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In this article we follow a previously developed theoretical approach, based in the tools of the singular semi-Riemannian geometry, to push the limits of time beyond the primordial spacetime singularity. By complexifying the Friedmann-Lemaitre-Robertson-Walker (FLRW) metric and Friedmann's equations we model a branch cut universe, in which the cosmic FLRW metric scale factor is analytically continued to the complex plane, and becomes equivalent from a conceptual point of view of describing a hypothetical general metric of maximally symmetric and homogeneous superposed multiple universes.

In this contribution we identify two scenarios for the evolutionary branch cut universe. In the first scenario, the universe evolves continuously from the negative complex cosmological time sector, prior to a primordial singularity, to the positive one, circumventing continuously a branch cut, and no primordial singularity occurs in the imaginary sector, only branch points. In the second scenario, the branch cut and branch point disappear after the realisation of the imaginary component of the complex time by means of a Wick rotation, which is replaced by the thermal time. In the second scenario, the universe has its origin in the Big Bang, but the model contemplates simultaneously a mirrored parallel evolutionary universe going backwards in the cosmological thermal time negative sector. A quantum formulation based on the WDW equation is sketched and preliminary conclusions are drawn.

Assuming a geometrically closed universe, we predict a value for the cosmic curvature, , a value within current observational bounds. We also propose a thermodynamic heat engine model for the universe, which bypasses the need for an inflaton field. Our model is based on a Carnot Cycle where we have isothermal expansion, followed by adiabatic expansion, followed by isothermal contraction, followed by adiabatic contraction, bringing us back to our original starting point. For the working substance, we focus specifically on the CMB radiation filling the collective voids in the universe. Using this construct, we identify cosmic inflation as the isothermal expansion phase, which lasts just under, . The collective CMB volume we see today only increases by a factor of 5.65 times during this process, and homogeneity and perturbations in the CMB are explained. The singularity problem is avoided and we have a clear mechanism for the work done by the cosmos in causing expansion, and later contraction. For scaling laws with respect to the density parameters in Friedmann’s equations, we will assume a susceptibility model for space, where, , the smeared cosmic susceptibility, decreases with increasing cosmic scale parameter, . Within this framework, we can predict a maximum Hubble volume with minimum CMB temperature for the voids before contraction begins, as well as a minimum volume with maximum CMB temperature when expansion starts. The thermodynamic heat cycle deviates from efficiency in converting heat energy into mechanical energy (expansion) by a minuscule amount, namely, . The significance of this number is not known.

On the orthodox interpretation of bounce cosmologies, a preceding universe was compressed to a small size before ``bouncing'' to form the present expanding universe. William Lane Craig and James Sinclair have argued that the orthodox interpretation is incorrect if the entropy reaches a minimum at the bounce. In their view, the interface between universes represents the birth of two expanding universes, i.e., a ``double bang'' instead of a ``big bounce''. Here, I reply to Craig and Sinclair in defense of the orthodox interpretation. Contrary to their interpretation, features of one universe explain features of the other universe and so must precede the other universe in time. Moreover, contrary to a crucial part of Craig and Sinclair's interpretation, there are bounce cosmologies in which the thermodynamic arrow of time is continuous through the bounce even though the entropy is ``reset'' at the bounce., 34 pages, Published in Erkenntnis

We construct and study a simple noncommutative scheme (theta-deformation) for the effective loop quantum cosmology of the flat Friedmann-Lema\^{\i}tre-Robertson-Walker model in the presence of a homogeneous scalar field $\ensuremath{\phi}$ with a potential $\mathcal{V}(\ensuremath{\phi})=\frac{1}{2}{m}^{2}{\ensuremath{\phi}}^{2}$. We first conduct a simple analysis from the corresponding Hamilton equations of motion considering a generic term $\mathcal{V}(\ensuremath{\phi})$. It is observed that the characteristic big bounce of loop quantum cosmology is preserved under such noncommutative extension. When specializing to the quadratic case, numerical solutions to the corresponding Hamilton equations exhibiting an early inflationary epoch with a sufficiently large number of $e$-foldings are found. It is concluded that, in this noncommutative setup, solutions exist which are in the overall compatible with the early universe predicted by standard (effective) Loop Quantum Cosmology (i.e., a bouncing and inflationary early universe). The issue of the genericness of a sufficiently long inflationary period on the space of solutions in this noncommutative construct remains to be addressed.

To investigate the cosmic future of the universe, first, we obtain the particle and event horizons, and their evolution in time for three well-known varying cosmological constant models. We investigate the implications of these varying cosmological constant models on the particle and event horizons, and their time evolution during the universe history and future. We study the behaviours around the origin and at the far future of the universe for all cases. Finally, we obtained the general behaviours of the horizons and time evolution functions with respect to the general scale factor a for each of the three cases of varying cosmological constant. The results show that for two of our three cases, a big bounce scenario is inevitable for the universe starting from the big bang and ending up with a bouncing re-collapse to its initial state.

While the standard, six-parameter, spatially flat $\Lambda$CDM model has been highly successful, certain anomalies in the cosmic microwave background bring out a tension between this model and observations. The statistical significance of any one anomaly is small. However, taken together, the presence of two or more of them imply that according to standard inflationary theories we live in quite an exceptional universe. We revisit the analysis of the PLANCK collaboration using loop quantum cosmology, where an unforeseen interplay between the ultraviolet and the infrared makes the \emph{primordial} power spectrum scale dependent at very small $k$. Consequently, we are led to a somewhat different $\Lambda$CDM universe in which anomalies associated with large scale power suppression and the lensing amplitude are both alleviated. The analysis also leads to new predictions for future observations. This article is addressed both to cosmology and LQG communities, and we have attempted to make it self-contained., Comment: 30 pages, 9 figures

In cosmology dark energy and dark matter are included in the CDM model, but they are still completely unknown. On the other hand the trans-Planckian problem leads to unlikely high photon energies for black holes. We introduce a model with quantized black hole matter. This minimizes the trans- Planckian problem extremely and leads to a scalar field in the oscillating universe model. We show that the scalar field has the same characteristics as a vacuum energy field and leads to the same Casimir effect. Shortly after the beginning of the big bounce this field decays locally and leads to the production of dark matter. In this model no inflation theory is needed. We emphasize that this model is mainly a phenomenological approach with the aim of new impetus to the discussion.

This article introduces recursive Heaviside step functions, as a potential of the known universe, for the first time in the history of mathematics, science, and engineering. In modern cosmology, various bouncing models have been suggested based on the postulation that the current universe is the result of the collapse of a previous universe. However, all Big Bounce models leave unanswered the question of what powered inflation. Recursive Heaviside step functions are analyzed to represent the warpage of spacetime during the crunch-bounce transition. In particular, the time shift appeared during the transition is modeled in the form of recursive Heaviside step functions and suggested as a possible answer for the immeasurable energy appeared for the Big Bounce.

The causal set approach to the problem of quantum gravity is based on the hypothesis that spacetime is fundamentally discrete. Spacetime discreteness opens the door to novel types of dynamical law for cosmology and the Classical Sequential Growth (CSG) models of Rideout and Sorkin form an interesting class of such laws. It has been shown that a renormalisation of the dynamical parameters of a CSG model occurs whenever the universe undergoes a Big Crunch–Big Bang bounce. In this paper we propose a way to model the creation of a new universe after the singularity of a black hole. We show that renormalisation of dynamical parameters occurs in a CSG model after such a creation event. We speculate that this could realise aspects of Smolin's Cosmological Natural Selection proposal.

In this article, we argue that the past of the Universe, extrapolated from standard physics and measured cosmological parameters, might be a non-singular bounce. We also show that, in this framework, quite stringent constraints can be put on the reheating temperature and number of inflationary e-folds, basically fixing $$T_{RH}\sim T_{GUT}$$TRH∼TGUT and $$N\sim 70$$N∼70. We draw some conclusions about the shape of the inflaton potential and raise the “naturalness” issue in this context. Finally, we argue that this could open a very specific window on the “pre big bounce" universe.

General relativity (GR) and gravitation in flat space-time (GFST) are covariant theories to describe gravitation. The metric of GR is given by the form of proper-time and the metric of GFST is a flat space-time form different from that of proper-time. The source of GR is the matter tensor and the Einstein tensor describes the gravitational field. The source of GFST is the total energymomentum including gravitation. The field is described by a non-linear differential operator of order two in divergence form. The results of the two theories agree for weak gravitational fields to the order of measurable accuracy. It is well-known that homogeneous, isotropic, cosmological models of GR start from a point singularity of the universe, the so called big bang. The density of matter is infinite. Therefore, our observable big universe implies an expansion of space, in particular an inflationary expansion in the beginning. Doubts are stated because infinities don’t exist in physics. An explanation to the present, controversial discussion of expanding accelerating or non-accelerating universe as well as non-expanding universe is given. GFST starts in the beginning from a homogeneous, isotropic universe with uniformly distributed energy and no matter. In the course of time matter is created out of energy where the total energy is conserved. There is no singularity, i.e. no big bang. The space is flat and non-expanding.

In a recent paper, John J. Park argues (1) that an abstract object can bring a universe into existence, and (2) that, according to the Big Bang Theory, the initial singularity is an abstract object that brought the universe into existence. According to Park, if (1) and (2) are true, then the kalam cosmological argument fails to show that the cause of the universe must be divine. I argue, however, that both (1) and (2) are false. In my argument I analyse the abstract/concrete distinction and conclude that, by its nature, an abstract object is causally inefficacious in the sense that it cannot bring something into existence.

We analyze the dynamics of a homogeneous and isotropic universe in the Einstein--Cartan theory of gravity. The spin of fermions produces spacetime torsion that prevents gravitational singularities and replaces the big bang with a nonsingular big bounce. We show that a closed universe exists only when a particular function of its scale factor and temperature is higher than some threshold value, whereas an open and a flat universes do not have such a restriction. We also show that a bounce of the scale factor is double: as the temperature increases and then decreases, the scale factor decreases, increases, decreases, and then increases., Comment: 5 pages, 3 tables, 2 figures

We analyze some relevant semiclassical and quantum features of the implementation of Polymer Quantum Mechanics to the phenomenology of the flat isotropic Universe. We firstly investigate a parallelism between the semiclassical polymer dynamics of the flat isotropic Universe, as reduced to the effect of a modified simplectic structure, and the so-called Generalized Uncertainty Principle. We show how the difference in the sign of the fundamental Poisson bracket is reflected in a sign of the modified source term in the Friedmann equation, responsible for the removal of the initial singularity in the polymer case and for the survival of a singular point in the Universe past, when the Generalized Uncertainty Principle is concerned. Then, we study the regularization of the vacuum energy of a free massless scalar field, by implementing a second quantization formalism in the context of Polymer Quantum Mechanics. We show that, from this reformulation, naturally emerges a Cosmological Constant term for the isotropic Universe, whose value depends directly on the polymer parameter of the regularization. Finally, we investigate the behaviour of gravitational waves on the background of a modified dynamics, according to the semiclassical Friedmann equation. We demonstrate that the presence of a Bounce in the Universe past, naturally removes the divergence of the gravitational wave amplitude and they can, in principle, propagate across the minimum volume turning point. This result offers the intriguing perspective for the detection of gravitational signals coming from the pre-Big Bounce collapsing Universe., Comment: New submission to match published version

We analyze the cosmological implementation of Palatini $f(R)$ theories, constructed with a Nieh-Yan term and solved with respect to the torsion. We consider the relevant case of the quadratic correction to the Hilbert-Palatini action in the Ricci scalar, mimicking the Starobinsky model of the metric formulation. We point out the emergence of peculiar cosmological scenarios, depending on the sign of such correction, able to reproduce bouncing settings and to restore the standard Universe dynamics in the late asymptotic limit. Furthermore, we outline the settling of Little-Rip dynamics, which calls for a deeper investigation in order to be regularized via matter creation. Finally, we also show that in our model the Immirzi field is asymptotically frozen in time, resembling the morphology of Loop Quantum Gravity standard formulation., Comment: 9 pages

We consider the model of evolution of the Universe where the Big Bang is regarded as an explosion of a photon superstar. The inflationary epoch is not necessary in the model. The model describes the fundamental phenomena observed: the Universe is expanding at an increasing rate, it is homogeneous and isotropic and contains no antimatter, and its metrics is almost flat.

This paper studied the revisions to Einstein’s theory of relativity, introduced the concept of “size mass” and put forward the new relativity mass-velocity formula; and then it put forward Liu’s Cosmological Model, analyzed the nascence, birth and development of the universe, obtained the Universe Moving Equations, and calculated the present universe’s parameters; and it analyzed the conditions that a celestial body occurs the similar big bang and the model that the Galaxy occurred the second big bang. The results show that at its nascence, the universe was a big neutron of which the temperature was 8.876×1012℃, the radius was r0=4.84×1011m and that was at rest, under the action of temperature energy (heat energy) releasing, the center of this big neutron generated repulsive force to the surrounding. Under the common action of the repulsive force and gravitation, at the moment tb=6.77×10-5s, the Big Bang occurred. Since the Big Bang, most celestial bodies have been leaving the center of the universe and spreading around with velocities above 0.47c, and the universe is constantly expanding. When an object moves relative to the absolute frame of reference, its three-dimensional size will shrink by the same proportion. The four-dimensional Minkowski space-time is meaningless. The size mass of a system is reduced, if its temperature is maintained unchangeable, then its energy will be correspondingly reduced, and the other system accepts an increase of size mass, if its temperature is maintained unchangeable, then its energy is correspondingly increased.

This paper posits that the Big Bang was started by the creation of the reverse Higgs field as the massless particle-generating field derived from the absorption of the interuniversal void outside of the universe in the reversible multiverse. The interuniversal void surrounding every universe is to prevent the collision of expanding universes which have the inexhaustible resources of space-time to expand. The collision of expanding universes is permanently irreversible, forbidden in the reversible multiverse. To prevent the collision, the interuniversal void detaches the incoming mass-energy in the interuniversal void to keep expanding universes apart without collision. Inside of the universe, the absorbed interuniversal void with the property of the detachment of mass-energy was transformed into the reverse Higgs field that detached adjacent mass-energy in the universe, resulting in the conversion of rest mass (massive particles) into kinetic energy (massless particles) starting the Big Bang. During the Big Bang, the creation of the reverse Higgs field was followed by the conversion of massless particles except photons into massive particles through the absorption of the Higgs bosons. The absorption of the interuniversal void with zero vacuum energy also started the inflation by converting the high vacuum energy universe into the zero vacuum energy universe. The inflation followed by the Big Bang is a part of the reversible cyclic universe which explains the four force fields (the strong force, gravity, the electromagnetic force, and the weak force) and dark energy. During the Big Bang, the Higgs field and the reverse Higgs field produced the digital space structure consisting of attachment space (the Higgs field) denoted as 1 and detachment space (the reverse Higgs field) denoted as 0.

Various versions of standard Big Bang Model (BBM) including the current LCDM cosmology require an “inflationary” phase for the nascent universe ( Δ t ∼ 10 - 32 s) during which the size of the universe blows up by a factor of ∼ 10 78 . However, the so-called R h = ct cosmology (Melia, 2013a) claims that the isotropy and homogeneity of the present universe can be understood without assuming any inflationary phase. To this effect, Melia and his coworkers have often invoked “Weyl’s Postulate” and “Birkhoff’s Theorem” to qualitatively argue for this novel model. On the other hand, here, we explore for a cogent analytical basis of the R h = ct proposal which is claimed to have such a profound implication. First we show that (i) if the spatial flatness of the BBM would be presumed, R h = ct cosmology may indeed follow. To further explore this issue without prior assumption of flatness (ii) we equate the twin expressions for the Energy Complex (EC) associated with BBM computed by using the same Einstein pseudo-tensor and quasi-Cartesian coordinates (Mitra, 2013b). This exercise surprisingly shows that BBM has tacit and latent self-consistency constraints: it is spatially flat and its scale factor a ( t ) ∝ t . Accordingly, it seems that, there is no scope for the other models including inflationary and cyclic ones. The real lumpy universe may be too complex for the simplistic Big Bang model.

Autistics and the plane of complex numbers suggest that if the accelerating expansion of our universe and the anti-universe succeeded a coasting expansion 8.8 billion years after the Big Bang, an accelerating contraction will start in 3.8 billion years. Mirroring the expansion phase, a coasting contraction of the two universes in cosmic space will come up in 12.6 billion years. The end of the fourth section of 8.8 billion years will host two Big Crunches, two White Holes, and a new Big Bounce. The reason for that paradox solves the “cosmological constant problem” and joins general relativity to particle physics. The z-plane and autism can also help us cross science with the arts and religion; retain the search for truth, beauty, and goodness by our descendants; and reach the message of progress buried in the Ark of the Covenant, the Great Pyramid, and Giza’s Sphinx: A selfish brain hides a selfless heart.

A model of induced gravity with Higgs potential is analysed for the FLRW cosmology. Conditions of acceleration and signatures for the primeval universe along with the inflation are discussed. It is shown that the scalar-field excitations act quintessentially within effective pressure terms for a negative deceleration parameter. The violation of energy conditions and primeval acceleration appears naturally in the present model in view of the notions for inflationary universe with the avoidance of the Big Bang singularity., 23 pages, 3 figures, Dedicated to 75th birth anniversary of Heinz Dehnen

Science and technology has unraveled many mysteries of our universe but the biggest question of all times still remains an enigma that how our universe came to an existence and what was there before the existence of our universe. A correct explanation will not only let us to understand our birth but will also provide insight to intriguing questions like will our universe have an end and if not how it is going to be. This might give a new outlook to seeing our universe and provide us with the theory of everything. .This paper talks about what was before the big bang, how extra dimensions can be seen, where cosmic censorship can be violated, the constraint energy of the universe, the negative energy and its role in our universe.

General relativity predicts a singularity in the beginning of the universe being called big bang. Recent developments in loop quantum cosmology avoid the singularity and the big bang is replaced by a big bounce. A classical theory of gravitation in flat space-time also avoids the singularity under natural conditions on the density parameters. The universe contracts to a positive minimum and then it expands during all times. It is not symmetric with regard to its minimum implying a finite age measured with proper time of the universe. The space of the universe is flat and the total energy is conserved. Under the assumption that the sum of the density parameters is a little bit bigger than one the universe is very hot in early times. Later on, the cosmological model agrees with the one of general relativity. A new interpretation of a non-expanding universe may be given by virtue of flat space-time theory of gravitation., Comment: 7 pages, no figures, pdf

In the present study, an oscillatory model of the universe is proposed wherein the universe undergoes a sequence of big bang, expansion, contraction, big bang—repeated ad infinitum. The universe comprises of a “World” and an “Antiworld” in both of which matter operates in the positive time zone and antimatter in the negative time zone. Big bang is predicted as the violent encounter between matter and antimatter. It is suggested that antimatter has negative mass and is hugely abundant. It is also shown why it is extremely rare in spite of its abundance. It is predicted that a built in transformation converts matter to antimatter and vice versa. Finally, it is established that symmetry between matter and antimatter in the universe is maintained throughout.

The emergent universe scenario provides a possible alternative to bouncing cosmology to avoid the Big Bang singularity problem. In this paper we study the realization of the emergent universe scenario by making use of Quintom matter with an equation of state across the cosmological constant boundary. We will show explicitly the analytic and numerical solutions of emergent universe in two Quintom models, which are a phenomenological fluid and a nonconventional spinor field, respectively., Comment: 9 pages, 4 figures. Comments are welcome

Supernovae and gamma-ray bursts are the most powerful explosions in observed Universe. This educational review tells about supernovae and their applications in cosmology. It is explained how to understand the production of light in the most luminous events with minimum required energy of explosion. These most luminous phenomena can serve as primary cosmological distance indicators. Comparing the observed distance dependence on red shift with theoretical models one can extract information on evolution of the Universe from Big Bang until our epoch.

Inflationary models of the early universe provide a natural mechanism for the formation of large scale structure. This success brings to forefront the question of naturalness: Does a sufficiently long slow roll inflation occur generically or does it require a careful fine tuning of initial parameters? In recent years there has been considerable controversy on this issue. In particular, for a quadratic potential, Kofman, Linde and Mukhanov have argued that the probability of inflation with at least 65 e-foldings is close to one, while Gibbons and Turok have argued that this probability is suppressed by a factor of ~ $\10^{-85}$. We first clarify that such dramatically different predictions can arise because the required measure on the space of solutions is intrinsically ambiguous in general relativity. We then show that this ambiguity can be naturally resolved in loop quantum cosmology (LQC) because the big bang is replaced by a big bounce and the bounce surface can be used to introduce the structure necessary to specify a satisfactory measure. The second goal of the paper is to present a detailed analysis of the inflationary dynamics of LQC using analytical and numerical methods. By combining this information with the measure on the space of solutions, we address a sharper question than those investigated in the literature: What is the probability of a sufficiently long slow roll inflation WHICH IS COMPATIBLE WITH THE SEVEN YEAR WMAP DATA? We show that the probability is very close to 1. The material is so organized that cosmologists who may be more interested in the inflationary dynamics in LQC than in the subtleties associated with measures can skip that material without loss of continuity., 34 pages, 3 figures

We analyze the dynamics of a homogeneous and isotropic universe in the Einstein$--$Cartan theory of gravity. The coupling between the spin and torsion prevents gravitational singularities and replaces the Big Bang with a nonsingular big bounce, at which the universe transitions from contraction to expansion. We show that a closed universe exists only when the product of the scale factor and temperature is higher than a particular threshold, contrary to a flat universe and an open universe, which are not restricted. During inflation, this product must increase to another threshold, so that the universe can reach dark-energy acceleration., 10 pages, 1 table, 4 figures; published version

We will examine the Bianchi Type I universe under the Rainbow Gravity formalism and calculate various quantities like the dynamical equation for the energy density and the negative energy density. Finally, we apply the analysis to a specific Rainbow Gravity model.

The evolution of the Robertson-Walker type universes consisting of radiating perfect fluid distribution coupled with zero-mass scalar field in which the gravitational parameter G varies with cosmic time t are studied. Unified descriptions of the early evolution of the universe consisting of different phases are investigated. The different properties of the cosmological solutions are discussed and the physical behaviour of the model universes during the radiation-dominated era and also during the big bang scenario are studied. Here we obtain models which are geometrically closed and are thereby ever expanding and evolve from rest from a non-singular hot origin with maximum (finite) energy density and temperature and a small minimum (non-zero) gravitational coupling G.

It has been recently shown that, since in general relativity (GR), given one time label t, one can choose any other time label t → t*= f(t), the pressure of a homogeneous and isotropic fluid is intrinsically zero (Mitra, Astrophys. Sp. Sc. 333, 351, 2011). Here we explore the physical reasons for the inevitability of this mathematical result. The essential reason is that the Weyl Postulate assumes that the test particles in a homogeneous and isotropic spacetime undergo pure geodesic motion without any collisions amongst themselves. Such an assumed absence of collisions corresponds to the absence of any intrinsic pressure. Accordingly, the “Big Bang Model” (BBM) which assumes that the cosmic fluid is not only continuous but also homogeneous and isotropic intrinsically corresponds to zero pressure and hence zero temperature. It can be seen that this result also follows from the relevant general relativistic first law of thermodynamics (Mitra, Found. Phys. 41, 1454, 2011). Therefore, the ideal BBM cannot describe the physical universe having pressure, temperature and radiation. Consequently, the physical universe may comprise matter distributed in discrete non-continuous lumpy fashion (as observed) rather than in the form of a homogeneous continuous fluid. The intrinsic absence of pressure in the “Big Bang Model” also rules out the concept of a “Dark Energy”.

The usual Einstein's equations is modified as a one parameter family of equations in the framework of rainbow gravity. In this paper we derive the modified Friedmann-Robertson-Walker (FRW) equations when the cosmological evolution of radiation particles is taken into account. In particular, given some specific dispersion relations, the big bounce solutions to the modified FRW equations can be derived. Notably, to obtain a well defined rainbow metric at the moment of the big bounce, we find it seems necessary to introduce a cosmological constant which depends on the energy of probes as well, implying that a universe with a positive cosmological constant more likely undergoes a big bounce at least at this phenomenological level., 8pages, 5figures. Final version published in PLB.

What if our universe didn't emerge from nothing, but is a recycled version of one that went before? Anil Ananthaswamy investigates

We review the recent status of big bounce genesis as a new possibility of using dark matter particle's mass and interaction cross section to test the existence of a bounce universe at the early stage of evolution in our currently observed universe. To study the dark matter production and evolution inside the bounce universe, called big bounce genesis for short, we propose a model independent approach. We shall present the motivation for proposing big bounce as well the model independent predictions which can be tested by dark matter direct searches. A positive finding shall have profound impact on our understanding of the early universe physics., Comment: 25 pages, 6 figures

A background-independent quantization of Universe near its Big Bang singularity is considered. Several conceptual issues are addressed in Heisenberg picture. (1) The observable spatial-geometry non-covariant characteristics of an empty-space expanding Universe are sampled by (quantized) distances \(Q=Q(t)\) between space-attached observers. (2) In Q(t) one of the Kato’s exceptional-point times \(t=\tau _{(EP)}\) is postulated real-valued. At such an instant the widely accepted “Big Bounce” regularization of the Big Bang singularity gets replaced by the full-fledged quantum degeneracy. Operators \(Q(\tau _{(EP)})\) acquire a non-diagonalizable Jordan-block structure. (3) During our “Eon” (i.e., at all \(t>\tau _{(EP)}\)) the observability status of operators Q(t) is guaranteed by their self-adjoint nature with respect to an ad hoc Hilbert-space metric \(\varTheta (t) \ne I\). (4) In adiabatic approximation the passage of the Universe through its \(t=\tau _{(EP)}\) singularity is interpreted as a quantum phase transition between the preceding and the present Eon.

The dynamics of a (3 + 1) dimensional homogeneous anisotropic universe is modified by Loop Quantum Cosmology and, consequently, it has generically a big bounce in the past instead of a big-bang singularity. This modified dynamics can be well described by effective equations of motion. We generalise these effective equations of motion empirically to (d + 1) dimensions. The generalised equations involve two functions and may be considered as a class of LQC -- inspired models for (d + 1) dimensional early universe cosmology. As a special case, one can now obtain a universe which has neither a big bang singularity nor a big bounce but approaches asymptotically a `Hagedorn like' phase in the past where its density and volume remain constant. In a few special cases, we also obtain explicit solutions., Comment: Version 1: 29 pages. Version 2: 33 pages. Subsection (3.1) added to improve the presentation. A few minor changes made. A reference added. Version 3: 34 pages, contains minor modifications and a few more references. To appear in General Relativity and Gravitation

Summary In spite of the paradigmatic status of the Big Bang model of the universe, the genesis of this idea has never been examined in detail. This paper investigates how the Belgian physicist and cosmologist Georges Lemaitre in 1931 arrived at the hypothesis that the universe had begun in a Big Bang, or what he called a ‘primeval atom’. Four years earlier, he had suggested a closed expanding model in which the universe slowly inflated from an equilibrium Einstein state, but in 1931 he advocated an abrupt beginning from an initial, superdense concentration of nuclear matter. Why did Lemaitre believe that the universe had a definite beginning a finite time ago? It turns out that the law of increase of entropy was one motivation, and that the existence of long-lived radioactive substances was another. Contrary to what is often stated, he most likely had the idea of an exploding universe before 1931. Among his chief inspirations to think about the origin of the universe, we draw attention to his persistent f...

Hysteresis is a phenomenon occurring naturally in several magnetic and electric materials in condensed matter physics. When applied to cosmology, aka cosmological hysteresis, has interesting and vivid implications in the scenario of a cyclic bouncy universe. Most importantly, this physical prescription can be treated as an alternative proposal to inflationary paradigm. Cosmological hysteresis is caused by the asymmetry in the equation of state parameter during expansion and contraction phase of the universe, due to the presence of a single scalar field. This process is purely thermodynamical in nature, results in a non-vanishing hysteresis loop integral $(\oint pdV)$ in cosmology. When applied to variants of modified gravity models -1) Dvali-Gabadadze-Porrati (DGP) brane world gravity, 2) Cosmological constant dominated Einstein gravity, 3) Loop Quantum Gravity (LQG), 4) Einstien-Gauss-Bonnet brane world gravity and 5) Randall Sundrum single brane world gravity (RSII), under certain circumstances, this phenomenon leads to the increase in amplitude of the consecutive cycles and to a universe with older and larger successive cycles, provided we have physical mechanisms to make the universe bounce and turnaround. This inculcates an arrow of time in a dissipationless cosmology. Remarkably, this phenomenon appears to be widespread in several cosmological potentials in variants of modified gravity background, which we explicitly study for- i) Hilltop, ii) Natural and iii) Colemann-Weinberg potentials, in this paper. Semi-analytical analysis of these models, for different potentials with minimum/minima, show that the conditions which creates a universe with an ever increasing expansion, depend on the signature of the hysteresis loop integral $(\oint pdV)$ as well as on the variants of model parameters., Comment: 180 pages, 31 figures, 1 table, Final version, Accepted for publication in Astroparticle Physics

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

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

The gravitational field of matter and that of antimatter could differ. This might be one signature of quantum gravity. We show that primordial Big Bang Nucleosynthesis restricts such a possibility., 11 pages, 3 figures. Reference added

How did the Universe begin? Does time have a beginning and an end? Does space have edges? Einstein's theory of relativity replied to these ancient questions with three startling predictions: that the Universe is expanding from a Big Bang; that black holes so distort space and time that time stops at their edges; and that a dark energy could be pulling space apart, sending galaxies forever beyond the edge of the visible Universe. Observations confirm these remarkable predictions, the last finding only four years ago. Yet Einstein's legacy is incomplete. His theory raises – but cannot answer – three profound questions: What powered the Big Bang? What happens to space, time and matter at the edge of a black hole? and, What is the mysterious dark energy pulling the Universe apart? The Beyond Einstein program within NASA's office of space science aims to answer these questions, employing a series of missions linked by powerful new technologies and complementary approaches to shared science goals. The program also serves as a potent force with which to enhance science education and science literacy.

We study the time evolution of a wave function for the spatially flat Friedmann-Lemaitre-Robertson-Walker universe governed by the Wheeler-DeWitt equation in both analytical and numerical methods. We consider a Brown-Kuchar dust as a matter field in order to introduce a "clock" in quantum cosmology and adopt the Laplace-Beltrami operator-ordering. The Hamiltonian operator admits an infinite number of self-adjoint extensions corresponding to a one-parameter family of boundary conditions at the origin in the minisuperspace. For any value of the extension parameter in the boundary condition, the evolution of a wave function is unitary and the classical initial singularity is avoided and replaced by the big bounce in the quantum system. Exact wave functions show that the expectation value of the spatial volume of the universe obeys the classical time evolution in the late time but its variance diverges., 36 pages, 6 figures, 4 tables; v2, revised version; v3, fully revised version with improved analytical and numerical results, accepted for publication in Classical and Quantum Gravity

In a recent paper [Phys. Rev. D{\bf 85}, 023528 (2012)] the authors proposed a generalized Born-Infeld electrodynamics coupled to general relativity which produces a nonsingular bouncing universe. For a magnetic universe the resulting cosmic evolution inevitably interpolates between asymptotic de Sitter states. Here we shall show that (i) the above theory does not have the standard weak field Maxwell limit, (ii) a sudden curvature singularity -- not better than the big bang -- arises, (iii) the speed of sound squared is a negative quantity signaling instability against small perturbations of the background energy density, and that (iv) the conclusion about the inevitability of the asymptotic vacuum regime in a magnetic universe is wrong., 6 pages, 6 eps figures, here we have shown that Born-Infeld magnetic universes either are singular or are unstable against small perturbations of the background energy density or both

We consider an isotropic and homogeneous universe in loop quantum cosmology. We assume that the matter content of the universe is dominated by dust matter in early time and a phantom matter at late time which constitutes the dark energy component. The quantum gravity modifications to the Friedmann equation in this model indicate that the classical big bang singularity and the future big rip singularity are resolved and are replaced by quantum bounce. It turns out that the big bounce and recollapse in the herein model contribute to a cyclic scenario for the universe. We then study the quantum theory of a massive, non-minimally coupled scalar field undergoing cosmological evolution from primordial bounce towards the late time bounce. In particular, we solve the Klein-Gordon equation for the scalar field in the primordial and late time regions, in order to investigate particle production phenomena at late time. By computing the energy density of created particles at late time, we show that this density is negligible in comparison to the quantum background density at Planck era. This indicates that the effects of quantum particle production do not influence the future bounce., 10 pages, 2 figures

We confront the big bang for the beginning of the universe with an equivalent picture of a slow freeze - a very cold and slowly evolving universe. In the freeze picture the masses of elementary particles increase and the gravitational constant decreases with cosmic time, while the Newtonian attraction remains unchanged. The freeze and big bang pictures both describe the same observations or physical reality. We present a simple "crossover model" without a big bang singularity. In the infinite past space-time is flat. Our model is compatible with present observations, describing the generation of primordial density fluctuations during inflation as well as the present transition to a dark energy dominated universe., Comment: new material on absence of singularity, 9 pages, 1 figure

Inspired by quantum gravity proposal, we construct a deformed phase space which supports the UV and IR cutoffs. We show that the Liouville theorem is satisfied in the deformed phase space which allows us to formulate the thermodynamics of the early Universe in the semiclassical regime. Applying the proposed method to the Snyder noncommutative space, we find a temperature dependent equation of state which opens a new window for natural realization of inflation as a phase transition from quantum gravity regime to the standard radiation dominated era. Also we obtain finite energy and entropy densities for the Universe, when at least the Weak Energy Condition is satisfied. We show that there is a minimum size for the Universe which is proportional to the Planck length and consequently the Big Bang singularity is removed., 11 pages, 4 figures, Revised for PRD, title changed