Bianchi type-I cosmology in f(R,T) gravity

We investigate the exact solutions of a Bianchi type-I space-time in the context of f(R, T) gravity [1], where f(R, T) is an arbitrary function of the Ricci scalar R and the trace of the energy-momentum tensor T. For this purpose, we find two exact solutions using the assumption of a constant deceleration parameter and the variation law of the Hubble parameter. The obtained solutions correspond to two different models of the Universe. The physical behavior of these models is also discussed.     

Commentary on "Mechanical properties of monodomain side-chain nematic elastomers" by P. Martinoty, P. Stein, H. Finkelmann, H. Pleiner and H.R. Brand

We discuss the background to static and dynamic soft elasticity. The evidence in the static case and the symmetry basis for soft and semi-soft elasticity is well understood. By contrast the dynamic analogy is less clear. Lack of clean time scale separation clouds the interpretation of director relaxation keeping up, or not, with imposed strains. However, the reduction in modulus between geometries obtaining at low frequencies and being lost at high frequencies confirms that director reaction indeed determines dynamical semi-softness.     

The Stability of Matter in Quantum Mechanics,by E.H. Lieb and R. Seiringer

Laser spectroscopy of atomic hydrogen has been important in the recent development of Doppler-free laser techniques and offers stringent tests of atomic theory together with precise measurements of fundamental atomic constants. In this review we outline the theory of the structure of atomic hydrogen and describe the techniques of Doppler-free laser spectroscopy. This field has been extremely active in recent years and we bring together the most recent results of measurements of the Rydberg constant and the ground-state Lamb shift.     

$${f(\mathcal R)}$$ quantum cosmology

We have quantized a flat cosmological model in the context of the metric models, using the causal Bohmian quantum theory. The equations are solved and then we have obtained how the quantum corrections influence the classical equations.     

Inertia,relativity and cosmology

Starting with the idea that the inertia of bodies is a general property of all kinds of their potential energy, the author arrives at the two fundamental megaphysical equations (I, II)⁰ +c²=0,⁰ =0 where⁰ is the scalar gravitational potential due to the smoothed-out universe,⁰ is its electrostatic potential andc denotes the light velocity in vacuo.The first equation means physically that the cosmic potential⁰ determines uniquely the velocity of light and consequently the pseudo-Euclidean geometry in an inertial frame, in the absence of local gravitational fields. This fact implies the validity of the law of inertia in a non-empty universe only, in full agreement with Mach's principle.If we adopt, for the cosmic potential, that of Seeliger, differing from the Newtonian potential by the exponential factor exp (–r/r_g), we can use Eq. (I) to estimate the lower limit of the range r_g of gravitational interaction within the limits (10¹⁰–10¹²) light years. This suggests a steadystate model of the universe consisting of an unlimited number of finite regions (sub-universes) oscillating independently of each other. Such a superlarge-scale model universe is in agreement with the observed galactic red shift and yet it fulfils the perfect cosmological principle.