Linear stability of Einstein and de Sitter universes in the quadratic theory of modified gravity

We consider the Einstein static and the de Sitter universe solutions and examine their instabilities in a subclass of quadratic modified theories for gravity. This modification proposed by Nash is an attempt to generalize general relativity. Interestingly, we discover that the Einstein static universe is unstable in the context of the modified gravity. In contrast to Einstein static universe, the de Sitter universe remains stable under metric perturbation up to the second order.

Wave-Like Exact Models with Symmetry of Spatial Homogeneity in the Quadratic Theory of Gravity with a Scalar Field

Exact solutions are obtained in the quadratic theory of gravity with a scalar field for wave-like models of space–time with spatial homogeneity symmetry and allowing the integration of the equations of motion of test particles in the Hamilton–Jacobi formalism by the method of separation of variables with separation of wave variables (Shapovalov spaces of type II). The form of the scalar field and the scalar field functions included in the Lagrangian of the theory is found. The obtained exact solutions can describe the primary gravitational wave disturbances in the Universe (primary gravitational waves).

Robust Multi-view Learning via Half-quadratic Minimization

Although multi-view clustering is capable to usemore information than single view clustering, existing multi-view clustering methods still have issues to be addressed, such as initialization sensitivity, the specification of the number of clusters,and the influence of outliers. In this paper, we propose a robust multi-view clustering method to address these issues. Specifically, we first propose amulti-view based sum-of-square error estimation tomake the initialization easy and simple as well asuse a sum-of-norm regularization to automaticallylearn the number of clusters according to data distribution. We further employ robust estimators constructed by the half-quadratic theory to avoid theinfluence of outliers for conducting robust estimations of both sum-of-square error and the numberof clusters. Experimental results on both syntheticand real datasets demonstrate that our method outperforms the state-of-the-art methods.

BIANCHI I SOLUTIONS OF EFFECTIVE QUADRATIC GRAVITY

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. Numerical solutions for the anisotropic generalization of the Friedmann "flat" model E3 for this effective gravity are given. It must be emphasized that although numeric, these solutions are exact in the sense that they depend only on the precision of the machine. The solutions are identified asymptotically in a certain sense. It is found solutions which asymptote de Sitter space, Minkowski space and a singularity. This work is a generalization for nondiagonal spatial metrics of a previous result obtained by one of us and a collaborator for Bianchi I spaces.

HOMOGENEOUS SOLUTIONS OF QUADRATIC GRAVITY

It is believed that soon after the Planck time, Einstein's general relativity theory should be corrected to an effective quadratic theory. In this work we present the 3 + 1 decomposition for the zero vorticity case for arbitrary spatially homogenous spaces. We specialize for the particular Bianchi I diagonal case. The 3- curvature can be understood as a generalized potential, and the Bianchi I case is a limiting case where this potential is negligible to the dynamics. The spirit should be analogous, in some sense to the BKL solution. In this sense, a better understanding of the Bianchi I case could shed some light into the general Bianchi case.

CONSTRUCTION OF LAGRANGIAN LOCAL SYMMETRIES FOR GENERAL QUADRATIC THEORY

We propose a procedure which allows one to construct local symmetry generators of general quadratic Lagrangian theory. Manifest recurrence relations for generators in terms of the so-called structure matrices of the Dirac formalism are obtained. The procedure fulfill in terms of initial variables of the theory, and does not imply either separation of constraints on first and second class subsets or any other choice of basis for constraints.