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.

It is known that in contrast with the E-mode polarization, the B-mode polarization of the Cosmic Microwave Background cannot be generated by the Compton scattering in the case of scalar mode of metric perturbation. However it is possible to generate the B-mode by the Compton scattering in the case of tensor mode of metric perturbation. For this reason, the ratio of tensor to scalar modes of metric perturbation (r ∼ C Bl /C El ) is estimated by comparing the B-mode power spectrum with the E-mode at least for small l. We study the CMB polarization specially B-mode due to the weak interaction of Cosmic Neutrino Background (CNB) and CMB, in addition to the Compton scattering in both cases of scalar and tensor metric perturbations. It is shown that the power spectrum C Bl of the B-mode polarization receives some contributions from scalar and tensor modes, which have effects on the value of r-parameter. We also show that the B-mode polarization power spectrum can be used as an indirect probe into the CNB.

The thermal spectrum of relic gravitational waves enhances the usual spectrum. Our analysis shows that there exist some chances for detection of the thermal spectrum in addition to the usual spectrum by comparison with sensitivity of Adv.LIGO of GW150914 and detector based on the maser light. The behavior of the inflation and reheating stages are often known as power law expansion like S(η) ∝ η 1+β , S(η) ∝ η 1+β s , respectively, with constraints 1+β < 0, 1+β s > 0. The β and β s have an unique effect on the shape of the spectrum. We find some values of the β and β s by considering the mentioned comparison. As obtained results give us more information about the evolution of inflation and reheating stages.

We derive an integro-differential equation for propagation of cosmological gravitation waves in spatially closed cosmology whereas the traceless transverse tensor part of the anisotropic stress tensor is free streaming neutrinos (including antineutrinos), which have been traveling essentially without collision since temperature dropped below about $ 10^{10} K$. We studied the short wavelengths and long wavelengths of gravitational waves (GWs) that enter the horizon in closed spacetime. The solution shows that the anisotropic stress reduces the squared amplitude by 76% for wavelengths that enter the horizon during radiation-dominated phase and this reduction is less for the wavelength that enter the horizon at later times. At the end we compare the results to theComment: 10 pages, 1 figur