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The existence of a positive and possibly varying Lambda-term opens a much wider field of possibilities for the future of our Universe than it was usually thought before. Definite predictions may be made for finite (though very large)…
A primordial inflationary phase allows one to erase any possible anisotropic expansion thanks to the cosmic no-hair theorem. If there is no global anisotropic stress, then the anisotropic expansion rate tends to decrease. What are the…
We show that in the case of positively-curved Friedmann-Lema\^{\i}tre universes $(k=+1)$, an inflationary period in the early universe will for most initial conditions not solve the horizon problem, no matter how long inflation lasts. It…
Model independent arguments following from the Covariant Entropy Principle imply that causal diamonds in the very early universe were entirely filled with a single equilibrated system with finite entropy. A universe where this condition…
In this article we study closed inflationary universe models proposed by Linde in a brane world cosmological context. In this scenario we determine and characterize the existence of a closed universe, in presence of one self-interacting…
Problem of cosmological singularity of general relativity theory is discussed. The possible resolution of this problem in the framework of inflationary cosmology is proposed. Physical conditions leading to bouncing inflationary solutions in…
While cosmological inflation can erase primordial inhomogeneities, it is possible that inflation may not begin in a significantly inhomogeneous universe. This issue is particularly pressing in multifield scenarios, where even the…
An introductory account is given of the inflationary cosmology, which postulates a period of accelerated expansion during the Universe's earliest stages. The historical motivation is briefly outlined, and the modelling of the inflationary…
We propose an explanation for the present accelerated expansion of the universe that does not invoke dark energy or a modification of gravity and is firmly rooted in inflationary cosmology.
Non-singular bouncing cosmologies are well--motivated models for the early universe. Recent observational data are consistent with positive spatial curvature and allow for a natural collapsing and bouncing phase in the very early universe.…
The Big Bang singularity in standard model cosmology suggests a program of study in 'early universe' quantum gravity phenomenology. Inflation is usually thought to undermine this program's prospects by means of a dynamical diluting…
We show why the universe started in an unstable de Sitter state. The quantum origin of our universe implies one must take a `top down' approach to the problem of initial conditions in cosmology, in which the histories that contribute to the…
The mechanism for triggering the universe inflation could be that at very early periods the time variable was discrete instead of smooth. Alternatively, and perhaps equivalently, it could be the consequence that the metrics of the early…
The influence of recent detections of a finite vacuum energy ("cosmological constant") on our formulation of anthropic conjectures, particularly the so-called Final Anthropic Principle is investigated. It is shown that non-zero vacuum…
A macroscopic universe may emerge naturally from a Planck cell fluctuation by unfolding through a stage of exponential expansion towards a homogeneous cosmological background. Such primordial inflation requires a large and presumably…
Eternal inflation requires upward fluctuations of the energy in a Hubble volume, which appear to violate the energy conditions. In particular, a scalar field in an inflating spacetime should obey the averaged null energy condition, which…
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…
Cosmological singularity theorems such as that of Hawking and Penrose assume local curvature conditions as well as global ones like the existence of a compact (achronal) slice. Here, we prove a new singularity theorem for chronological…
The theory of the inflationary multiverse changes the way we think about our place in the world. According to its most popular version, our world may consist of infinitely many exponentially large parts, exhibiting different sets of…
Eternal inflation is a seemingly generic consequence of theories that give rise to accelerated expansion of the universe and possess multiple vacuum states. Making predictions in an eternally inflating universe is notoriously difficult…