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.

Here I develop the connection between thermodynamics, entanglement, and gravity. I begin by showing that the classical null energy condition (NEC) can arise as a consequence of the second law of thermodynamics applied to local holographic screens. This is accomplished by essentially reversing the steps of Hawking's area theorem, leading to the Ricci convergence condition as an input, from which an application of Einstein's equations yields the NEC. Using the same argument, I show logarithmic quantum corrections to the Bekenstein-Hawking entropy formula do not alter the form of the Ricci convergence condition, but obscure its connection to the NEC. Then, by attributing thermodynamics to the stretched horizon of future lightcones -- a timelike hypersurface generated by a collection of radially accelerating observers with constant and uniform proper acceleration -- I derive Einstein's equations from the Clausius relation. Based on this derivation I uncover a local first law of gravity, connecting gravitational entropy to matter energy and work. I then provide an entanglement interpretation of stretched lightcone thermodynamics by extending the entanglement equilibrium proposal. Specifically I show that the condition of fixed volume can be understood as subtracting the irreversible contribution to the thermodynamic entropy. Using the AdS/CFT correspondence, I then provide a microscopic explanation of the 'thermodynamic volume' -- the conjugate variable to the pressure in extended black hole thermodynamics -- and reveal the super-entropicity of three-dimensional AdS black holes is due to the gravitational entropy overcounting the number of available dual CFT states. Finally, I conclude by providing a recent generlization of the extended first law of entanglement, and study its non-trivial 2+1- and 1+1-dimensional limits. This thesis is self-contained and pedagogical by including useful background content relevant to emergent gravity.

Measurements of the response of superconducting nanowire single photon detector (SNSPD) devices to changes in various forms of input power can be used for characterization of the devices and for probing device-level physics. Two niobium nitride (NbN) superconducting nanowires developed for use as SNSPD devices are embedded as the inductive (L) component in resonant inductor/capacitor (LC) circuits coupled to a microwave transmission line. The capacitors are low loss commercial chip capacitors which limit the internal quality factor of the resonators to approximately $Qi = 170$. The resonator quality factor, approximately $Qr = 23$, is dominated by the coupling to the feedline and limits the detection bandwidth to on the order of 1MHz. In our experiments with this first generation device, we measure the response of the SNSPD devices to changes in thermal and optical power in both the time domain and the frequency domain. Additionally, we explore the non-linear response of the devices to an applied bias current. For these nanowires, we find that the band-gap energy is $\Delta_0 \approx 1.1$meV and that the density of states at the Fermi energy is $N_0 \sim 10^{10}$/eV/$\mu$m$^3$.

We present the results of experimentation with a superconducting nanowire that can be operated in two detection modes: i) as a kinetic inductance detector (KID) or ii) as a single photon detector (SPD). When operated as a KID mode in linear mode, the detectors are AC-biased with tones at their resonant frequencies of 45.85 and 91.81MHz. When operated as an SPD in Geiger mode, the resonators are DC biased through cryogenic bias tees and each photon produces a sharp voltage step followed by a ringdown signal at the resonant frequency of the detector. We show that a high AC bias in KID mode is inferior for photon counting experiments compared to operation in a DC-biased SPD mode due to the small fraction of time spent near the critical current with an AC bias. We find a photon count rate of $\Gamma_{KID} = 150~$photons/s/mA in a critically biased KID mode and a photon count rate of $\Gamma_{SPD} = 10^6~$photons/s/mA in SPD mode.

This dissertation additionally presents simulations of a DC-biased, frequency-multiplexed readout of SNSPD devices in Advanced Design System (ADS), LTspice, and Sonnet. A multiplexing factor of 100 is achievable with a total count rate of $>5$MHz. This readout could enable a 10000-pixel array for astronomy or quantum communications. Finally, we present a prototype array design based on lumped element components. An early implementation of the array is presented with 16 pixels in the frequency range of 74.9 to 161MHz. We find good agreement between simulation and experimental data in both the time domain and the frequency domain and present modifications for future versions of the array.

Two ideas that extends on the theory of General Relativity are introduced and then the phenomenology they can offer is explored. The first idea shows how certain types of $f(R)$ gravity allows for traversable wormholes among its vacuum solutions. This is surprising to find in such simple setting as these type of solutions usually requires fairly complex constructions to satisfy the equations of motion of a gravitational theory. The second idea is the matter bounce description of the early universe where a fairly unique feature of the model is identified. Consequences of this feature could allow the paradigm to distinguish itself from other alternative descriptions, such as inflation, through late time observations. An explicit example of this claim is worked out by studying a model involving an interaction in the dark sector. Results of a more astrophysical nature, where a careful analysis of the morphology of blazar halos is performed, are also presented in the Appendix. The analysis determined that the $Q$-statistic is an appropriate tool to probe the properties of the intergalactic magnetic fields responsible for the halos formation.

The work presented in this dissertation examines three different nonequilibrium particle physics processes that could play a role in answering the question “how was the particle content of today’s universe produced after the big bang?” Cosmic strings produced from spontaneous breaking of a hidden sector $U(1)_{\rm X}$ symmetry could couple to Standard Model fields through Higgs Portal or Kinetic Mixing operators and radiate particles that contribute to the diffuse gamma ray background. In this work we calculate the properties of these strings, including finding effective couplings between the strings and Standard Model fields. Explosive particle production after inflation, known as preheating, would have produced a stochastic background of gravitational waves (GW). This work shows how the presence of realistic additional fields and interactions can affect this prediction dramatically. Specifically, it considers the inflaton to be coupled to a light scalar field, and shows that even a very small quartic self-interaction term will reduce the amplitude of the gravitational wave spectrum. For self-coupling $\lambda_{\chi} \gtrsim g^2$, where $g^2$ is the inflaton-scalar coupling, the peak energy density goes as $\Omega_{\rm GW}^{(\lambda_{\chi})} / \Omega_{\rm GW}^{(\lambda_{\chi}=0)} \sim (g^2/\lambda_{\chi})^{2}$. Finally, leptonic charge-parity (CP) violation could be an important clue to understanding the origin of our universe's matter-antimatter asymmetry, and long-baseline neutrino oscillation experiments in the coming decade may uncover this. The CP violating effects of a possible fourth ``sterile" neutrino can interfere with the usual three neutrinos; this work shows how combinations of various measurements can help break those degeneracies.

The muon problem of flavor physics presents a rich opportunity to study beyond standard model physics. The as yet undiscovered bound state (μ+μ-), called true muonium, presents a unique opportunity to investigate the muon problem. The near-future experimental searches for true muonium will produce it relativistically, preventing the easy application of non-relativistic quantum mechanics. In this thesis, quantum field theory methods based on light-front quantization are used to solve an effective Hamiltonian for true muonium in the Fock space of |μ+μ-> , |μ+μ-γ> , |e+e->, |e+e-γ>, |τ+τ-> , and |τ+τ-γ> . To facilitate these calculations a new parallel code, True Muonium Solver With Front-Form Techniques (TMSWIFT), has been developed. Using this code, numerical results for the wave functions, energy levels, and decay constants of true muonium have been obtained for a range of coupling constants α. Work is also presented for deriving the effective interaction arising from the |γγ sector’s inclusion into the model.

This thesis explores the different aspects of higher curvature gravity. The "membrane paradigm" of black holes in Einstein gravity is extended to black holes in f(R) gravity and it is shown that the higher curvature effects of f(R) gravity causes the membrane fluid to become non-Newtonian. Next a modification of the null energy condition in gravity is provided. The purpose of the null energy condition is to filter out ill-behaved theories containing ghosts. Conformal transformations, which are simple redefinitions of the spacetime, introduces serious violations of the null energy condition. This violation is shown to be spurious and a prescription for obtaining a modified null energy condition, based on the universality of the second law of thermodynamics, is provided. The thermodynamic properties of the black holes are further explored using merger of extremal black holes whose horizon entropy has topological contributions coming from the higher curvature Gauss-Bonnet term. The analysis refutes the prevalent belief in the literature that the second law of black hole thermodynamics is violated in the presence of the Gauss-Bonnet term in four dimensions. Subsequently a specific class of higher derivative scalar field theories called the galileons are obtained from a Kaluza-Klein reduction of Gauss-Bonnet gravity. Galileons are null energy condition violating theories which lead to violations of the second law of thermodynamics of black holes. These higher derivative scalar field theories which are non-minimally coupled to gravity required the development of a generalized method for obtaining the equations of motion. Utilizing this generalized method, it is shown that the inclusion of the Gauss-Bonnet term made the theory of gravity to become higher derivative, which makes it difficult to make any statements about the connection between the violation of the second law of thermodynamics and the galileon fields.

In this thesis, we present the study of several physical properties of relativistic mat- ters under extreme conditions. We start by deriving the rate of the nonleptonic weak processes and the bulk viscosity in several spin-one color superconducting phases of quark matter. We also calculate the bulk viscosity in the nonlinear and anharmonic regime in the normal phase of strange quark matter. We point out several qualitative effects due to the anharmonicity, although quantitatively they appear to be relatively small. In the corresponding study, we take into account the interplay between the non- leptonic and semileptonic weak processes. The results can be important in order to relate accessible observables of compact stars to their internal composition. We also use quantum field theoretical methods to study the transport properties in monolayer graphene in a strong magnetic field. The corresponding quasi-relativistic system re- veals an anomalous quantum Hall effect, whose features are directly connected with the spontaneous flavor symmetry breaking. We study the microscopic origin of Fara- day rotation and magneto-optical transmission in graphene and show that their main features are in agreement with the experimental data.

This thesis addresses certain quantum aspects of the event horizon using the AdS/CFT correspondence. This correspondence is profound since it describes a quantum theory of gravity in d + 1 dimensions from the perspective of a dual quantum field theory living in d dimensions. We begin by considering Rindler space which is the part of Minkowski space seen by an observer with a constant proper acceleration. Because it has an event horizon, Rindler space has been studied in great detail within the context of quantum field theory. However, a quantum gravitational treatment of Rindler space is handicapped by the fact that quantum gravity in flat space is poorly understood. By contrast, quantum gravity in anti-de Sitter space (AdS), is relatively well understood via the AdS/CFT correspondence. Taking this cue, we construct Rindler coordinates for AdS (Rindler-AdS space) in d + 1 spacetime dimensions. In three spacetime dimensions, we find novel one-parameter families of stationary vacua labeled by a rotation parameter β. The interesting thing about these rotating Rindler-AdS spaces is that they possess an observer-dependent ergoregion in addition to having an event horizon. Turning next to the application of AdS/CFT correspondence to Rindler-AdS space, we posit that the two Rindler wedges in AdSd+1 are dual to an entangled conformal field theory (CFT) that lives on two boundaries with geometry R × Hd-1. Specializing to three spacetime dimensions, we derive the thermodynamics of Rindler-AdS space using the boundary CFT. We then probe the causal structure of the spacetime by sending in a time-like source and observe that the CFT “knows” when the source has fallen past the Rindler horizon. We conclude by proposing an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space. Towards the end, we consider the concept of weak measurements in quantum mechanics, wherein the measuring instrument is weakly coupled to the system being measured. We consider such measurements in the context of two examples, viz. the decay of an excited atom, and the tunneling of a particle trapped in a well, and discuss the salient features of such measurements.