We study the dynamics of states perturbatively expanded about a harmonic system of loop quantum cosmology, exhibiting a bounce. In particular, the evolution equations for the first and second order moments of the system are analyzed. These moments back-react on the trajectories of the expectation values of the state and hence alter the energy density at the bounce. This analysis is performed for isotropic loop quantum cosmology coupled to a scalar field with a small but non-zero constant potential, hence in a regime in which the kinetic energy of matter dominates. Analytic restrictions on the existence of dynamical coherent states and the meaning of semi-classicality within these systems are discussed. A numerical investigation of the trajectories of states that remain semi-classical across the bounce demonstrates that, at least for such states, the bounce persists and that its properties are similar to the standard case, in which the moments of the states are entirely neglected. However the bounce density does change, implying that a quantum bounce may not be guaranteed to happen when the potential is no longer negligible.
In the frame of the scalar field model with non minimal kinetic coupling to gravity, we study the cosmological solutions of the Chaplygin gas model of dark energy. By appropriately restricting the potential, we found the scalar field, the potential and coupling giving rise to the Chaplygin gas solution. Extensions to the generalized and modified Chaplygin gas have been made.
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.
If string theory controls physics at the string scale, the dynamics of the early universe before the GUT era will be governed by the low-energy string equations of motion. Studying these equations for FRW spacetimes, we find that depending on the initial conditions when the stringy era starts, and on the time when it ends, there are a wide variety of qualitatively distinct types of evolution. We classify these, and present the general solution to the equations of motion.
A scalar-tensor model with Gauss-Bonnet and non-minimal kinetic couplings is considered, in which ghost modes are eliminated via a Lagrange multiplier constraint. A reconstruction procedure is deviced for the scalar potential and Lagrange multiplier, valid for any given cosmological scenario. In particular, inflationary and dark energy cosmologies of different types (power-law, Little-Rip, de Sitter, quasi de Sitter) are reconstructed in such models. It is shown that, for various choices of the kinetic coupling terms, it is possible to obtain a viable inflationary phenomenology compatible with…
The Dirac-Born-Infeld (DBI) field theory in string theory is important and can provide the field of the universe's inflation. At the same time, it provides a causal mechanism for generating the original density perturbation, thereby providing the necessary density perturbation for existing the dense and sparse matter distributions of the universe. However, there is the paradox of the conversion of potential energy and kinetic energy in equal rights in string theory. Therefore, we give a new general DBI action, which enables the kinetic energy and potential energy in the action to be converted …
We study the loop quantum cosmology of a flat Friedmann-Lemaitre-Robertson-Walker space-time with a Maxwell field. We show that many of the qualitative properties derived for the case of a massless scalar field also hold for a Maxwell field. In particular, the big-bang singularity is replaced by a quantum bounce, and the operator corresponding to the matter energy density is bounded above by the same critical energy density. We also numerically study the evolution of wave functions that are sharply peaked in the low energy regime, and derive effective equations which very closely approximate t…
We develop the general scheme for modified $f(R)$ gravity reconstruction from any realistic FRW cosmology. We formulate several versions of modified gravity compatible with Solar System tests where the following sequence of cosmological epochs occurs: a. matter dominated phase (with or without usual matter), transition from decceleration to acceleration, accelerating epoch consistent with recent WMAP data b. $Λ$CDM cosmology without cosmological constant. As a rule, such modified gravities are expressed implicitly (in terms of special functions) with late-time asymptotics of known type (for in…
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 discuss the creation of massless particles in a Universe, which transits from a radiation-dominated era to any other expansion law. We calculate in detail the generation of gravitons during the transition to a matter dominated era. We show that the resulting gravitons generated in the standard radiation/matter transition are negligible. We use our result to constrain one or more previous matter dominated era, or any other expansion law, which may have taken place in the early Universe. We also derive a general formula for the modification of a generic initial graviton spectrum by an early m…
We analyse quantum--kinetic effects in the early Universe. We show that quantum corrections to the Vlasov equation give rise to a dynamical variation of the gravitational constant. The value of the gravitational constant at the Grand Unification epoch is shown to differ from its present value to about $10^{-4} ÷10^{-3} \% $.
We make a case for setting initial conditions for inflation at the Planck epoch in the kinetically dominated regime. For inflationary potentials with a plateau or a hill, i.e. potentials that are bounded from above within a certain region of interest, we cannot claim complete ignorance of the energy distribution between kinetic and potential energy, and equipartition of energy at the Planck epoch becomes questionable. We analyse different classes of potentials in phase-space and quantify the fraction of the Planck surface that is kinetically dominated. For the small amplitudes of the potential…
We present non-perturbative numerical relativity simulations of slowly contracting spacetimes in which the scalar field driving slow contraction is coupled to a second scalar field through an exponential non-linear sigma model-type kinetic interaction. These models are important because they can generate a nearly scale-invariant spectrum of super-Hubble density fluctuations fully consistent with cosmic microwave background observations. We show that the non-linear evolution rapidly approaches a homogeneous, isotropic and flat Friedmann- Robertson-Walker (FRW) geometry for a wide range of inhom…
We generalize the scalar tensor bigravity models to the non-minimal kinetic coupling scalar tensor bigravity models with two scalar fields whose kinetic terms are non-minimally coupled to two Einstein tensors constructed by two metrics. We show that a broad class of expanding universes can be explained by some solutions of this model. Then, we study the stability issue of the solutions by means of imposing homogeneous perturbation on the equations of motion and extract the stable solutions.
We consider cosmological dynamics in the theory of gravity with the scalar field possessing the nonminimal kinetic coupling to curvature given as $κG^{μν}ϕ_{,μ}ϕ_{,ν}$, and the Higgs-like potential $V(ϕ)=\fracλ{4}(ϕ^2-ϕ_0^2)^2$. Using the dynamical system method, we analyze stationary points, their stability, and all possible asymptotical regimes of the model under consideration. We show that the Higgs field with the kinetic coupling provides an existence of accelerated regimes of the Universe evolution. There are three possible cosmological scenarios with acceleration: (i) {\em The late-time …
A Friedmann-Robertson-Walker cosmological model dominated by tachyonic -- faster-than-light -- dark matter can exhibit features similar to those of a standard dark energy/dark matter or $Lambda$CDM model. It can undergo expansion which decelerates to a minimum rate, passes through a "cosmic jerk," then accelerates. But some features of a tachyon-dominated model are sufficiently distinct from those of the standard model that the two possibilities might be distinguished observationally. As a demonstration of concept, the distance-redshift relation of such a model is compared here with some obser…
A non-singular bouncing cosmology is generically obtained in loop quantum cosmology due to non-perturbative quantum gravity effects. A similar picture can be achieved in standard general relativity in the presence of a scalar field with a non-standard kinetic term such that at high energy densities the field evolves into a ghost condensate and causes a non-singular bounce. During the bouncing phase, the perturbations can be stabilized by introducing a Horndeski operator. Taking the matter content to be a dust field and an ekpyrotic scalar field, we compare the dynamics in loop quantum cosmolog…
In the matter bounce scenario, a dust-dominated contracting space-time generates scale-invariant perturbations that, assuming a nonsingular bouncing cosmology, propagate to the expanding branch and set appropriate initial conditions for the radiation-dominated era. Since this scenario depends on the presence of a bounce, it seems appropriate to consider it in the context of loop quantum cosmology where a bouncing universe naturally arises. For a pressureless collapsing universe in loop quantum cosmology, the predicted power spectrum of the scalar perturbations after the bounce is scale-invaria…
We consider cosmological scenarios in which density perturbations are generated by the quantum fluctuations of the inflaton field at early times; the late time dynamics involves a modulus which first dominates the energy density of the universe and then decays to reheat the visible sector. By examining the evolution of energy density of the universe from the time of horizon exit of a pivot mode to the present day, and the fact that a modulus field decays via Planck suppressed interactions, we arrive at a relation which relates the mass of the modulus, inflationary observables/parameters and br…
The cosmology of flat FLRW universes dominated by a single scalar field is discussed. General features of the evolution of the universe and the scalar field are illustrated by specific examples. In particular the role of critical points, where the scalar field is stationary, is emphasized and their classification and interpretation as stable or unstable end points, or turning points is explained.
We review the results of a model of how nucleation of a new universe occurs, assuming a di quark identification for soliton-anti soliton constituent parts of a scalar field. Initially, we employ a false vacuum potential system; however ,when cosmological expansion is dominated by the Einstein cosmological constant at the end of chaotic inflation, the initial di quark scalar field is not consistent with respect to a semi classical consistency conditions we analyze as the potential changes to the chaotic inflationary potential utilized by Guth. We use Scherrer's derivation of a sound speed being…
A new cosmological scenario driven by a slow rolling homogeneous scalar field whose exponential potential $V(Φ)$ has a quadratic dependence on the field $Φ$ in addition to the standard linear term is discussed. The derived equation of state for the field predicts a transient accelerating phase, in which the Universe was decelerated in the past, began to accelerate at redshift $z \sim 1$, is currently accelerated, but, finally, will return to a decelerating phase in the future. This overall dynamic behavior is profoundly different from the standard $Λ$CDM evolution, and may alliviate some confl…
In this paper the scalar-tensor theory is applied to the study of perturbations in a multi-fluid universe, using the 1+3 covariant approach. Both scalar and harmonic decompositions are instituted on the perturbation equations. In particular, as an application, we study perturbations on a background FRW cosmology consisting of both radiation and dust in the presence of a scalar field. We consider both radiation-dominated and dust-dominated epochs, respectively, and study the results. During the analysis, quasi-static approximation is instituted. It is observed that the fluctuations of the energ…
This paper studies the cosmological equations for a scalar field Phi in the framework of a quantum gravity modified Einstein--Hilbert Lagrangian where G and Lambda are dynamical variables. It is possible to show that there exists a Noether symmetry for the point Lagrangian describing this scheme in a FRW universe. Our main result is that the Noether Symmetry Approach fixes both Lambda = Lambda(G) and the potential V = V(Phi) of the scalar field. The method does not lead, however, to easily solvable equations, by virtue of the higher dimensionality of the reduced configuration space involved, t…
A special model of a massless vector-field is presented, which has an extra modified-gravity-type interaction term in the action. The cosmology of the model is studied with standard noninteracting relativistic matter added. It is found that this cosmology can have an early phase where the vector-field starts to compensate a (Planck-scale) cosmological constant and a late Friedmann-Robertson-Walker (FRW) phase where the relativistic-matter energy density dominates the dynamic vacuum energy density.
We study the phase space for an scalar-tensor string inspired model of dark energy with non minimal kinetic and Gauss Bonnet couplings. The form of the scalar potential and of the coupling terms is of the exponential type, which give rise to appealing cosmological solutions. The critical points describe a variety of cosmological scenarios that go from matter or radiation dominated universe to dark energy dominated universe. There were found trajectories in the phase space departing from unstable or saddle fixed points and arriving to the stable scalar field dominated point corresponding to lat…
In this work, we revisit the dynamics of pre-inflationary universe with a family of $α-$attractor potentials, in the framework of loop quantum cosmology, in which the big bang singularity is generically resolved purely with quantum geometric effects, and replaced by a quantum bounce. At the bounce, the background evolution is divided into two distinct classes, the first is dominated by the kinetic energy of the inflaton field and the second by the potential energy. In both classes, we find the physically viable initial conditions numerically that provide not only the slow-roll inflation, but a…
We explore the dynamics of neutrinos in a vacuum dominated cosmology. First we show that such a geometry will induce a phase change in the eigenstates of a massive neutrino and we calculate the phase change. We also calculate the delay in the neutrino flight times in this geometry. Applying our results to the presently observed background vacuum energy density, we find that for neutrino sources further than $1.5 Gpc$ away both effects become non-trivial, being of the order of the standard relativistic corrections. Such sources are within the obsevable Hubble Deep Field. The results which are t…
We present a phase-plane analysis of cosmologies containing a scalar field $ϕ$ with an exponential potential $V \propto \exp(-λκϕ)$ where $κ^2 = 8πG$ and $V$ may be positive or negative. We show that power-law kinetic-potential scaling solutions only exist for sufficiently flat ($λ^2<6$) positive potentials or steep ($λ^2>6$) negative potentials. The latter correspond to a class of ever-expanding cosmologies with negative potential. However we show that these expanding solutions with a negative potential are to unstable in the presence of ordinary matter, spatial curvature or anisotropic shear…
We formulate the Lagrangian of the Newtonian cosmology where the cosmological constant is also introduced. Following the affine quantization procedure, the Hamiltonian operator is derived. The wave functions of the Newtonian universe and the corresponding eigenvalues for the case of matter dominated by a negative cosmological constant are given.
Scalar fields with an energy density dominated by its kinetic part may have played a relevant role in the very early stages of the Universe. Compared to the standard inflationary paradigm, they may lead to modifications in observable quantities, e.g. the anisotropies found in the cosmic microwave background. Kinetically dominated regimes arise in classical fast-roll scenarios as well as in quantum bouncing cosmologies. For instance, kinetic dominance is typical in interesting preinflationary phases of Loop Quantum Cosmology. In this work, we analyze the leading-order effects that the presence …
The evolution of a universe modelled as a mixture of generalised Chaplygin gas and ordinary matter field is studied for a Robertson Walker type of spacetime. This model could interpolate periods of a radiation dominated, matter dominated and a cosmological constant dominated universe. Depending on the arbitrary constants appearing in our theory the instant of flip changes. Interestingly we also get a bouncing model when the signature of one of the constants changes. The velocity of sound may become imaginary under certain situations pointing to a perturbative state and consequently the possibi…
In the framework of a bimetric model, we discuss a relation between the (modified) Friedmann equations and a mechanical system similar to the quantum Hall effect problem. Firstly, we show how these modified Friedmann equations are mapped to an anisotropic two-dimensional charged harmonic oscillator in the presence of a constant magnetic field, with the frequencies of the oscillator playing the role of the cosmological constants. This problem has two energy scales leading to the identification of two different regimes, namely, one dominated by the cosmological constants, with exponential expans…
We consider cosmological dynamics in the theory of gravity with the scalar field possessing a nonminimal kinetic coupling to gravity, $κG_{μν}ϕ^μϕ^ν$, and the power-law potential $V(ϕ)=V_0ϕ^N$. Using the dynamical system method, we analyze all possible asymptotical regimes of the model under investigation and show that for sloping potentials with $0<N<2$ there exists a quasi-de Sitter asymptotic $H={1}/{\sqrt{9κ}}$ corresponding to an early inflationary Universe. In contrast to the standard inflationary scenario, the kinetic coupling inflation does not depend on a scalar field potential and is…
We investigate the behavior of dark energy interacting with dark matter and unparticle in the framework of loop quantum cosmology. In four toy models, we study the interaction between the cosmic components by choosing different coupling functions representing the interaction. We found that there are only two attractor solutions namely dark energy dominated and dark matter dominated Universe. The other two models are unstable, as they predict either a dark energy filled Universe or one completely devoid of it.
Unlike Noether symmetry, a metric independent general conserved current exits for non-minimally coupled scalar-tensor theory of gravity, if the trace of the energy momentum tensor vanishes. Thus, in the context of cosmology, a symmetry exists both in the early vacuum and radiation dominated era. For slow roll, symmetry is sacrificed, but at the end of early inflation, such a symmetry leads to a Friedmann-like radiation era. Late time cosmic acceleration in the matter dominated era is realized in the absence of symmetry, in view of the same decayed and red-shifted scalar field. Thus, unificatio…
We systematically study the preinflationary dynamics of the spatially flat Friedmann-Lemaitre-Robertson-Walker universe filled with a single scalar field that has the generalized $α-$attractor potentials, in the framework of loop quantum cosmology, in which the big bang singularity is replaced generically by a non-singular quantum bounce due to purely quantum geometric effects. The evolution can be divided into two different classes, one is dominated initially (at the quantum bounce) by the kinetic energy of the scalar field, and one is not. In both cases, we identify numerically the physicall…
A bouncing cosmology with an initial matter-dominated phase of contraction during which scales which are currently probed with cosmological observations exit the Hubble radius provides a mechanism alternative to inflation for producing a nearly scale-invariant spectrum of cosmological perturbations. In this review article I first discuss the evolution of cosmological fluctuations in the matter bounce scenario, and then discuss various attempts at realizing such a scenario. Observational signatures which will allow the matter bounce to be distinguished from the inflationary paradigm are also di…
In this paper, by establishing a Brans-Dicke (BD) cosmology by means of a deformed phase space, in the absence of any scalar potential, cosmological constant and ordinary matter, we show that it is feasible to overcome obstacles reported in the corresponding commutative (non-deformed) frameworks. More concretely, by applying the Hamiltonian formalism and introducing a dynamical deformation, between the momenta associated to the FLRW scale factor and the BD scalar field, we obtain the modified equations of motion. In particular, these equations reduce to their standard counterparts when the non…
We generalize the time-variable dark energy scalar field $Φ$ model ($Φ$CDM) to nonflat space. We show that even in the space-curvature-dominated epoch the scalar field solution is a time-dependent fixed point or attractor, with scalar field energy density that grows relative to the energy density in spatial curvature. This is the first example of a physically consistent and complete model of dynamical dark energy in a nonflat geometry.
Recently, States of Low Energy (SLEs) have been proposed as viable vacuum states of primordial perturbations within Loop Quantum Cosmology (LQC). In this work we investigate the effect of the high curvature region of LQC on the definition of SLEs. Shifting the support of the test function that defines them away from this regime results in primordial power spectra of perturbations closer to those of the so-called Non-oscillatory (NO) vacuum, which is another viable choice of initial conditions previously introduced in the LQC context. Furthermore, through a comparison with the Hadamard-like SLE…
Cosmological models based on f(R)-gravity may exhibit a natural acceleration mechanism without introducing a dark energy component. In this paper, we investigate cosmological consequences of the so-called Hu-Sawicki f(R)-gravity in the Palatini formalism. We derive theoretical constraints on the model parameters and perform a statistical analysis to determine the parametric space allowed by current observational data. We find that this class of models is indistinguishable from the standard ΛCDM model at the background level. Differently, from previous results in the metric approach, we show th…
We study the cosmology of a general scalar field and barotropic fluid during the early stage of a brane-world where the Friedmann constraint is dominated by the square of the energy density. Assuming both the scalar field and fluid are confined to the brane, we find a range of behaviour depending on the form of the potential. Generalising an approach developed for a standard Friedmann cosmology, in \cite{delaMacorra:1999ff}, we show that the potential dependence $V(ϕ)$ can be described through a parameter $λ\equiv -\sqrt{2} m_5^{3/2} V'/(\sqrt{H}V)$, where $m_5$ is the 5-dimensional Planck mas…
We show that the effective dynamics of the recently proposed isotropic condensate state of group field theory with Laplacian kinetic operator can be equivalent to that of homogeneous and isotropic loop quantum cosmology in the improved dynamics quantization scheme, where the area of elementary holonomy plaquettes is constant. This constitutes a somewhat surprising example of a cosmological model of quantum gravity where the operations of minisuperspace symmetry reduction and quantization can actually commute.
The holographic bound in Brans-Dicke $k=1$ matter dominated Cosmology is discussed. In this talk, both the apparent horizon and the particle horizon are taken for the holographic bound. The covariant entropy conjecture proposed by Bousso is also discussed.
We consider the coupled evolution of density, (scalar) metric and dilaton perturbations in the transition from a ``stringy" phase of growing curvature and gravitational coupling to the standard radiation-dominated cosmology. We show that dilaton production, with a spectrum tilted towards large frequencies, emerges as a general property of this scenario. We discuss the frame-independence of the dilaton spectrum and of the inflationary properties of the metric background by using, as model of source, a pressureless gas of weakly interacting strings, which is shown to provide an approximate but c…
In this paper, we have considered a cosmological model with the non--minimal kinetic coupling terms and investigated its cosmological implications with respect to the logarithmic entropy-- corrected holographic dark energy (LECHDE). The correspondence between LECHDE in flat FRW cosmology and the phantom dark energy model with the aim to interpret the current universe acceleration is also examined.
Some models are presented in which the strength of the gravitational coupling of the potential energy relative to the same coupling for the kinetic energy is, in a precise sense, adjustable. The gauge symmetry of these models consists of those coordinate changes with unit jacobian.
The effects of the gravitational back reaction of cosmological perturbations are investigated in a cosmological model where the universe is dominated by phantom energy. We assume a COBE normalized spectrum of cosmological fluctuations at the present time and calculate the effective energy-momentum tensor of the gravitational back-reactions of cosmological perturbations whose wavelengths at the time when the back-reactions are evaluated are larger than the Hubble radius. Our results reveal that the effects of gravitational back-reactions will counteract that of phantom energy sooner or later an…
In this paper, we investigate the dynamics of pre-inflation with Hilltop potential in the framework of loop quantum cosmology. The initial conditions of inflaton field at the quantum bounce is categorized into two classes, first one is dominated by kinetic energy and second one by potential energy. In both cases, the physically viable initial values of inflaton field at the bounce are obtained numerically that generate the desired slow-roll inflation and also sufficient number of $e$-folds. To be consistent with observations at least 60 $e$-folds are required. In case of kinetic energy dominat…
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 $P_{eff}=-{1/9}ρ_{eff}$.
From the Wheeler-Dewitt solutions, the scale factor of the initial universe is discussed. In this study, scale factors from Wheeler-Dewitt solutions, loop quantum gravity, and phantom energy dominated stages are compared. Certain modifications have been attempted in scale factor and quantum potentials driven by canonical quantum gravity approaches. Their results are discussed in this work. Despite an increment of phantom energy density, avoidance of Big Rip is reported. Scale factors predicted from various models are discussed in this work. The relationship between scale factors and the smooth…
Super--inflation driven by dilaton/moduli kinetic energy is naturally realized in compactified string theory. Discussed are selected topics of recent development in string inflationary cosmology: kinematics of super-inflation, graceful exit triggered by quantum back reaction, and clasical and quantum power spectra of density and metric perturbations.
