In this article, we investigate some features of the perturbation theory in a spatially closed universe. We will show that the perturbative field equations in a spatially closed universe always have two independent adiabatic solutions provided that the wavelengths of perturbation modes are very much longer than the Hubble horizon. It will be revealed that these adiabatic solutions do not depend on the curvature directly. We also propose a new interpretation for the curvature perturbation in terms of the unperturbed background geometry.

On the basis of the quantum Boltzmann equation governing the time-evolution of the density matrix of polarized CMB photons in the primordial scalar perturbations of metric, we calculate the B-mode spectrum of polarized CMB photons contributed from the scattering of CMB photons and CNB neutrinos (Cosmic Neutrino Background). We show that such contribution to the B-mode spectrum is negligible for small ℓ, however is significantly large for 50 < ℓ < 200 by plotting our results together with the BICEP2 data. Our study and results imply that in order to theoretically better understand the origin of the observed Bmode spectrum of polarized CMB photons (r-parameter), it should be necessary to study the relevant and dominate processes in both tensor and scalar perturbations. PACS numbers: 13.15.+g, 98.80.Es, 98.70.Vc. a rmohammadi@ipm.ir b xue@icra.it

The standard scenario of cosmology predicts a measurable amount for linear polarization of the Cosmic Microwave Background radiation (CMB) via Thomson scattering, while through this scenario, the generation of circular polarization is excluded. On the another hand, the circular polarization of CMB has not been excluded in observational evidence. The generation of CMB photons circular polarization via their Compton scattering with polarized cosmic electrons is considered in this paper. Our motivation for considering polarized Compton scattering comes from the effects of the external magnetic field in large scale, the chiral magnetic instability and new physics interactions of the cosmic electrons. It is shown that damping term of polarized Compton scattering in the presence of scalar perturbation can generate circular polarization in CMB radiation, so that the power spectrum of circular polarization of CMB C V (S) l is proportional to the power spectrum of temperature anisotropy of CMB C

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Various approaches to quantum gravity, such as string theory, predict a minimal measurable length and a modification of the Heisenberg Uncertainty Principle near the Plank scale, known as the Generalized Uncertainty Principle (GUP). Here we study the effects of GUP which preserves the rotational symmetry of the spacetime, on the Kepler problem. By comparing the value of the perihelion shift of the planet Mercury in Schwarzschild-de Sitter spacetime with the resulted value of GUP, we find a relation between the minimal measurable length and the cosmological constant of the spacetime. Now, if the cosmological constant varies with time, we have a variable minimal length in the spacetime. Finally, we investigate the effects of GUP on the stability of circular orbits.