* Astronomy

Title: The gravitational equation in higher dimensions
Authors: Naresh Dadhich

Like the Lovelock Lagrangian which is a specific homogeneous polynomial in Riemann curvature, for an alternative derivation of the gravitational equation of motion, it is possible to define a specific homogeneous polynomial analogue of the Riemann curvature, and then the trace of its Bianchi derivative yields the corresponding polynomial analogue of the divergence free Einstein tensor defining the differential operator for the equation of motion. We propose that the general equation of motion is G^{(n)}_{ab} = -\Lambda g_{ab} +\kappa_n T_{ab} for d=2n+1, \, 2n+2 dimensions with the single coupling constant \kappa_n, and n=1 is the usual Einstein equation. It turns out that gravitational behaviour is essentially similar in the critical dimensions for all n. All static vacuum solutions asymptotically go over to the Einstein limit, Schwarzschild-dS/AdS. The thermodynamical parameters bear the same relation to horizon radius, for example entropy always goes as r_h^{d-2n} and so for the critical dimensions it always goes as r_h, \, r_h^2. In terms of the area, it would go as A^{1/n}. The generalised analogues of the Nariai and Bertotti-Robinson solutions arising from the product of two constant curvature spaces, also bear the same relations between the curvatures k_1=k_2 and k_1=-k_2 respectively.

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Title: Weyl-Cartan-Weitzenböck gravity
Authors: Zahra Haghani, Tiberiu Harko, Hamid Reza Sepangi, Shahab Shahidi

We consider a gravitational model in a Weyl-Cartan space-time, in which the Weitzenbock condition of the vanishing of the sum of the curvature and torsion scalar is also imposed. Moreover, a kinetic term for the torsion is also included in the gravitational action. The field equations of the model are obtained from a Hilbert-Einstein type variational principle, and they lead to a complete description of the gravitational field in terms of two fields, the Weyl vector and the torsion, respectively, defined in a curved background. The cosmological applications of the model are investigated for a particular choice of the free parameters in which the torsion vector is proportional to the Weyl vector. Depending on the numerical values of the parameters of the cosmological model, a large variety of dynamic evolutions can be obtained, ranging from inflationary/accelerated expansions to non-inflationary behaviours. In particular we show that a de Sitter type late time evolution can be naturally obtained from the field equations of the model. Therefore the present model leads to the possibility of a purely geometrical description of the dark energy, in which the late time acceleration of the Universe is determined by the intrinsic geometry of the space-time.

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Title: Constraining f(T) Theories with the Varying Gravitational Constant
Authors: Hao Wei, Hao-Yu Qi, Xiao-Peng Ma

As is well known, a varying effective gravitational "constant" is one of the common features of most modified gravity theories. Of course, as a modified gravity theory, f(T) theory is not an exception. Noting that the observational constraint on the varying gravitational "constant" is very tight, in the present work we try to constrain f(T) theories with the varying gravitational "constant". We find that the allowed model parameter n or \beta has been significantly shrunk to a very narrow range around zero. The results are very impressive.

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Title: Is geometry bosonic or fermionic?
Authors: Taylor L. Hughes, Andrew Randono

It is generally assumed that the gravitational field is bosonic. Here we show that a simple propagating torsional theory can give rise to localized geometric structures that can consistently be quantized as fermions under exchange. To demonstrate this, we show that the model can be formally mapped onto the Skyrme model of baryons, and we use well-known results from Skyrme theory. This begs the question:  Is geometry bosonic or fermionic (or both)?

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