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Singularities in General Relativity are regions where the description of spacetime in terms of a pseudo-Riemannian geometry breaks down. The theory seems unable to predict the evolution of the physical degrees of freedom around and beyond…
The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of the Universe, a causal theory for the origin of primordial density fluctuations which may explain the observed density…
Starobinsky's $R^2$ inflation manifests a best-fit scenario for the power spectrum of primordial density fluctuations. Observables derived from the slow-roll picture of the $R^2$ model in the Einstein frame relies on the conformal…
In this work we construct a bottom-up reconstruction technique for Loop Quantum Cosmology scalar-tensor theories, from the observational indices. Particularly, the reconstruction technique is based on fixing the functional form of the…
Inflation elegantly provides initial conditions for the standard model of cosmology, while solving the horizon, flatness, and magnetic monopole problems. Inflationary models make predictions for the tensor-to-scalar ratio $r$ and the…
Though predictions of the simplest inflationary cosmological models with cold dark matter, flat space and approximately flat initial spectrum of adiabatic perturbations are remarkably close to observational data, we have to go beyond them…
Following the 2015 Planck release, we briefly comment on the status and some ongoing opportunities in the interface between inflationary cosmology, string theory, and CMB data. The constraints in the $r$-$n_s$ plane introduce a new…
We obtain cosmological constraints on models of inflation which exhibit rapid roll solutions. Rapid roll attractors exist for potentials with large mass terms and are thus of interest for inflationary model building within string theory. We…
Inflation is a bold and expansive extension of the Standard Cosmology. It holds the promise to extend our understanding of the Universe to within 10^{-32}sec of the big bang and answer most of the pressing questions in cosmology. Its…
We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is $f(R)=R+\alpha R^2+\beta R^2 \ln R$. These terms are expected to arise from one loop corrections involving matter…
The theory of cosmological perturbations is the main tool which connects theories of the early universe (based on new fundamental physics such as string theory) with cosmological observations. In these lectures, I will provide an…
The description of the accelerated phases for the current and primordial cosmos has been obtained in the framework of R\'{e}nyi cosmology. The results show that corrections to the Friedmann equations, originated from differences between…
A four-dimensional universe, arising from a flux compactification of Type IIB string theory, contains scalar fields with a potential determined by topological and geometric parameters of the internal -hidden- dimensions. We show that…
The theory of eternal inflation in an inflaton potential with multiple vacua predicts that our universe is one of many bubble universes nucleating and growing inside an ever-expanding false vacuum. The collision of our bubble with another…
A pressing problem in comparing inflationary models with observation is the accurate calculation of correlation functions. One approach is to evolve them using ordinary differential equations ("transport equations"), analogous to the…
Cosmic inflation provides a window to the highest energy densities accessible in nature, far beyond those achievable in any realistic terrestrial experiment. Theoretical insights into the inflationary era and its observational probes may…
The $R+R^2$, shortly named "$R^2$" ("Starobinsky") inflationary model, represents a fully consistent example of a one-parameter inflationary scenario. This model has a "graceful exit" from inflation and provides a mechanism for subsequent…
Brane inflation is a specific realization of the inflationary universe scenario in the early universe within the brane world framework in string theory. The naturalness and robustness of this realistic scenario is explained. Its predictions…
The basic workings of inflationary models are summarized, along with the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are…
We generalise Starobinsky's model of inflation to space-times with $D>4$ dimensions, where $D-4$ dimensions are compactified on a suitable manifold. The $D$-dimensional action features Einstein-Hilbert gravity, a higher-order curvature…