Superstring theory posits that as complicated as nature may seem to the naive observer, the variety of observed phenomena may be explained by postulating that at the fundamental scale, matter is composed of lines of energy, namely strings. These oscillating lines would be elementary and would hence have no substructure. They are expected to be incredibly tiny, their line-like structure would become noticeable at scales close to the string scale (which may lie anywhere from the TeV scale all the way up to the Planck scale) and would appear to be point-like to the macroscopic observer. Internal consistency then also requires the presence of higher dimensional objects, namely D-branes, all of which conspire and combine in such a way so as to give rise to the observable Universe. Advances in cosmology suggest the early universe was much hotter and denser than is the Universe at present, that the Universe has expanded and continues to expand (exponentially in fact) at present. This in turn has led a number of theorists to point out the remarkable possibility that some of these strings or D-branes were also stretched with the expansion. The resulting macroscopic strings, the so-called cosmic strings, would potentially stretch across the entire Universe. Cosmic strings make their presence manifest by oscillating, scattering off other structures, by decaying, producing gravitational waves and so on, and this in turn hints at the available handles that may be used to observe them. Before we can hope to observe cosmic strings however, the first step is then clearly to understand these properties which determine their evolution. A number of approximate (classical) descriptions of cosmic strings have been constructed to date, but approximations break down, especially when potentially interesting things happen (e.g. close to cusps, i.e. points on the string that reach the speed of light) and can obscure the physics. Thankfully, one can go beyond these approximations: all properties of cosmic strings can be concisely and accurately contained or encoded in a single object, the so-called fundamental cosmic string vertex operator. In the present thesis I construct precisely this, covariant vertex operators for general cosmic strings and this is the first such construction. Cosmic strings, being macroscopic, are likely to exhibit classical behaviour in which case they would most accurately be described by a string theory analogue of the well known harmonic oscillator coherent states. By minimally extending the standard definition of coherent states, so as to include the string theory requirements, I go on to construct both open and closed covariant coherent state vertex operators. The naive construction of the latter requires the existence of a lightlike compactification of spacetime. When the lightlike winding states in the underlying Hilbert space are projected out, the resulting vertex operators have a classical interpretation and can consistently propagate in noncompact spacetime. Using the DDF map I identify explicitly the corresponding general lightcone gauge classical solutions around which the exact macroscopic quantum states are fluctuating. We go on to show that both the covariant gauge coherent vertex operators, the corresponding lightcone gauge coherent states and the classical solutions all share the same mass and angular momenta, which leads us to conjecture that the covariant and lightcone gauge states are different manifestations of the same state and share identical interactions. Apart from the coherent state vertices I also present a complete set of covariant mass eigenstate vertex operators and these may also be relevant in cosmic string evolution. Finally, I also present the first amplitude computation with the coherent states, the graviton emission amplitude (including the effects of gravitational backreaction) for a simple class of cosmic string loops. As a byproduct of the above, I find that the fundamental building blocks of arbitrarily massive covariant string states are given by elementary Schur polynomials (equivalently complete Bell polynomials). This construction enables one to address the aforementioned questions concerning the properties of cosmic strings, their cosmological signatures, and may lead to the first observations of such objects in the sky. This in turn would be a remarkable way of verifying Superstring theory as the framework underlying the structure of our Universe.

This thesis aims to give an approach to dealing with Hierarchy problems in theoretical physics, plaguing theories that span a wide range of energy scales. At present, any theory that is formulated to connect observations of the Early Universe to results in present day particle physics, exhibits the necessity of (at least one) unnaturally fine-tuned parameter. This has encouraged the sectioning of of many separate, highly specialized fields - each dealing with Effective Field Theories (EFTs) valid at a limited range of energy scales only. Here I describe an effort to connect different energy scales while dynamically accounting for hierarchies. This thesis discusses the appeal of pseudo-Goldstone bosons (pGBs) for the generation of scales in Early Universe cosmology. In particular, I will show how models with pGBs address the radiative instability of mass scales in quantum mechanical theories. I will start with an introduction to the two hierarchy problems that will be the primary focus of the thesis: the electroweak hierarchy problem, or the puzzle of the lightness of the Higgs mass; and the inflationary hierarchy problem, or the flatness of the inflaton potential demanded by the nearly scale invariant spectrum of the Cosmic Microwave Background. I will briefly introduce how pGBs arise, and can be described, using an example of a compact Special Orthogonal group SO(n) breaking to its largest coset SO(n - 1). I will then explore various models that address the electroweak and the inflationary hierarchy problem, using appropriate EFT tools such as the Callan-Coleman-Wess-Zumino mechanism and 5D approaches. I will discuss the relative strength of these models compared to existing models in the literature. After this discussion I will show that it is possible to address both hierarchy problems in a unified model, in which an inflaton decays into the Higgs field after inflation, in a process called reheating. This section will include a detailed derivation of the model, and will explore the regions of parameter space that lead to inflation, reheating, and electroweak symmetry breaking compatible with the relevant experimental data. This is followed by an excursion in which I will discuss non-compact models, based on SO(n;1)=SO(n) cosets. I will show how such setups can also give rise to inflation compatible with the current data, and discuss different scenarios for reheating. I will finish with an epilogue of the prospects of (holographic) Composite Higgs models - in which the Higgs is a pGB of the breaking of a strong compact symmetry - at particle colliders.

Gravitational lensing of photons in the Cosmic Microwave Background (CMB) can be described by an integrated potential along the line of sight, the CMB lensing potential. Covariances in maps of the CMB are generated by the lensing effect, and are used to reconstruct the lensing potential itself, which is a useful probe of the matter distribution. The CMB lensing potential has been measured to high significance with CMB temperature data. However, signal to noise for lensing reconstruction from CMB polarization data is expected to be much better due to the presence of the lensing B-mode. Upcoming data from ground based CMB polarization instruments will provide high resolution maps over small patches of the sky. This will provide much better lensing reconstruction, but also presents data analysis challenges. This thesis begins with an introduction to the field of CMB lensing and CMB lensing reconstruction. The second chapter details the biases present in reconstructing the lensing potential from CMB polarization maps considering first the full sky, and then small patches of sky. It also shows that using the pure-B mode formalism for the CMB polarization leads to improved lensing reconstruction over the naive case on the cut sky. Given the upcoming improvement in the CMB lensing reconstruction, it is expected that cross-correlations of the CMB lensing with other structure tracers, such as galaxies, will yield improved information for cosmology. It is also expected that the CMB lensing will become useful to help constrain uncertainties in the galaxy power spectrum, and provide information on the linear galaxy bias and redshift distribution. The third chapter of the thesis forecasts the power of cross correlation science for a number of galactic and non-galactic parameters. Finally, the CMB lensing effects the level of non-Gaussianity observed in the CMB. The fourth chapter of the thesis is a study of the lensing effect on the primordial squeezed bispectrum. We conclude in the fifth chapter.

The knowledge of the dynamics and characteristics of space plasma during solar-terrestrial coupling has been greatly enriched by process that aids the determination of the instantaneous frequencies which support the non-stationary and non-linear nature of signals. Such plasmas are observed in the magnetosheath in the downstream of bow shock. In this thesis a technique was applied which extracts the various contributing oscillatory modes reflecting the waveforms observed in the space by Cluster spacecraft instruments such as FGM, CIS and EFW, and decompose the frequency of each extracted mode using Instantaneous Frequency method that is based on Simple Hilbert Transform (SHT). This is achieved through the use of Empirical Mode Decomposition (EMD). To eliminate the negative frequency of the various extracted modes referred to as intrinsic mode function which appears with Fourier transform, we apply Hilbert transform leading to analytic representation of the signals. This process aids the determination of the instantaneous frequencies of the extracted modes. The combined process of EMD and Hilbert transform is called the Hilbert-Huang transform. The results in this thesis have been based on the improved EMD. To contribute to the understanding of plasma dynamics, the computed instantaneous frequencies are compared with the results obtained from the application of Simple Hilbert Transform. Instantaneous frequencies of overriding waves are easily separated as opposed to the application of just SHT. They offer the advantage of 3-dimensional study of the spatial characteristics of waves. The understanding of the instantaneous wave number has been achieved through the EMD and SHT combination. This provides the results which give the wave vector for a known frequency at a given instant of time. The instantaneous dispersion relation is determined using the knowledge of the instantaneous frequency and wave vector in the satellite frame, the plasma bulk velocity and the spacecraft velocity (found to be negligible compared with the plasma bulk velocity). This is accomplished using a Doppler shift relation. Wave modes identifications have been carried out by considering the proton temperature anisotropies, plasma beta and plasma bulk velocity and instantaneous phase velocity in the satellite frame. We report Alfvén mode close to the bow shock, spreading out to mirror mode which dominates the middle of magnetosheath. The mirror mode then diminishes towards the magnetopause.