We study cosmological solutions for the very early universe beginning at the Planck scale for a universe containing radiation, curvature and, as a simplification of a possible scalar field potential, a cosmological constant term. The solutions are the natural counterpart of the well known results for a post-inflationary universe of non-relativistic matter, curvature and a cosmological constant. Contrary to the common belief that inflation arises independently of the initial curvature we show that in the positive curvature case the universe collapses again into a Big Crunch without allowing the cosmological term to dominate and to produce inflation. There is a critical value for the cosmological constant which divide the regions where inflation is allowed from those where inflation cannot occur. One can also have loitering solutions where the scale factor remains almost constant growing to produce inflation (or decreasing to a Big Crunch) after a time which depends on the amount of energy above (or below) the critical energy. At the critical energy the solution approaches asymptotically a particular value for the scale factor (Einstein's static pre-inflationary universe). The cases where the cosmological term vanishes or becomes negative are also studied providing a complete discussion of Friedmann models.
Mimetic gravity can be described as a formulation capable of mimicking different evolutionary scenarios regarding the universe dynamics. Notwithstanding its initial aim of producing a similar evolution to the one expected from the dark components of the standard cosmology, a recent association with loop quantum cosmology could also provide interesting results. In this work, we reinterpret the physics behind the curvature potential of mimetic gravity description of loop quantum cosmology. Furthermore, we also test the compatibility of our formulation for a Higgs-type field, proving that the mim…
Structure occurs over a vast range of scales in the universe. Our large-scale cosmological models are coarse-grained representations of what exists, which have much less structure than there really is. An important problem for cosmology is determining the influence the small-scale structure in the universe has on its large-scale dynamics and observations. Is there a significant, general relativistic, backreaction effect from averaging over structure? One issue is whether the process of smoothing over structure can contribute to an acceleration term and so alter the apparent value of the cosmol…
We propose a method for constructing the specific heat for the universe by following standard definitions of classical thermodynamics, in a spatially flat homogeneous and isotropic spacetime. We use cosmography to represent the specific heat in terms of measurable quantities, and show that a negative specific heat at constant volume and a zero specific heat at constant pressure are compatible with observational data. We derive the most general cosmological model which is compatible with the values obtained for the specific heat of the universe, and show that it overcomes the fine-tuning and th…
We study oscillatory universes within the context of Loop Quantum Cosmology. We make a comparative study of flat and positively curved universes sourced by scalar fields with either positive or negative potentials. We investigate how oscillating universes can set the initial conditions for successful slow-roll inflation, while ensuring that the semi-classical bounds are satisfied. We observe rich oscillatory dynamics with negative potentials, although it is difficult to respect the semi-classical bounds in models of this type.
The Friedmann-Robertson-Walker (FRW) universe and Bianchi I,II universes are investigated in the framework of the generalized uncertainty principle (GUP) with a linear and a quadratic term in Planck length and momentum, which predicts minimum measurable length as well as maximum measurable momentum. We get a dynamic cosmological bounce for the FRW universe. With Bianchi universe, we found that the universe may be still isotropic by implementing GUP. Moreover, the wall velocity appears to be stationary with respect to the universe velocity which means that when the momentum of the Universe evol…
We consider a model of the Universe in which the matter content is in the form of discrete islands, rather than a continuous fluid. In the appropriate limits the resulting large-scale dynamics approach those of a Friedmann-Robertson-Walker (FRW) universe. The optical properties of such a space-time, however, do not. This illustrates the fact that the optical and `average' dynamical properties of a relativistic universe are not equivalent, and do not specify each other uniquely. We find the angular diameter distance, luminosity distance and redshifts that would be measured by observers in these…
I review the "Trans-Planckian Censorship Conjecture" (TCC) and its implications for cosmology, in particular for the inflationary universe scenario. Whereas the inflationary scenario is tightly constrained by the TCC, alternative early universe scenarios are not restricted.
We study the third quantized formulation of the massive inflaton quantum cosmology for the Friedmann-Robertson-Walker universe. The Hamiltonian is equivalent to an infinite number of coupled oscillators whose couplings and frequencies are intrinsic time-dependent. We propose the invariant operators whose eigenstates provide the exact wave functions of the universe.
We consider a universe with an arbitrary number of extra dimensions, $N$. We present a new method for constructing the cosmological equations of motion and find analytic solutions with an explicit dependence on $N$. When we take the $N\rightarrow\infty$ limit we find novel, emergent behaviour which distinguishes it from normal Kaluza-Klein universes.
The primordial Universe can be used as a laboratory to set constraints on quantum gravity. In the framework of Loop Quantum Cosmology, we show that such a proposal for quantum gravity not only solves for the big bang singularity issue but also naturally generates inflation. Thanks to a quantitative computation of the amount of gravity waves produced in the loopy early Universe, we show that future cosmological datas on the polarized anisotropies of the Cosmic Microwave Background can be used to probe LQC model of the Universe.
Loop quantum cosmology is a tentative approach to model the universe down to the Planck era where quantum gravity settings are needed. The quantization of the universe as a dynamical space-time is inspired by Loop Quantum Gravity ideas. In addition, loop quantum cosmology could bridge contact with astronomical observations, and thus potentially investigate quantum cosmology modellings in the light of observations. To do so however, modelling both the background evolution and its perturbations is needed. The latter describe cosmic inhomogeneities that are the main cosmological observables. In t…
In these lectures I focus on early universe models which can explain the currently observed structure on large scales. I begin with a survey of inflationary cosmology, the current paradigm for understanding the origin of the universe as we observe it today. I will discuss some progress and problems in inflationary cosmology before moving on to a description of two alternative scenarios - the Matter Bounce and String Gas Cosmology. All early universe models connect to observations via the evolution of cosmological perturbations - a topic which will be discussed in detail in these lectures.
Assuming that superstring theory is the fundamental theory which unifies all forces of Nature at the quantum level, I argue that there are key limitations on the applicability of effective field theory techniques in describing early universe cosmology.
Observational cosmology is in its "golden age" with a vast amount of recent data on the distribution of matter and light in the universe. This data can be used to probe theories of the very early universe. It is small amplitude cosmological fluctuations which encode the information about the very early universe and relate it to current data. Hence, a central topic in these lectures is the "theory of cosmological perturbations", the theory which describes the generation of inhomogeneities in the very early universe and their evolution until the current time. I will apply this theory to three cl…
We show that the phase transition from the decelerating universe to the accelerating universe, which is of relevance to the cosmological coincidence problem, is possible in the semiclassically quantized two-dimensional dilaton gravity by taking into account the noncommutative field variables during the finite time. Initially, the quantum-mechanically induced energy from the noncommutativity among the fields makes the early universe decelerate and subsequently the universe is accelerating because the dilaton driven cosmology becomes dominant later.
We investigate the FLRW type cosmology of the Induced Dark Energy model and illustrate that the extra terms emerging from the fifth dimension can play the role of dark energy. The model predicts the expansion with deceleration at early time and acceleration in late time for an open universe.
In order to account for the observable Universe, any comprehensive theory or model of cosmology must draw from many disciplines of physics, including gauge theories of strong and weak interactions, the hydrodynamics and microphysics of baryonic matter, electromagnetic fields, and spacetime curvature, for example. Although it is difficult to incorporate all these physical elements into a single complete model of our Universe, advances in computing methods and technologies have contributed significantly towards our understanding of cosmological models, the Universe, and astrophysical processes w…
There is a wide consensus on the correct dynamics of the background in loop quantum cosmology. In this article we make a systematic investigation of the duration of inflation by varying what we think to be the most important "unknowns" of the model: the way to set initial conditions, the amount of shear at the bounce and the shape of the inflaton potential.
Specific dark energy models with linear inhomogeneous time-dependent equation of state, within the framework of 4d Friedman-Robertson-Walker (FRW) cosmology, are investigated. It is demonstrated that the choice of such 4d inhomogeneous fluid models may lead to a brane FRW cosmology without any explicit account of higher dimensions at all. Effectively, we thus obtain a brane dark energy universe without introducing the brane concept explicitly. Several examples of brane Rip cosmology arising from 4d inhomogeneous dark fluid models are given.
We examine the dynamical consequences of homogeneous cosmological magnetic fields in the framework of loop quantum cosmology. We show that a big-bounce occurs in a collapsing magnetized Bianchi I universe, thus extending the known cases of singularity-avoidance. Previous work has shown that perfect fluid Bianchi I universes in loop quantum cosmology avoid the singularity via a bounce. The fluid has zero anisotropic stress, and the shear anisotropy in this case is conserved through the bounce. By contrast, the magnetic field has nonzero anisotropic stress, and shear anisotropy is not conserved …
We show that standard puzzles of hot Big Bang cosmology that motivated the introduction of cosmological inflation, such as the smoothness and horizon problem, the flatness problem and the relic problem are also solved by holographic models for very early universe based on perturbative three dimensional QFT. In the holographic setup, cosmic evolution is mapped to inverse renormalization group (RG) flow of the dual QFT, and the resolution of the puzzles relies on properties of the RG flow.
Cosmological inflation is not the only early universe scenario consistent with current observational data. I will discuss the criteria for a successful early universe cosmology, compare a couple of the proposed scenarios (inflation, bouncing cosmologies, and the {\it emergent} scenario), focusing on how future observational data will be able to distinguish between them. I will argue that we need to go beyond effective field theory in order to understand the early universe, and that principles of superstring theory will yield a nonsingular cosmology.
It has long been a primary objective of cosmology to understand the apparent isotropy in our universe and to provide a mathematical formulation for its evolution. A school of thought for its explanation is quiescent cosmology, which already possesses a mathematical framework, namely the definition of an Isotropic Singularity, but only for the initial state of the universe. A complementary framework is necessary in order to also describe possible final states of the universe. Our new definitions of an Anisotropic Future Endless Universe and an Anisotropic Future Singularity, whose structure and…
We investigate the time neutral formulation of quantum cosmology of Gell-Mann and Hartle. In particular we study the proposal discussed by them that our Universe corresponds to the time symmetric decoherence functional with initial and final density matrix of low entropy. We show that our Universe does not correspond to this proposal by investigating the behaviour of small inhomogeneous perturbations around a Friedman-Robertson-Walker model. These perturbations cannot be time symmetric if they were small at the Big Bang.
We propose a new four-parameter entropy function that generalizes the Tsallis, Rényi, Barrow, Sharma-Mittal, Kaniadakis and Loop Quantum Gravity entropies for suitable limits of the parameters. Consequently, we address the early and late universe cosmology corresponding to the proposed four-parameter entropy function. As a result, it turns out that the entropic cosmology from the generalized entropy function can unify the early inflation to the late dark energy era of the universe. In such a unified scenario, we find that -- (1) the inflation era is described by a quasi de-Sitter evolution of …
In this work we have investigated the emergent scenario of the universe described by Loop quantum cosmology model, DGP brane model and Kaluza-Klein cosmology. Scalar field along with barotropic fluid as normal matter is considered as the matter content of the universe. In Loop quantum cosmology it is found that the emergent scenario is realized with the imposition of some conditions on the value of the density of normal matter in case of normal and phantom scalar field. This is a surprising result indeed considering the fact that scalar field is the dominating matter component. In case of Tach…
The quantum bounce a priori connects several (semi)classical epochs of Universe evolution, however determining if and how well the semiclassicality is preserved in this transition is highly nontrivial. We review the present state of knowledge in that regards in the isotropic sector of loop quantum cosmology. This knowledge is next extended by studies of an isotropic universe admitting positive cosmological constant (featuring an infinite chain of large Universe epochs). It is also shown, that such universe always admits a semiclassical epoch thanks to spontaneous spontaneous coherence, provide…
Recently, the tachyon cosmology has been represented as dark energy model to support the current acceleration of the universe without phantom crossing. In this paper, we study the dynamics of the tachyon cosmology in which the field plays the role of tachyon field and also non--minimally coupled to the matter lagrangian. The model shows current universe acceleration and also phantom crossing in the future. Two cosmological tests are also performed to validate the model; the difference in the distance modulus and the model independent Cosmological Redshift Drift (CRD) test.
Brane cosmology takes the unconventional form $H\sim \sqrtρ$. To recover the standard cosmology, we have to assume that the matter density is much less than the brane tension. We show that the assumption can be justified even near the end of inflation if we fine-tune the coupling constant of the inflaton potential. As a consequence, the standard cosmology is recovered after inflation.
In this article, we present an emergent universe scenario that can be derived from DHOST cosmology. The universe starts asymptotically Minkowski in the far past just like the regular Galileon Genesis, but evolves to a radiation dominated period at the late stage, and therefore, the universe has a graceful exit which is absent in the regular Galileon Genesis. We analyze the behavior of cosmological perturbations and show that both the scalar and tensor modes are free from the gradient instability problem. We further analyze the primordial scalar spectrum generated in various situations and disc…
Cosmological discoveries over the past century have completely changed our picture of our place in the universe. New observations have a realistic chance of probing nature on heretofore unimaginable scales, and as a result are changing the nature of fundamental science. Perhaps no other domain of science has an equal capacity to completely change our perspective of the world in which we live.
The quantum cosmological version of a nonsingular Universe presented by Mukhanov and Brandenberger in the early nineties has been developed and the Hamilton Jacobi equation has been found under semiclassical (WKB) approximation. It has been pointed out that, parameterization of classical trajectories with semiclassical time parameter, for such a classically constrained system, is a nontrivial task and requires Lagrangian formulation rather than the Hamiltonian formalism.
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…
In this article we study closed inflationary universe models using the Gauss-Bonnet Brane. We determine and characterize the existence of a universe with $Ω> 1$, with an appropriate period of inflation. We have found that this model is less restrictive in comparison with the standard approach where a scalar field is considered. We use recent astronomical observations to constrain the parameters appearing in the model.
The $f(R)$ theories of gravity are the most popular, simple and well succeeded extension of Einstein's General Relativity. They can account for some observational issues of standard cosmology with no need for evoking the dark sector of the universe. In the present letter we will investigate LRS Bianchi type-I space-time in $f(R)$ gravity theory within the phantom energy dominated era. We show that in this formalism the phantom energy dominated universe is a transient stage and in the further stage of the universe dynamics, it is dominated, once again, by dark energy. Such an important feature …
We study the ultraviolet complete non-relativistic theory recently proposed by Horava. After introducing a Lifshitz scalar for a general background, we analyze the cosmology of the model in Lorentzian and Euclidean signature. Vacuum solutions are found and it is argued the existence of non-singular bouncing profiles. We find a general qualitative agreement with both the picture of Causal Dynamical Triangulations and Quantum Einstein Gravity. However, inflation driven by a Lifshitz scalar field on a classical background might not produce a scale-invariant spectrum when the principle of detailed…
We consider some background tests of standard cosmology in the context of Horava gravity with different scaling dimensions for space and time, which has been proposed as a renormalizable, higher-derivative, Lorentz-violating quantum gravity model without ghost problems. We obtain the "very strong" and "strong" Bayesian evidence for our two cosmology models A and B, respectively, depending on the choice of parametrization based on Horava gravity, against the standard, spatially-flat, LCDM cosmology model based on general relativity. An MCMC analysis with observational data, including BAO, shows…
We investigate quantum cosmological models in an n-dimensional anisotropic universe in the presence of a massless scalar field. Our basic inspiration comes from Chodos and Detweiler's classical model which predicts an interesting behaviour of the extra dimension, shrinking down as time goes by. We work in the framework of a recent geometrical scalar-tensor theory of gravity. Classically, we obtain two distinct type of solutions. One of them has an initial singularity while the other represents a static universe considered as a whole. By using the canonical approach to quantum cosmology, we inv…
We present a new perspective on early cosmology based on Loop Quantum Gravity. We use projected spinnetworks, coherent states and spinfoam techniques, to implement a quantum reduction of the full Kinematical Hilbert space of LQG, suitable to describe inhomogeneous cosmological models. Some preliminary results on the solutions of the Scalar constraint of the reduced theory are also presented.
For the description of the early inflation, and acceleration expansion of the Universe, compatible with observational data, the 5D noncompact Kaluza--Klein cosmology is investigated. It is proposed that the 5D space is filled with a null perfect fluid, resulting a perfect fluid in 4D universe, plus one along the fifth dimension. By analyzing the reduced field equations for flat FRW model, we show the early inflationary behavior and current acceleration of the universe.
We explore the possibility of emergent cosmology using the effective potential formalism. We discover new models of emergent cosmology which satisfy the constraints posed by the cosmic microwave background (CMB). We demonstrate that, within the framework of modified gravity, the emergent scenario can arise in a universe which is spatially open/closed. By contrast, in general relativity (GR) emergent cosmology arises from a spatially closed past-eternal Einstein Static Universe (ESU). In GR the ESU is unstable, which creates fine tuning problems for emergent cosmology. However, modified gravity…
We present a special case of the Stephani solution with spherical symmetry while considering different values of spatial curvature. We investigate the dynamics of the universe evolution in our model, build the R--T-regions for the resulting spacetime and analyze the behavior of the deceleration parameter. The singularities of the model are also discussed. The geometry of the spatial part of the obtained solution is explored.
We apply the complex de Broglie-Bohm formulation of quantum mechanics [1] to a spatially closed homogeneous and isotropic early Universe whose matter content are radiation and dust perfect fluids. We then show that an expanding classical Universe can emerge from an oscillating (with complex scale factor) quantum Universe without singularity. Furthermore, the Universe obtained in this process has no horizon or flatness problems.
A nonsingular emergent universe cosmology can be realized by a nonconventional spinor field as first developed in \cite{Cai:2012yf}. We study the mechanisms of generating scale-invariant primordial power spectrum of curvature perturbation in the frame of spinor emergent universe cosmology. Particularly, we introduce a light scalar field of which the kinetic term couples to the bilinear of the spinor field. This kinetic coupling can give rise to an effective "Hubble radius" for primordial fluctuations from the scalar field to squeeze at large length scales as well as to form a nearly scale-inva…
We point out that $Λ$CDM cosmology has an ignored assumption. That is, the $Λ$ component of the universe moves synchronously with ordinary matters on Hubble scales. If cosmological constant is vacuum energy, this assumption may be very difficult to be understood. We then propose a new mechanism which can explain the accelerating recession of super-novaes. That is, considering the pressures originating from the random moving (including Hubble recession) of galaxy clusters and galaxies. We provide an new analytical solution of Einstein equation which may describe a universe whose pressures origi…
We study the cosmological evolutions of the equation of state (EoS) for the universe in the homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker (FLRW) space-time. In particular, we reconstruct the cyclic universes by using the Weierstrass and Jacobian elliptic functions. It is explicitly illustrated that in several models the universe always stays in the non-phantom (quintessence) phase, whereas there also exist models in which the crossing of the phantom divide can be realized in the reconstructed cyclic universes.
In a quantum cosmological model consisting of a Euclidean region and a Lorentzian region, Hartle-Hawking's no-bounary wave function, and Linde's wave function and Vilenkin's tunneling wave function are briefly described and compared with each other. We put a particular emphasis on semiclassical gravity from quantum cosmology and compare it with the conventional quantum field theory in curved spacetimes. Finally, we discuss the recent debate on catastrophic particle production in the tunneling universe between Rubakov and Vilenkin within the semiclassical gravity.
Jordan-Brans-Dicke cosmology with a standard kinetic term for the scalar field and no mass term has the same radiation dominated solution as standard Einstein cosmology without the cosmological constant. Because of this, the primordial nucleosynthesis (Big - Bang nucleosynthesis) result obtained for standard cosmology remains the same for Jordan-Brans-Dicke cosmology. We show that Jordan-Brans-Dicke cosmology with a mass term for the scalar field as well as explaining dark energy for the present era, can also explain radiation dominated cosmology for the primordial nucleosynthesis era.
Loop quantum cosmology applies techniques derived for a background independent quantization of general relativity to cosmological situations and draws conclusions for the very early universe. Direct implications for the singularity problem as well as phenomenology in the context of inflation or bouncing universes result, which will be reviewed here. The discussion focuses on recent new results for structure formation and generalizations of the methods.
Cosmological solutions for homogeneous isotropic models in the framework of the Poincaré gauge theory of gravity based on gravitational Lagrangian adopted in the paper by Kun-Feng Shie, James M. Nester and Hwei-Jang Yo (Phys. Rev. D \textbf{78}, 023522 (2008)) are discussed. Cosmological solutions for accelerating Universe obtained in referred paper are compared with corresponding solutions of standard $ΛCDM$-model and also with cosmological solution obtained by authors of this Comment.
Quantum cosmology is crucial to understand the evolution of the early universe. Despite significant progress, challenges still remain. For example, the role of time in quantum cosmology is unclear. Furthermore, the influence of the environment on the evolution of the quantum universe is challenging. In this work, we studied the evolution of the quantum universe non-perturbatively using the closed real-time path integral. The environments coupled to the quantum universe being considered are the radiation, the non-relativistic matter, or the dark matter. We evaluated the influence functional of …
We investigate the late time acceleration of the universe in the context of the Stephani model. This solution generalizes those of Friedmann-Lemaitre-Robertson-Walker (FLRW) in such a way that the spatial curvature is a function of of time. We show that the inhomogeneity of the models can lead to an accelerated evolution of the universe that is analogous to that obtained with FLRW models through a cosmological constant or any exotic component for matter.
We examine the possibility that Friedman-Robertson-Walker evolution is governed by an effective (rather then by the actual) energy density. A concrete example is provided by $Λ=0$ Regge-Teitelboim cosmology, where critical cosmology only requires subcritical matter density $(Ω_{m}<1)$, and the age of a flat matter dominated Universe gets enhanced by a factor of 9/8. Dual to the mature dilute Universe is the embryo Universe, the evolution of both is governed by $P_{eff}=-{1/9}ρ_{eff}$.
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 re…
We canonically quantize the dynamics of the brane universe embedded into the five-dimensional Schwarzschild-anti-deSitter bulk space-time. We show that in the brane-world settings the formulation of the quantum cosmology, including the problem of initial conditions, is conceptually more simple than in the 3+1-dimensional case. The Wheeler-deWitt equation is a finite-difference equation. It is exactly solvable in the case of a flat universe and we find the ground state of the system. The closed brane universe can be created as a result of decay of the bulk black hole.
Loop quantum cosmology (LQC) is very powerful to deal with the behavior of early universe. And the effective loop quantum cosmology gives a successful description of the universe in the semiclassical region. We consider the apparent horizon of the Friedmann-Robertson-Walker universe as a thermodynamical system and investigate the thermodynamics of LQC in the semiclassical region. The effective density and effective pressure in the modified Friedmann equation from LQC not only determine the evolution of the universe in LQC scenario but are actually also found to be the thermodynamic quantities.…
Unimodular quantum cosmology admits wavepacket solutions that evolve according to a kind of Schrödinger equation. Though this theory is equivalent to general relativity on the classical level, its canonical structure is different and the problem of time does not occur. We present an Ehrenfest theorem for the long term evolution of the expectation value of the scale factor for a spatially flat Friedmann universe with a scalar field. We find that the classical and the quantum behaviour in the asymptotic future coincide for the special case of a massless scalar field. We examine the general behav…
