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We propose the relation $M_\Lambda \sim (M_{Pl} M_U)^{1/2}$ where $M_\Lambda$, $M_{Pl},$ and $M_U$ denote the mass scale associated with the cosmological constant, the gravitational interaction, and the size of the universe respectively.
It has been claimed that the observed magnitude of the vacuum energy density is consistent with the distribution predicted in anthropic models, in which an ensemble of universes is assumed. This calculation is revisited, without making the…
The aim of this note is to remove an implausible assumption in Moser's theorem \cite{JM} to establish our new theorem 1 which gives a lower estimate for the sum $p+c^2\rho$ on Riemann hypothesis. Corollary 1 gives a rather plausible…
Despite its central role in modern cosmology, doubts are often expressed as to whether cosmological inflation is really a falsifiable theory. We distinguish two facets of inflation, one as a theory of initial conditions for the hot big bang…
I present a large set of high resolution simulations, called CosmicGrowth Simulations, which were generated with either 8.6 billion or 29 billion particles. As the nominal cosmological model that can match nearly all observations on…
Model-independent methods in cosmology has become an essential tool in order to deal with an increasing number of theoretical alternatives for explaining the late-time acceleration of the Universe. In principle, this provides a way of…
This contribution presents the cosmological models with extra dimensions that have been recently elaborated, which assume that ordinary matter is confined on a surface, called brane, embedded in a higher dimensional spacetime.
Understanding the behavior of the universe at large depends critically on insights about the smallest units of matter and their fundamental interactions. Inflationary cosmology is a highly successful framework for exploring these…
An introduction to modern theories for the origin of structure in the Universe is given. After a brief review of the growth of cosmological perturbations in an expanding Universe and a summary of some important observational results, the…
Perhaps the deepest mystery of our accelerating Universe in expansion is the existence of a tiny and rigid cosmological constant, $\Lambda$. Its size is many orders of magnitude below the expected one in the standard model of particle…
We present a brief history of the construction of models of the universe, followed by calculations of quantitative characteristics of basic geometric and kinematic properties of the Standard Cosmological Model ($\Lambda$CDM). Using the…
In the past several decades, multiple cosmological theories that are based on the contention that the Universe has a major axis have been proposed. Such theories can be based on the geometry of the Universe, or multiverse theories such as…
Recent observations of Type 1a supernovae indicating an accelerating universe have once more drawn attention to the possible existence, at the present epoch, of a small positive Lambda-term (cosmological constant). In this paper we review…
Certain results of observational cosmology cast critical doubt on the foundations of standard cosmology but leave most cosmologists untroubled. Alternative cosmological models that differ from the Big Bang have been published and defended…
Cosmological observables are used to construct cosmological models. Since cosmological observations are limited to the light cone, a fixed number of observables (even measured to arbitrary accuracy) may not uniquely determine a cosmological…
CMB anisotropy data could put powerful constraints on theories of the evolution of our Universe. Using the observations of the large number of CMB experiments, many studies have put constraints on cosmological parameters assuming different…
Planck will be the first mission to map the entire cosmic microwave background (CMB) sky with mJy sensitivity and resolution better than 10'. The science enabled by such a mission spans many areas of astrophysics and cosmology. In…
A simple and surprisingly realistic model of the origin of the universe can be developed using the Friedmann equation from general relativity, elementary quantum mechanics, and the experimental values of h, c, G and the proton mass. The…
This article gives a brief overview of some of the theory behind the inflationary cosmology, and discusses prospects for constraining inflation using observations. Particular care is given to the question of falsifiability of inflation or…
A convergence of ideas, observations and technology have led to the greatest period of cosmological discovery yet. Over the past three years we have determined the basic features of our Universe. We are now challenged to make sense of what…