Abstract. We propose a new mechanism of generating the µ distortion in cosmic microwave background (CMB) originated from primordial gravitational waves. Such µ distortion is generated by the damping of the temperature anisotropies through the Thomson scattering, even on scales larger than that of Silk damping. This mechanism is in sharp contrast with that from the primordial curvature (scalar) perturbations, in which the temperature anisotropies mainly decay by Silk damping effects. We estimate the size of the µ distortion from the new mechanism, which can be used to constrain the amplitude of primordial gravitational waves on smaller scales independently from the CMB anisotropies, giving more wide-range constraint on their spectral index by combining the amplitude from the CMB anisotropies.

Abstract. We derive general expressions of the C µX l , the cross correlation function between the cosmic microwave background spectral µ distortion and the linear perturbations in the cosmic microwave background such as the temperature perturbations and the polarizations. The cross correlations are known as new tests for the extremely squeezed shape of primordial non-Gaussianity, which is inaccessible through the direct observations of the temperature 3-point functions. Our formulae are applicable to the arbitrary combinations of the scalar and the tensor perturbations, and we discuss the potential for detecting these quantities. We provide signal-to-noise ratio of the µE as well as µT , based on an experiment like the Primordial Inflation Explorer. We also find the signal-to-noise ratio from the scale dependent nonlinearity. For instance, we show that f loc NL pk 1 , k 2 , k 3 q " pk 1 k 2 k 3 q 1{3 k´1 0 F 0 with k 0 " 0.05Mpc´1 can be detectable at 1σ level even for F 0 " Op1q.

Abstract. We propose to re-interpret the cosmic microwave background spectral distortions as solutions to the Boltzmann equation. This approach makes it possible to solve the second order Boltzmann equation explicitly, with the spectral y distortion and the momentum independent second order temperature perturbation, while generation of µ distortion cannot be explained even at second order in this framework. We also extend our method to higher order Boltzmann equations systematically and find new type spectral distortions, assuming that the collision term is linear in the photon distribution functions, namely, in the Thomson scattering limit. As an example, we concretely construct solutions to the cubic order Boltzmann equation and show that the equations are closed with additional three parameters composed of a cubic order temperature perturbation and two cubic order spectral distortions. The linear Sunyaev-Zel'dovich effect whose momentum dependence is different from the usual y distortion is also discussed in the presence of the next leading order Kompaneets terms, and we show that higher order spectral distortions are also generated as a result of the diffusion process in a framework of higher order Boltzmann equations. The method may be applicable to a wider class of problems and has potential to give a general prescription to non-equilibrium physics.

We develop the effective field theoretical (EFT) approach to time-translational symmetry breaking of nonequilibrium open systems based on the Schwinger-Keldysh formalism. In the Schwinger-Keldysh formalism, all the symmetries of the microscopic Lagrangian are doubled essentially because the dynamical fields are doubled to describe the time-evolution along the closed-time-path. The effective Lagrangian for open systems are then obtained by coarse-graining the microscopic Schwinger-Keldysh Lagrangian. As a consequence of coarse-graining procedure, there appear the noise and dissipation effects, which explicitly break the doubled time-translational symmetries into a diagonal one. We therefore need to incorporate this symmetry structure to construct the EFT for Nambu-Goldstone bosons in symmetry broken phases of open systems. Based on this observation together with the consistency of the Schwinger-Keldysh action, we construct and study the general EFT for time-translational symmetry breaking in particular, having in mind applications to synchronization, time crystal, and cosmic inflation. arXiv:1805.06240v2 [hep-th] 19 Aug 2018 Contents Here we neglect P R dependence of the noise amplitude A and the damping coefficient γ. Since we have the Schrödinger-like equation for the probability distribution function, 2 To be precise, this is not the equation known as the Fokker-Planck equation but known as the Kramers equation since we are considering the underdamped Langevin equation. 3 Alternatively, we can directly derive this Fokker-Planck Hamiltonian from the MSR formalism by using the Legendre transformation.Z[J 1 , J 2 ] = Z[J 1 , J 2 ] with J 1 (t) = T J J 1 (−t + iβ/2), J 2 (t) = T J J 2 (−t − iβ/2), (3.17)

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