Inflationary perturbation theory is geometrical optics in phase space

Space-Adiabatic Perturbation Theory

We study approximate solutions to the Schrödinger equation iε∂ψt(x)/∂t = H(x,−iε∇x)ψt(x) with the Hamiltonian H the Weyl quantization of the symbol H(q, p) taking values in the space of bounded operators on the Hilbert space Hf of fast “internal” degrees of freedom. By assumption H(q, p) has an isolated energy band. We prove that interband transitions are suppressed to any order in ε. As a cons...

Matrix Methods in Geometrical Optics

As well as the geometrical methods used for solving lens problems, and locating the size and position of images in optical systems, there is an alternate, perhaps more versatile, method involving matrix manipulation. Many of you will be familiar with the use of simple 2x2 matrices. Firstly, however, before I consider the use of matrices in optics, I will review the matrix solution of two simult...

Multiphase Computations in Geometrical Optics

In this work we propose a new set of partial diierential equations (PDEs) which can be seen as a generalization of the classical eikonal and transport equations, to allow for solutions with multiple phases. The traditional geometrical optics pair of equations suuer from the fact that the class of physically relevant solutions is limited. In particular, it does not include solutions with multipl...

The Theory Experiment Connection: Rn Space and Inflationary Cosmology

Based on a discussion of the theory experiment connection, it is proposed to tighten the connection by replacing the real and complex number basis of physical theories by sets R n , C n of length 2n finite binary string numbers. The form of the numbers in R n is based on the infinite hierarchy of 2n figure outputs from measurements of any physical quantity with an infinite range (distance, ener...

Electromagnetic Scintillation I. Geometrical Optics