If we accept that transport barriers should be material features for experimental verifiability, we must also remember a fundamental axiom of mechanics: material response of any moving continuum, including fluids, must be frame-indifferent.This means that the conclusions of different observers regarding material behavior must transform into each other by exactly the same rigid-body transformation that transforms the frames of the observers into each other. This requirement of the frame-indifference of material response is called objectivity in classical continuum mechanics. Its significance in fluid mechanics is often overlooked or forgotten, which prompts us to devote a whole chapter to this important physical axiom. We clarify some common misunderstandings of the principle of objectivity in fluid mechanics and discuss in detail the mathematical requirements imposed by objectivity on scalars, vectors and tensors to be used in describing transport barriers.

Here we discuss inflation, a period of accelerated expansion that occurred in the very early history of the universe. We motivate inflation by describing the flatness and horizon problems, then explain how inflation resolves them. We describe the early history of inflationary ideas, then move on to modern work where we outline the standard scalar-field model for inflation, and define the slow-roll parameters that phenomenologically describe the dynamics of inflation. We briefly outline how inflation leads to the generation of density fluctuations in the universe; we mathematically describe the spectrum of these fluctuations, and confront it with modern observations. We end by discussing more speculative ideas in this area, including eternal inflation and multiverse.

Here we review dark energy, the component that causes accelerated expansion of the universe. We start by reviewing the history of this fascinating discovery, describing in detail how type Ia supernovae were used to measure the expansion rate and find that the expansion is speeding up. We then outline modern evidence for the existence of dark energy, how dark energy is parametrically described, and what its phenomenological properties are. We review the cosmological-constant problem that encapsulates the tiny size of dark energy relative to expectations from particle physics. Next we introduce physical candidates for dark energy, including scalar fields and modified gravity. We end by explaining the controversial anthropic principle, and describe the possible future expansion histories of the universe dominated by dark energy.