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The problem of how mathematics and physics are related at a foundational level is of much interest. One approach is to work towards a coherent theory of physics and mathematics together. Here steps are taken in this direction by first…
Some aspects of replacing C based physics by C_{n} based physics are discussed. Here C_{n} ={R_{n},I_{n}} where R_{n} and I_{n} are the real and imaginary components of the numbers in C_{n}, and both R_{n} and I_{n}) are sets of length 2n…
The main aim of this paper is to provide a qualitative introduction to the cosmic inflation and its relationship with current cosmological observations. The inflationary model solves many of the fundamental problems that challenge the…
The values of, and connection between, the cosmological observables of the primordial power spectrum tilt $n_s$ and the inflationary tensor to scalar ratio $r$ are key guideposts to the physics of inflation. Universality classes can be…
In this article the reduction of a $n$-dimensional space to a $k$-dimensional space is considered as a reduction of $N^n$ states to $N^k$ states, where $N$ stands for the number of single-particle states per unit of spatial length. It turns…
We develop a possible cosmology for a Universe with n additional spatial dimensions of variable scale, and an associated scalar field, the radion, which is distinct from the field responsible for inflation, the inflaton. Based on a…
The study of reheating in inflationary models is crucial for understanding the early universe and gaining insights into inflationary dynamics and parameters. The reheating temperature $T_{re}$ and the duration of the reheating phase,…
When Inflation is embedded in a fundamental theory, such as string theory, it typically begins when the Universe is already substantially larger than the fundamental scale [such as the one defined by the string length scale]. This is…
On the occasion of a century from the proposal of General relativity by Einstein, I attempt to tackle some open issues in modern cosmology, via a toy but non-trivial model. Specifically, I would like to link together: (i) the smallness of…
Cosmological observations have provided us with the measurement of just three numbers that characterize the very early universe: $ 1-n_{s} $, $ N $ and $\ln\Delta_R^2$. Although each of the three numbers individually carries limited…
Closed string tachyon condensation in spacetime generates potentials on the worldsheet that model two-dimensional inflationary cosmology. These models illustrate and elucidate a variety of aspects of inflation, in particular the generation…
We consider inflation in a universe with a positive cosmological constant and a nonminimally coupled scalar field, in which the field couples both quadratically and quartically to the Ricci scalar. When considered in the Einstein frame and…
In this dissertation, we introduce a general way of modeling inflation in a framework that is independent of the exact nature of the inflationary potential. Because of the choice of our initial conditions and the continuity of the scale…
At its very beginning, the universe is believed to have grown exponentially in size via the mechanism of inflation. The almost scale-invariant density perturbation spectrum predicted by inflation is strongly supported by cosmological…
The inflationary paradigm provides a robust description of the peculiar initial conditions which are required for the success of the Hot Big Bang model of cosmology, as well as of the recent precision measurements of temperature…
Modifying the standard hot big bang model of cosmology with an inflationary event has been very successful in resolving most of the outstanding cosmological problems. The various inflationary mechanisms proposed depend on the production of…
This thesis is dedicated to the study of inflationary scenarios based on string theory. Inflation is a brief period of accelerated expansion in the very early Universe which gives natural explanations for problems of the Standard Big Bang…
The early time expansion of the space-time, namely inflation, is introduced to solve some cosmological problems. $F(R)$ gravity is a simple extension of the general relativity to induce the inflationary expansion. The precise observation of…
The source of the universe inflation is electromagnetic fields obeying rational nonlinear electrodynamics proposed earlier. Within this model the singularities of the electric field at the center of charges, the Ricci scalar, the Ricci…
In generic models of cosmological inflation, quantum fluctuations strongly influence the spacetime metric and produce infinitely many regions where the end of inflation (reheating) is delayed until arbitrarily late times. The geometry of…