Two aspects of Positive Operator Valued Measures (POVM) on the Euclidean plane (a basic Hilbert space!) are presented, namely their status as quantum observables and their role as quantizers in the integral quantization procedure. The compatibility of POVMs in the ensuing quantum formalism is discussed, and a Naimark dilation is found for the quantum operators. The relation with Toeplitz quantization is explained. Within this framework, we describe the linear polarization of the light with the use of Stokes parameters and its interaction with a polariser as a quantum measurement (Malus’ law).

Gravity can be embedded into a renormalizable theory by means of adding quadratic in curvature terms. 
However, this at first leads to the presence of the Weyl ghost. It is possible to get rid of this ghost if the 
locality assumption is weakened and the propagator of the graviton is represented by an entire function 
of the d'Alembertian operator without new poles and zeros. Models of this type admit a cosmological 
solution describing the R^2, or Starobinsky, inflation. We study graviton production after inflation in 

We consider the massless minimally coupled scalar field in the de Sitter ambient space formalism as a gauge potential or connection field. We construct the scalar gauge theory by helping an arbitrary constant five-vector field B analogous to the standard gauge theory. The Lagrangian density of the interaction between the scalar and spinor fields is presented in this framework. The Yukawa potential can be extracted from this Lagrangian density at the null curvature limit by an appropriate choice of a constant five-vector field.

Multi-messenger data of high energy neutrinos by IceCube and  gamma-rays by Tibet AS-gamma show new signal at 100 TeV energies outside of Galactic plane but below 20 degrees from it. This mysterious signal challenge conventional cosmic ray models, which predict major Galactic signal from Galactic plane and no significant flux at high galactic latitudes, as seen at GeV energies by Fermi LAT telescope.

Here we show that main assumption of continues distribution of cosmic rays in Galaxy is broken at PeV energies. 

Abstract:
It is now recognized that primordial black holes (PBHs) may be produced in various models of inflation in the early universe. In this talk, I review several different scenarios of PBH formation from inflation, each of which has rather distinct features. Then I discuss how these models may be observationally tested in the not-so-distant future, particularly by gravitational wave observations.