in \(^{(3)}H_{\mu \nu }\) implying equations of motion that contain sixth order derivatives of the metric. Also these terms can be treated by making use of conformal transformations [223].

  10. 10.

    Note, however, that the distinction between gravitational and non-gravitational fields becomes representation-dependent in ETGs, together with the various formulations of the EP.

  11. 11.

    The dynamics of such scalar fields is usually given by the corresponding Klein-Gordon Equation, which is second order.

  12. 12.

    These polarizations are defined in the physical three-space. The polarization vectors are orthogonal to each another and are normalized according to \(e_{\mu \sigma }e^{\sigma \nu } =2\delta _{\mu }^{\nu }\). The other modes are not traceless, in contrast to the ordinary “plus” and “cross” polarization modes of GR.

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Authors and Affiliations

  1. Dipartimento di Fisica, Universitá di Napoli “Federico II”, Napoli, Italy

    Salvatore Capozziello

  2. INFN Sez. di Napoli, Compl. Univ. di Monte S. Angelo, Edificio G, Via Cinthia, 80126, Napoli, Italy

    Salvatore Capozziello

  3. Gran Sasso Science Institute, Viale F. Crispi 7, 67100, L’aquila, Italy

    Salvatore Capozziello, Eugenio Coccia & Viviana Fafone

  4. Dipartimento di Fisica, Universitá di Tor Vergata, Via della Ricerca Scientifica, 00133, Roma, Italy

    Eugenio Coccia & Viviana Fafone

  5. INFN Sez. Roma Tor Vergata, Via della Ricerca Scientifica, 00133, Roma, Italy

    Eugenio Coccia & Viviana Fafone

  6. Institute for Theoretical Physics, Goethe University, Max-von-Laue-Str. 1, 60438, Frankfurt, Germany

    Mariafelicia De Laurentis

  7. Tomsk State Pedagogical University, ul. Kievskaya, 60, 634061, Tomsk, Russia

    Mariafelicia De Laurentis

  8. Lab. Theor. Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 634050, Tomsk, Russia

    Mariafelicia De Laurentis

Authors
  1. Salvatore Capozziello
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  2. Eugenio Coccia
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  3. Mariafelicia De Laurentis
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  4. Viviana Fafone
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Corresponding author

Correspondence to Salvatore Capozziello .

Editor information

Editors and Affiliations

  1. Gran Sasso Science Institute, L’Aquila, Italy

    Roberto Aloisio

  2. Gran Sasso Science Institute, L’Aquila, Italy

    Eugenio Coccia

  3. Gran Sasso Science Institute, L’Aquila, Italy

    Francesco Vissani

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Capozziello, S., Coccia, E., De Laurentis, M., Fafone, V. (2018). Gravitational Physics: From Quantum to Waves. In: Aloisio, R., Coccia, E., Vissani, F. (eds) Multiple Messengers and Challenges in Astroparticle Physics. Springer, Cham. https://doi.org/10.1007/978-3-319-65425-6_5

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