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RE: Gravity
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How much does the Earth weigh?

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f(R) gravity
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Title: Constraints on perturbative f(R) gravity via neutron stars
Authors: A. Savas Arapoglu, Cemsinan Deliduman, K. Yavuz Eksi

We study the structure of neutron stars in perturbative f(R) gravity models with realistic equations of state. We obtain mass-radius relations in a gravity model of the form f(R)=R+\alpha R^2. We find that deviations from the results of general relativity, comparable to the variations due to using different equations of state (EoS'), are induced for |alpha| ~ 10^9 cm^2. Some of the soft EoS' that are excluded within the framework of general relativity can be reconciled with the 2 solar mass neutron star recently observed for certain values of alpha within this range. For some of the EoS' we find that a new solution branch, which allows highly massive neutron stars, exists for values of alpha greater than a few 10^9 cm^2. We find constraints on alpha for a variety of EoS' using the recent observational constraints on the mass-radius relation. These are all 5 orders of magnitude smaller than the recent constraint obtained via Gravity Probe B for this gravity model. The associated length scale \sqrt{alpha} ~ 10^5 cm is only an order of magnitude smaller than the typical radius of a neutron star, the probe used in this test. This implies that real deviations from general relativity can be even smaller.

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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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Gravitons
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Recently a silent revolution has swept through physicists' understanding of particle collisions. The concepts introduced by the iconic physicist Richard Feynman have reached the limit of their usefulness for many applications, and the authors and their colleagues have developed a fresh approach.
Using it, physicists can describe more reliably how ordinary particles behave under the extreme conditions at the Large Hadron Collider at CERN, aiding experimentalists in their search for exotic particles and forces.
More profoundly, the novel methods breathe new life into a unified theory that physicists left for dead in the 1980s. The force of gravity looks like two copies of the strong subnuclear interactions working in unison.

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RE: Gravity
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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: The Direction of Gravity
Authors: Eric V. Linder

Gravity directs the paths of light rays and the growth of structure. Moreover, gravity on cosmological scales does not simply point down: it accelerates the universal expansion by pulling outward, either due to a highly negative pressure dark energy or an extension of general relativity. We examine methods to test the properties of gravity through cosmological measurements. We then consider specific possibilities for a sound gravitational theory based on the Galileon shift symmetry. The evolution of the laws of gravity from the early universe to the present acceleration to the future fate -- the paths of gravity -- carries rich information on this fundamental force of physics and on the mystery of dark energy.

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Gravitational Constant
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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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RE: Gravity
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Title: Degrees of freedom of f(T) gravity
Authors: Miao Li, Rong-Xin Miao, Yan-Gang Miao

We investigate the Hamiltonian formulation of f(T) gravity and find that there are five degrees of freedom. The six first class constraints corresponding to the local Lorentz transformation in Teleparallel gravity become second class constraints in f(T) gravity, which leads to the appearance of three extra degrees of freedom and the violation of the local Lorentz invariance in f(T) gravity. In general, there are D-1 extra degrees of freedom for f(T) gravity in D dimensions, and this implies that the extra degrees of freedom correspond to one massive vector field or one massless vector field with one scalar field.

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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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Title: The Breakdown of Classical Gravity?
Authors: X. Hernandez, M. A. Jimenez, C. Allen

Assuming Newton's gravity and GR to be valid at all scales, leads to the dark matter hypothesis as a forced requirement demanded by the observed dynamics and measured baryonic content at galactic and extra galactic scales. Alternatively, one can propose a contrasting scenario where gravity exhibits a change of regime at acceleration scales a<a_{0}, and obtain just as good a fit to observations across astrophysical scales. A critical experiment in this debate is offered by wide orbit binary stars. Since for 1 solar mass systems the acceleration drops below a_{0} at scales of around 7000 AU, an statistical survey of relative velocities and binary separations reaching beyond 10^{4} AU should yield a conclusive answer to the above debate. By performing such a study we show Kepler's third law to fail precisely beyond a \approx a_{0} scales, precisely as predicted by modified gravity theories designed not to require any dark matter at galactic scales and beyond.

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