To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution

Gravitational Field of a Spinning Mass as an Example of Algebraically Special Metrics

We review different dark energy cosmologies. In particular, we present the ΛCDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the ΛCDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the ΛCDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes F(R) gravity as well as F(R) Hořava-Lifshitz gravity and the teleparallel f(T) gravity. The cosmology of such models representing the ΛCDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.

Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests

We review different dark energy cosmologies. In particular, we present the $\Lambda$CDM cosmology, Little Rip and Pseudo-Rip universes, the phantom and quintessence cosmologies with Type I, II, III and IV finite-time future singularities and non-singular dark energy universes. In the first part, we explain the $\Lambda$CDM model and well-established observational tests which constrain the current cosmic acceleration. After that, we investigate the dark fluid universe where a fluid has quite general equation of state (EoS) [including inhomogeneous or imperfect EoS]. All the above dark energy cosmologies for different fluids are explicitly realized, and their properties are also explored. It is shown that all the above dark energy universes may mimic the $\Lambda$CDM model currently, consistent with the recent observational data. Furthermore, special attention is paid to the equivalence of different dark energy models. We consider single and multiple scalar field theories, tachyon scalar theory and holographic dark energy as models for current acceleration with the features of quintessence/phantom cosmology, and demonstrate their equivalence to the corresponding fluid descriptions. In the second part, we study another equivalent class of dark energy models which includes $F(R)$ gravity as well as $F(R)$ Hořava-Lifshitz gravity and the teleparallel $f(T)$ gravity. The cosmology of such models representing the $\Lambda$CDM-like universe or the accelerating expansion with the quintessence/phantom nature is described. Finally, we approach the problem of testing dark energy and alternative gravity models to general relativity by cosmography. We show that degeneration among parameters can be removed by accurate data analysis of large data samples and also present the examples.

We extend the notion of phantom energy, which is generally accepted for homogeneously distributed matter with $wl\ensuremath{-}1$ in the universe, on inhomogeneous spherically symmetric spacetime configurations. A spherically symmetric distribution of phantom energy is shown to be able to support the existence of static wormholes. We find an exact solution describing a static spherically symmetric wormhole with phantom energy and show that a spatial distribution of the phantom energy is mainly restricted by the vicinity of the wormhole's throat. The maximal size of the spherical region, surrounding the throat and containing the most part of the phantom energy, depends on the equation-of-state parameter $w$ and cannot exceed some upper limit.

Wormholes supported by a phantom energy

We consider a gravitational theory of a scalar field $\ensuremath{\phi}$ with nonminimal derivative coupling to curvature. The coupling terms have the form ${\ensuremath{\kappa}}_{1}R{\ensuremath{\phi}}_{,\ensuremath{\mu}}{\ensuremath{\phi}}^{,\ensuremath{\mu}}$ and ${\ensuremath{\kappa}}_{2}{R}_{\ensuremath{\mu}\ensuremath{\nu}}{\ensuremath{\phi}}^{,\ensuremath{\mu}}{\ensuremath{\phi}}^{,\ensuremath{\nu}}$, where ${\ensuremath{\kappa}}_{1}$ and ${\ensuremath{\kappa}}_{2}$ are coupling parameters with dimensions of length squared. In general, field equations of the theory contain third derivatives of ${g}_{\ensuremath{\mu}\ensuremath{\nu}}$ and $\ensuremath{\phi}$. However, in the case $\ensuremath{-}2{\ensuremath{\kappa}}_{1}={\ensuremath{\kappa}}_{2}\ensuremath{\equiv}\ensuremath{\kappa}$, the derivative coupling term reads $\ensuremath{\kappa}{G}_{\ensuremath{\mu}\ensuremath{\nu}}{\ensuremath{\phi}}^{,\ensuremath{\mu}}{\ensuremath{\phi}}^{,\ensuremath{\nu}}$ and the order of corresponding field equations is reduced up to second one. Assuming $\ensuremath{-}2{\ensuremath{\kappa}}_{1}={\ensuremath{\kappa}}_{2}$, we study the spatially-flat Friedman-Robertson-Walker model with a scale factor $a(t)$ and find new exact cosmological solutions. It is shown that properties of the model at early stages crucially depend on the sign of $\ensuremath{\kappa}$. For negative $\ensuremath{\kappa}$, the model has an initial cosmological singularity, i.e., $a(t)\ensuremath{\sim}(t\ensuremath{-}{t}_{i}{)}^{2/3}$ in the limit $t\ensuremath{\rightarrow}{t}_{i}$; and for positive $\ensuremath{\kappa}$, the Universe at early stages has the quasi-de Sitter behavior, i.e., $a(t)\ensuremath{\sim}{e}^{Ht}$ in the limit $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, where $H=(3\sqrt{\ensuremath{\kappa}}{)}^{\ensuremath{-}1}$. The corresponding scalar field $\ensuremath{\phi}$ is exponentially growing at $t\ensuremath{\rightarrow}\ensuremath{-}\ensuremath{\infty}$, i.e., $\ensuremath{\phi}(t)\ensuremath{\sim}{e}^{\ensuremath{-}t/\sqrt{\ensuremath{\kappa}}}$. At late stages, the Universe evolution does not depend on $\ensuremath{\kappa}$ at all; namely, for any $\ensuremath{\kappa}$ one has $a(t)\ensuremath{\sim}{t}^{1/3}$ at $t\ensuremath{\rightarrow}\ensuremath{\infty}$. Summarizing, we conclude that a cosmological model with nonminimal derivative coupling of the form $\ensuremath{\kappa}{G}_{\ensuremath{\mu}\ensuremath{\nu}}{\ensuremath{\phi}}^{,\ensuremath{\mu}}{\ensuremath{\phi}}^{,\ensuremath{\nu}}$ is able to explain in a unique manner both a quasi-de Sitter phase and an exit from it without any fine-tuned potential.

Exact cosmological solutions with nonminimal derivative coupling

We investigate cosmological scenarios with a nonminimal derivative coupling between the scalar field and the curvature, examining both the quintessence and the phantom cases in zero and constant potentials. In general, we find that the universe transits from one de Sitter solution to another, determined by the coupling parameter. Furthermore, according to the parameter choices and without the need for matter, we can obtain a big bang, an expanding universe with no beginning, a cosmological turnaround, an eternally contracting universe, a big crunch, a big rip avoidance, and a cosmological bounce. This variety of behaviors reveals the capabilities of the present scenario.

Quintessence and phantom cosmology with nonminimal derivative coupling

A fundamental ingredient in wormhole physics is the flaring-out condition at the throat which, in classical general relativity, entails the violation of the null energy condition. In this work, we present the most general conditions in the context of modified gravity, in which the matter threading the wormhole throat satisfies all of the energy conditions, and it is the higher order curvature terms, which may be interpreted as a gravitational fluid, that support these nonstandard wormhole geometries. Thus, we explicitly show that wormhole geometries can be theoretically constructed without the presence of exotic matter but are sustained in the context of modified gravity.

/pdf/modified-gravity-wormholes-without-exotic-matter-4ugdwq52ft.pdf

Sergey V. Sushkov

Papers

Wormholes supported by a phantom energy

Exact cosmological solutions with nonminimal derivative coupling

Quintessence and phantom cosmology with nonminimal derivative coupling

Modified-gravity wormholes without exotic matter

Quintessence and phantom cosmology with nonminimal derivative coupling