Quantum Mechanics and Thermodynamics in Expanding Spacetimes

Much attention has been given to the behavior of quantum fields in expanding Freidmann-Lema\^itre-Robertson-Walker (FLRW) spacetimes, and de Sitter spacetime in particular. In such spacetimes, the S-matrix is ill-defined, so new observables must be constructed that are accessible to both computation and measurement. The most common observable in theories of inflation is an equal-time correlation function, typically computed in the in-in formalism. Weinberg improved upon in-in perturbation theory by reducing the perturbative expansion to a series of nested commutators. Several authors noted a technical difference between Weinberg's formula and standard in-in perturbation theory. In this work, a proof of the order-by-order equivalence of Weinberg's commutators to traditional in-in perturbation theory is presented for all masses and commonly studied spins in a broad class of FLRW spacetimes. Then, a study of the effects of a sector of conformal matter coupled solely to gravity is given. The results can constrain N-naturalness as a complete solution of the hierarchy problem, given a measurement of the tensor fluctuations from inflation. The next part of this work focuses on the thermodynamics of de Sitter. It has been known for decades that there is a temperature associated with a cosmological horizon, which matches the thermal response of a comoving particle detector in de Sitter. A model of a perfectly reflecting cavity is constructed with fixed physical size in two-dimensional de Sitter spacetime. The natural ground state inside the box yields no response from a comoving particle detector, implying that the box screens out the thermal effects of the de Sitter horizon. The total energy inside the box is also shown to be smaller than an equivalent volume of the Bunch-Davies vacuum state. The temperature difference across the wall of the box might drive a heat engine, so an analytical model of the Szil\'ard engine is constructed and studied. It is found that all relevant thermodynamical quantities can be computed exactly at all stages of the engine cycle.