We present a three dimensional non-relativistic model of gravity that is invariant under the central extension of the symmetry group that leaves the recently constructed Newtonian gravity action invariant. We show that the model arises from the contraction of a bi-metric model that is the sum of the Einstein gravity in Lorentzian and the Euclidean signatures. We also present the supersymmetric completion of this action which provides one of the very few examples of an action for non-relativistic supergravity.
We provide a systematic analysis of three-dimensional N = 2 extended Bargmann superalgebra and its Newton-Hooke, Lifshitz and Schrödinger extensions. These algebras admit invariant non-degenerate bi-linear forms which we utilized to construct corresponding Chern-Simons supergravity actions.
We study the interaction of a massless quantized spinor field with the gravitational field of N parallel static cosmic strings by using a perturbative approach. We show that the presence of more than one cosmic string gives rise to an additional contribution to the energy density of vacuum fluctuations, thereby leading to a vacuum force of attraction between two parallel cosmic strings.
We present an explicit detailed theoretical and observational investigation of an anisotropic massive Brans-Dicke (BD) gravity extension of the standard ΛCDM model, wherein the extension is characterized by two additional degrees of freedom; the BD parameter, ω, and the present day density parameter corresponding to the shear scalar, Ω σ 2 ,0 . The BD parameter, determining the deviation from general relativity (GR), by alone characterizes both the dynamics of the effective dark energy (DE) and the redshift dependence of the shear scalar. These two affect each other depending on ω, namely, the shear scalar contributes to the dynamics of the effective DE, and its anisotropic stress -which does not exist in scalar field models of DE within GR-controls the dynamics of the shear scalar deviating from the usual ∝ (1 + z) 6 form in GR. We mainly confine the current work to non-negative ω values as it is the right sign -theoretically and observationally-for investigating the model as a correction to the ΛCDM. By considering the current cosmological observations, we find that ω 250, Ω σ 2 ,0 10 −23 and the contribution of the anisotropy of the effective DE to this value is insignificant. We conclude that the simplest anisotropic massive BD gravity extension of the standard ΛCDM model exhibits no significant deviations from it all the way to the Big Bang Nucleosynthesis. We also point out the interesting features of the model in the case of negative ω values; for instance, the constraints on Ω σ 2 ,0 could be relaxed considerably, the values of ω ∼ −1 (relevant to string theories) predict dramatically different dynamics for the expansion anisotropy.
We provide a Lie algebra expansion procedure to construct three-dimensional higher-order Schrödinger algebras which relies on a particular subalgebra of the fourdimensional relativistic conformal algebra. In particular, we reproduce the extended Schrödinger algebra and provide a new higher-order Schrödinger algebra. The structure of this new algebra leads to a discussion on the uniqueness of the higher-order non-relativistic algebras. Especially, we show that the recent d-dimensional symmetry algebra of an action principle for Newtonian gravity is not uniquely defined but can accommodate three discrete parameters. For a particular choice of these parameters, the Bargmann algebra becomes a subalgebra of that extended algebra which allows one to introduce a mass current in a Bargmann-invariant sense to the extended theory.April 15, 2020
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