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Modern cosmology began in 1917 when Einstein published his model of a static Universe built on general relativity. A few months later de Sitter came forward with a competing, but also static model which contained no matter but had the intriguing quality that the spectrum of a test particle appeared redshifted to a distant observer. It was thought that de Sitter's model might explain the redshifted spectra observed by Slipher in spiral nebulae. However, in 1927 Lemaître showed that de Sitter's model violated the principle of homogeneity. He then formulated a dynamical cosmological model and combined it with the available observations, showing that our Universe is expanding. He theoretically derived the linear distance–velocity relationship which today is called the "Hubble-relation." Hubble confirmed the relation in 1929 on purely observational grounds. 80 years ago, in 1931 in a letter to Nature, Lemaître suggested that the Universe had a definite beginning in a rapid expansion out of a highly condensed state: the primeval atom. This event became later known as the Big Bang.

Torsion is a geometrical object, required by quantum mechanics in curved spacetime, which may naturally solve fundamental problems of general theory of relativity and cosmology. The black-hole cosmology, resulting from torsion, could be a scenario uniting the ideas of the big bounce and inflation, which were the subject of a recent debate of renowned cosmologists., Comment: 5 pages, 2 figures; published version. This essay received an Honorable Mention in the 2018 Essay Competition of the Gravity Research Foundation

We give a mathematically exact and physically faithful embedding of curved 4D cosmology in a flat 5D space, thereby enabling visualization of the big bang in a new and informative way. In fact, in unified theories of fields and particles with real extra dimensions, it is possible to dispense with the initial singularity.

We study the SO(1, 1) dark energy model with the inverse power law potential, V = V0Φ-n, and find for n

Loop quantum cosmology provides a new paradigm on the genesis of our universe in which the classical expanding branch is joined via a quantum geometric bridge to a classical contracting branch. The evolution between two phases of our universe is non-singular and deterministic, which is a direct manifestation of incorporating non-perturbative quantum geometric features of loop quantum gravity. Using analytical and numerical techniques, details of the quantum nature of big bang can be quantified and reliable physical predictions can be made. The quantum description can also be well approximated by an effective theory which leads to ρ2 modifications to the Friedmann equation in the Planck regime.

We study the accelerating expansion and the induced dark energy of the $5D$ Ricci-flat universe which is characterized by having a big bounce as opposed to a big bang. We show that the arbitrary function $\mu(t)$ contained in the $5D$ solutions can be rewritten in terms of the redshift $z$ as a new arbitrary function $f(z)$, and we find that there is a correspondence between this $f(z)$ and the potential $V(\phi)$ of the 4D quintessence models. Using this correspondence, the arbitrary function $f(z)$ and the $5D$ solution could be specified for a given form of the potential $V(\phi)$., Comment: ws-mpla.cls, 10 pages, 4 figures, to be published in MPLA, one reference added, four eps figures changed

We model the standard [Formula: see text]CDM model of the universe by the spatially flat FLRW line element [Formula: see text] which we extend for all time [Formula: see text]. Although there is a cosmological singularity at the big bang [Formula: see text], since the spatial part of the metric collapses to zero, nevertheless, this line element is defined for all time [Formula: see text], is [Formula: see text] for all [Formula: see text], is [Formula: see text] differentiable at [Formula: see text], and is non-degenerate and solves Friedmann’s equation for all [Formula: see text]. Thus, we can use this extended line element to model the universe from its past-asymptotic initial state [Formula: see text] at [Formula: see text], through the big bang at [Formula: see text], and onward to its future-asymptotic final state [Formula: see text] at [Formula: see text]. Since in this model the universe existed before the big bang, we conclude that (1) the universe was not created de novo at the big bang and (2) cosmological singularities such as black holes or the big bang itself need not be an end to spacetime. Our model shows that the universe was asymptotically created de novo out of nothing at [Formula: see text] from an unstable vacuum negative half de Sitter [Formula: see text] initial state and then dies asymptotically at [Formula: see text] as the stable positive half de Sitter [Formula: see text] final state. Since the de Sitter states are vacuum matter states, our model shows that the universe was created from nothing at [Formula: see text] and dies at [Formula: see text] to nothing.

An alternative to the Big Bang cosmologies is obtained by the Big Bounce cosmologies. In this paper, we study a bounce cosmology with a Type IV singularity occurring at the bouncing point in the context of [Formula: see text] modified gravity. We investigate the evolution of the Hubble radius and we examine the issue of primordial cosmological perturbations in detail. As we demonstrate, for the singular bounce, the primordial perturbations originating from the cosmological era near the bounce do not produce a scale-invariant spectrum and also the short wavelength modes after these exit the horizon, do not freeze, but grow linearly with time. After presenting the cosmological perturbations study, we discuss the viability of the singular bounce model, and our results indicate that the singular bounce must be combined with another cosmological scenario, or should be modified appropriately, in order that it leads to a viable cosmology. The study of the slow-roll parameters leads to the same result indicating that the singular bounce theory is unstable at the singularity point for certain values of the parameters. We also conformally transform the Jordan frame singular bounce, and as we demonstrate, the Einstein frame metric leads to a Big Rip singularity. Therefore, the Type IV singularity in the Jordan frame becomes a Big Rip singularity in the Einstein frame. Finally, we briefly study a generalized singular cosmological model, which contains two Type IV singularities, with quite appealing features.

This brief review provides an overview of work exploring the hypothesis that the Universe “tunneled into being” as a quantum fluctuation. The basic picture is formulated within the context of a semiclassical description, in which the tunneling is interpreted as a gravitational instanton interpolating between some Planck-sized, metrically and topologically complicated, pretunneling entity and a rapidly expanding, topologically trivial, post-tunneling Universe. It is argued that the tunneling hypothesis may provide a simple explanation of gross observed features of the current Universe, such as the fact that it is big, nearly homogeneous and nearly flat, and that the massless particles contained therein seem characterized by a near-thermal distribution.

This letter uses ideas developed recently in semiclassical quantum gravity to argue that many qualitative features of the Hot Big Bang generally assumed in cosmology may be explained by the hypothesis that, interpreted semiclassically, the Universe “tunnelled into being” via a quantum fluctuation from a small (Planck-sized), topologically complex entity to a topolo-gically trivial entity (like a Friedmann Universe) that rapidly grew to a more macroscopic size.

We show that the significant Tolman-Bondi metrics originated by a synchronous big bang can be divided, according to the initial conditions, into three classes. The elements of one of these classes give the dynamical description of the formation of a black hole in the background of an expanding universe.

We present a cosmological model in which the Universe emerges out of the collapse of a five-dimensional (5D) star as a spherical three-brane. The initial singularity of the big bang becomes hidden behind a causal horizon. Near scale-invariant primordial curvature perturbations can be induced on the brane via a thermal atmosphere that is in equilibrium with the brane, circumventing the need for a separate inflationary process and providing an important test of the model.

Many cosmological scenarios envisage either a bounce of the universe at early times, or a collapse locally to form a black hole which re-expands into a new expanding universe region. Energy conditions preclude this phenomena for ordinary matter in general relativistic universe, but scalar or other types of fields can violate some of these conditions, and so can, possibly, provide conditions for a bouncing universe. In this paper, we have investigated the necessary conditions for a bounce in Kantowski–Sachs (KS) and Bianchi type models in some modified theories of gravity like Hoyle–Narlikar creation field theory, Lyra geometry, general class of scalar–tensor theories, Einstein's theory with variable cosmological term.

Albert Einstein's real "biggest blunder" was not the 1917 introduction into his gravitational field equations of a cosmological constant term \Lambda, rather was his failure in 1916 to distinguish between the entirely different concepts of active gravitational mass and passive gravitational mass. Had he made the distinction, and followed David Hilbert's lead in deriving field equations from a variational principle, he might have discovered a true (not a cut and paste) Einstein-Rosen bridge and a cosmological model that would have allowed him to predict, long before such phenomena were imagined by others, inflation, a big bounce (not a big bang), an accelerating expansion of the universe, dark matter, and the existence of cosmic voids, walls, filaments, and nodes., Comment: 4 pages, LaTeX, 11 references, Honorable Mention in 2012 Gravity Research Foundation Essay Awards

Hawking’s theory of quantum cosmology is the most important stage in understanding our universe since the big bang model. In principle, one can predict everything in the universe solely from physical laws. All main results within this framework have been reviewed in this paper.