Executive SummaryPrecision cosmological measurements push the boundaries of our understanding of the fundamental physics that governs our universe. In the coming years, cosmologists will be in a position to make major breakthroughs in our understanding of the physics of the very early universe and be able to probe particle physics and gravity at the highest energy scales yet accessed. A major leap forward in the sensitivity of cosmological experiments is within our technological reach, leveraging past and current experience to tackle some of the most interesting fundamental physics questions.Cosmic inflation, the theory that the universe underwent a violent, exponential expansion during the first moments of time, is the leading theoretical paradigm for the earliest history of the universe and for the origin of the structure in the universe. Current measurements of the cosmic microwave background (CMB) and observations of the large-scale distributions of dark matter and galaxies in the universe are in stunning agreement with the concept of inflation. The next generations of experiments in observational cosmology are poised to decide central questions about the mechanism behind inflation. In this short document, we highlight the importance of experimentally determining the nature of inflation in the early universe and the unique opportunity these experiments provide to explore the physics of space, time, and matter at the highest energies possible: those found at the birth of the universe.

Warm Inflation seems to be the most befitting single-field slow-roll inflation scenario in the context of the recently proposed Swampland Criteria. We investigate the constraints these Swampland Criteria impose on Warm Inflation parameters and show that Warm Inflation is in accordance with both the current cosmological observations and the proposed Swampland Criteria in both weak and strong dissipative regimes depending on the value of the parameter c which limits the slope of the inflaton potential according to the criteria.

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It was pointed out some time ago that there can be two variations in which the divergences of a quantum field theory can be tamed using the ideas presented by Lee and Wick. In one variation the Lee-Wick partners of the normal fields live in an indefinite metric Hilbert space but have positive energy and in the other variation the Lee-Wick partners can live in a normal Hilbert space but carry negative energy. Quantum mechanically the two variations mainly differ in the way the fields are quantized. In this article the second variation of Lee and Wick's idea is discussed. Using statistical mechanical methods the energy density, pressure and entropy density of the negative energy Lee-Wick fields have been calculated. The results exactly match with the thermodynamic results of the conventional, positive energy Lee-Wick fields. The result sheds some light on the second variation of Lee-Wick's idea. The result seems to say that the thermodynamics of the theories do not care about the way they are quantized.