Two Provocative Papers On Gravity

http://arxiv.org/abs/1212.0454
Gravity can be neither classical nor quantized
Sabine Hossenfelder
(Submitted on 3 Dec 2012)
I argue that it is possible for a theory to be neither quantized nor classical. We should therefore give up the assumption that the fundamental theory which describes gravity at shortest distances must either be quantized, or quantization must emerge from a fundamentally classical theory. To illustrate my point I will discuss an example for a theory that is neither classical nor quantized, and argue that it has the potential to resolve the tensions between the quantum field theories of the standard model and general relativity.
7 pages, third prize in the 2012 FQXi essay contest "Which of our basic physical assumptions are wrong?"

Hossenfelder's essay considers the possibility that Planck's constant runs with the energy level of the environment, in an amount only discernable at very high energies, and reaches zero at the temperatures seen in the early days of the Big Bang and inside black holes.  This causes the gravitational constant to run to zero at these energy levels, so rather than reaching infnity and creating singularities, gravity turns itself off when temperatures get great enough.

http://arxiv.org/abs/1212.0371
Not on but of
Olaf Dreyer
(Submitted on 3 Dec 2012)
In physics we encounter particles in one of two ways. Either as fundamental constituents of the theory or as emergent excitations. These two ways differ by how the particle relates to the background. It either sits on the background, or it is an excitation of the background. We argue that by choosing the former to construct our fundamental theories we have made a costly mistake. Instead we should think of particles as excitations of a background. We show that this point of view sheds new light on the cosmological constant problem and even leads to observable consequences by giving a natural explanation for the appearance of MOND-like behavior. In this context it also becomes clear why there are numerical coincidences between the MOND acceleration parameter, the cosmological constant and the Hubble parameter.
9 pages. This article received a forth prize in the 2012 FQXi essay contest "Questioning the Foundations".

Dreyer constructs a formalism in which particles are excitations of space-time.  In this construction, ground state energy in the vacuum is zero and the Casimir effect can be explained by means other than vacuum energy. 

The energy of the vacuum in this formulation is described by changes in the gravitational ground state energy, in a vacuum at zero temperature without considering entropy, produces the familiar Newtonian gravitational constant. 

But, when entropy is considered, gravity weakens at non-zero temperatures (in a derivation based on the definition of free energy in a system with entropy).  The entropic effect is composed of contributions from wavelengths of all lengths, but the wavelengths longer than the size of the universe (the maximal wavelengths) cannot contribute.  Taking this limitation into effect, it is remarkable that the Hubble scale for the size of the universe, and the square root of the inverse of the cosmological constant both produce cutoff scales that change the strength of the gravitational constant at a cutoff value on the same order of magnitude of Milgrom's MOND regime's empirically determined cutoff value. 

Hence, entropy effects on a gravitational force in the context of particles seen as excitations of space-time naturally produces MOND-like gravitational effects that mirror an empirically derived modification of gravity that captures essentially all effects attributed to dark matter at the galactic scale and some of the effects attributed to dark matter at the galactric cluster scale (where ordinary but invisible matter could in theory account for the additional dark matter effects observed in galactic clusters whose composition and structure are still not fully understood).

Dreyers cites many recent papers in the literature at the close of his essay that have combined the ideas of Verlinde and Milgrom in a similar way, arguing that his approach is notable because it does not use a holographic approach and is three dimensional. 

Other essays in the contest can be found here.

As a bonus, a recent paper on quark-lepton complementarity that integrates the latest empirical data can be found here and here and here and here by an overlapping group of Chinese investigators.  They examine different parameterization regimes to determine which ones might be consistent with both QLC and the empirical data and suggests that measurements of CP violation in neutrino oscillations is critical to discriminating between the possible options.  Another investigator, independent of that group, looks at the issues here.  A third team looks at related problems here.  A related investigation in the CKM matrix itself is here and focuses on a number of interesting relationships between the mass matrix and mixing matrixes there.