Journal•ISSN: 0219-8878

# International Journal of Geometric Methods in Modern Physics

About: International Journal of Geometric Methods in Modern Physics is an academic journal. The journal publishes majorly in the area(s): Gravity (chemistry) & Gravitation. It has an ISSN identifier of 0219-8878. Over the lifetime, 2409 publication(s) have been published receiving 22282 citation(s).

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TL;DR: In this paper, a review of modified gravities considered as a gravitational alternative for dark energy is presented, and the possibility to explain the coincidence problem as the manifestation of the universe expansion in such models is mentioned.

Abstract: We review various modified gravities considered as gravitational alternative for dark energy. Specifically, we consider the versions of f(R), f(G) or f(R, G) gravity, model with non-linear gravitational coupling or string-inspired model with Gauss-Bonnet-dilaton coupling in the late universe where they lead to cosmic speed-up. It is shown that some of such theories may pass the Solar System tests. On the same time, it is demonstrated that they have quite rich cosmological structure: they may naturally describe the effective (cosmological constant, quintessence or phantom) late-time era with a possible transition from decceleration to acceleration thanks to gravitational terms which increase with scalar curvature decrease. The possibility to explain the coincidence problem as the manifestation of the universe expansion in such models is mentioned. The late (phantom or quintessence) universe filled with dark fluid with inhomogeneous equation of state (where inhomogeneous terms are originated from the modifi...

2,590 citations

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Koç University

^{1}TL;DR: A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly as mentioned in this paper.

Abstract: A diagonalizable non-Hermitian Hamiltonian having a real spectrum may be used to define a unitary quantum system, if one modifies the inner product of the Hilbert space properly. We give a comprehensive and essentially self-contained review of the basic ideas and techniques responsible for the recent developments in this subject. We provide a critical assessment of the role of the geometry of the Hilbert space in conventional quantum mechanics to reveal the basic physical principle motivating our study. We then offer a survey of the necessary mathematical tools, present their utility in establishing a lucid and precise formulation of a unitary quantum theory based on a non-Hermitian Hamiltonian, and elaborate on a number of relevant issues of fundamental importance. In particular, we discuss the role of the antilinear symmetries such as ${\mathcal{P}\mathcal{T}}$, the true meaning and significance of the so-called charge operators $\mathcal{C}$ and the ${\mathcal{C}\mathcal{P}\mathcal{T}}$-inner products,...

727 citations

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TL;DR: In this article, the authors identify a deformation of the N = 2 supersymmetric sigma model on a Calabi-Yau manifold X which has the same effect on B-branes as a non-commutative deformation on X and show that for hyperkahler X such deformations allow one to interpolate continuously between the A-model and the B-model.

Abstract: We identify a deformation of the N=2 supersymmetric sigma model on a Calabi–Yau manifold X which has the same effect on B-branes as a noncommutative deformation of X. We show that for hyperkahler X such deformations allow one to interpolate continuously between the A-model and the B-model. For generic values of the noncommutativity and the B-field, properties of the topologically twisted sigma-models can be described in terms of generalized complex structures introduced by N. Hitchin. For example, we show that the path integral for the deformed sigma-model is localized on generalized holomorphic maps, whereas for the A-model and the B-model it is localized on holomorphic and constant maps, respectively. The geometry of topological D-branes is also best described using generalized complex structures. We also derive a constraint on the Chern character of topological D-branes, which includes A-branes and B-branes as special cases.

193 citations

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TL;DR: In this paper, the field equations following from a Lagrangian L(R) were deduced and solved for special cases, and it was shown that these equations are of fourth order in the metric.

Abstract: The field equations following from a Lagrangian L(R) will be deduced and solved for special cases. If L is a non-linear function of the curvature scalar, then these equations are of fourth order in the metric. In the introduction, we present the history of these equations beginning with the paper of H. Weyl from 1918, who first discussed them as alternative to Einstein's theory. In the third part, we give details about the cosmic no hair theorem, i.e. the details of how within fourth order gravity with L= R + R2, the inflationary phase of cosmic evolution turns out to be a transient attractor. Finally, the Bicknell theorem, i.e. the conformal relation from fourth order gravity to scalar-tensor theory, will be shortly presented.

192 citations

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TL;DR: In this paper, a dimension-independent theory of alignment in Lorentzian geometry is developed and applied to the tensor classification problem for the Weyl and Ricci tensors.

Abstract: We develop a dimension-independent theory of alignment in Lorentzian geometry, and apply it to the tensor classification problem for the Weyl and Ricci tensors. First, we show that the alignment condition is equivalent to the principal null direction equation. In 4 dimensions this recovers the usual Petrov types are recovered. For higher dimensions we prove that, in general, a Weyl tensor does not possess any aligned directions. We then go on to describe a number of additional algebraic types for the various alignment configurations. For the case of second-order symmetric (Ricci) tensors, we perform the classification by considering the geometric properties of the corresponding alignment variety.

167 citations