Genericness of inflation in isotropic loop quantum cosmology

Nonperturbative corrections from loop quantum cosmology (LQC) to the scalar matter sector are already known to imply inflation. We prove that the LQC modified scalar field generates exponential inflation in the small scale factor regime, for all positive definite potentials, independent of initial conditions and independent of ambiguity parameters. For positive semidefinite potentials it is always possible to choose, without fine-tuning, a value of one of the ambiguity parameters such that exponential inflation results, provided zeros of the potential are approached at most as a power law in the scale factor. In conjunction with the generic occurrence of bounce at small volumes, particle horizon is absent, thus eliminating the horizon problem of the standard big bang model.     

Ab-initio calculations of electric field gradient in Ru compounds and their implication on the nuclear quadrupole moments of $$^{99}\hbox {Ru}$$ and $$^{101}\hbox {Ru}$$101Ru

We study a spatially homogeneous and anisotropic cosmological model in the Einstein gravitational theory with a minimally coupled scalar field. We consider a non-interacting combination of scalar field and perfect fluid as the source of matter components which are separately conserved. The dynamics of cosmic scalar fields with a zero rest mass and an exponential potential are studied, respectively. We find that both assumptions of potential along with the average scale factor as an exponential function of scalar field lead to the logarithmic form of scalar field in each case which further gives power-law form of the average scale factor. Using these forms of the average scale factor, exact solutions of the field equations are obtained to the metric functions which represent a power-law and a hybrid expansion, respectively. We find that the zero-rest-mass model expands with decelerated rate and behaves like a stiff matter. In the case of exponential potential function, the model decelerates, accelerates or shows the transition depending on the parameters. The isotropization is observed at late-time evolution of the Universe in the exponential potential model.     

Vacuum stability conditions from copositivity criteria

In this paper, we introduce a non-minimally conformally coupled scalar field and dark matter in F(T) cosmology and study their dynamics. We investigate the stability and phase space behavior of the parameters of the scalar field by choosing an exponential potential and cosmologically viable form of F(T). We found that the dynamical system of equations admits two unstable critical points; thus no attractor solutions exist in this cosmology. Furthermore, taking into account the scalar field mimicking quintessence and phantom energy, we discuss the corresponding cosmic evolution for both small and large times. We investigate the cosmological implications of the model via the equation of state and deceleration parameters of our model and show that the late-time Universe will be dominated by phantom energy and, moreover, phantom crossing is possible. Our results do not lead to explicit predictions for inflation and the early Universe era.     

Background Dynamics of Pre-inflationary Scenario in Brans-Dicke Loop Quantum Cosmology

Recently the background independent nonperturbative quantization has been extended to various theories of gravity and the corresponding quantum effective cosmology has been derived, which provides us with necessary avenue to explore the pre-inflationary dynamics. Brans-Dicke (BD) loop quantum cosmology (LQC) is one of such theories whose effective background dynamics is considered in this article. Starting with a quantum bounce, we explore the pre-inflationary dynamics of a universe sourced by a scalar field with the Starobinsky potential in BD-LQC. Our study is based on the idea that though Einstein's and Jordan's frames are classically equivalent up to a conformal transformation in BD theory, this is no longer true after quantization. Taking the Jordan frame as the physical one we explore in detail the bouncing scenario which is followed by a phase of a slow roll inflation. The three phases of the evolution of the universe, namely, bouncing, transition from quantum bounce to classical universe, and the slow roll inflation, are noted for an initially kinetic energy dominated bounce. In addition, to be consistent with observations, we also identify the allowed phase space of initial conditions that would produce at least 60 e-folds of expansion during the slow roll inflation.     

Power-Law Inflation in Spacetimes Without Symmetry

We consider models of accelerated cosmological expansion described by the Einstein equations coupled to a nonlinear scalar field with a suitable exponential potential. We show that homogeneous and isotropic solutions are stable under small nonlinear perturbations without any symmetry assumptions. Our proof is based on results on the nonlinear stability of de Sitter spacetime and Kaluza-Klein reduction techniques.     

Inflationary solutions in general scalar tensor theory of gravitation

Extended inflation solution in Brans-Dicke theory given by Mathiazhagan and Johri (MJ) is shown as the unique solution only if the scale factor is assumed to be a power function of the scalar field. Only the consistent solution amongst the set of solutions given by Patra, Roy and Ray is found identical to the MJ solution. Both exponential inflation and power function inflation are studied in general scalar tensor theory where the parameter to is a function of the scalar, field. It is noted that exponential inflation is forbidden in Brans-Dicke theory wherew is a constant.     

Time reparameterization in Bianchi type I spinor cosmology

The problem of time reparameterization is addressed at both the classical and quantum levels in a Bianchi-I universe in which the matter source is a massive Dirac spinor field. We take the scale factors of the metric as the intrinsic time and their conjugate momenta as the extrinsic time. A scalar character of the spinor field is identified as a representation of the extrinsic time. The construction of the field equations and quantization of the model is achieved by solving the Hamiltonian constraint after time identification has been dealt with. This procedure leads to a true Hamiltonian whose exact solutions for the above choices of time are presented.     

On quintessential cosmological models and exponential potentials

We first study dark energy models with a minimally-coupled scalar field and generalized exponential potentials, admitting exact solutions for the cosmological equations: actually, it turns out that for this class of potentials the Einstein field equations exhibit alternative Lagrangians, and are completely integrable and separable. We analyze their analytical solutions, especially discussing when they are compatible with a late time quintessential expansion of the universe. As a further issue, we discuss how quintessential scalar fields with exponential potentials can be connected to the inflationary phase, building up a quintessential inflationary scenario: actually, it turns out that the transition from inflation toward late-time exponential quintessential tail admits a kination period, which is an indispensable ingredient of this kind of theoretical models. All such considerations have been made by including also radiation into the model.     

Setting initial conditions for inflation with reaction–diffusion equation

We discuss the issue of setting appropriate initial conditions for inflation. Specifically, we consider natural inflation model and discuss the fine tuning required for setting almost homogeneous initial conditions over a region of order several times the Hubble size which is orders of magnitude larger than any relevant correlation length for field fluctuations. We then propose to use the special propagating front solutions of reaction–diffusion equations for localized field domains of smaller sizes. Due to very small velocities of these propagating fronts we find that the inflaton field in such a field domain changes very slowly, contrary to naive expectation of rapid roll down to the true vacuum. Continued expansion leads to the energy density in the Hubble region being dominated by the vacuum energy, thereby beginning the inflationary phase. Our results show that inflation can occur even with a single localized field domain of size smaller than the Hubble size. We discuss possible extensions of our results for different inflationary models, as well as various limitations of our analysis (e.g. neglecting self gravity of the localized field domain).     

Exact Perturbations for Inflation with Smooth Exit

Toy models for the Hubble rate or the scalar field potential have been used to analyze the amplification of scalar perturbations through a smooth transition from inflation to the radiation era. We use a Hubble rate that arises consistently from a decaying vacuum cosmology, which evolves smoothly from nearly de Sitter inflation to radiation domination. We find exact solutions for super-horizon perturbations (scalar and tensor), and for sub-horizon perturbations in the vacuum- and radiation-dominated eras. The standard conserved quantity for super-horizon scalar perturbations is exactly constant for the growing modes, and zero for the decaying modes.     

Extended inflation in higher-dimensional spacetime with a Brans-Dicke scalar field

Starting from an assumption of homogeneity of matter-energy tensor and Brans-Dicke (BD) scalar field we obtain a Robertson-Walker type of metric form in five-dimensional spacetime with the essential difference that our model is spatially inhomogeneous. The model exhibits an interesting feature in that as we approach the centre of symmetry the compact dimension becomes very large, with the implication that the Kaluza-Klein excitations become very light when located there and that the origin may represent a singular concentration of matter with motion in the extra dimension. Following Wesson the effective 4D properties of matter from the 5D vacuum solutions are also briefly discussed. Assuming particular functional relationships between and as also between the scale factor and scalar field, we obtain exact solutions which may be of relevance to the early universe and its extended inflation in the BD type of theory. We also discuss very briefly rollover time immediately after tunneling to the true vacuum state to explore if dimensionality has any marked influence on the situation.     

Power-law inflation with exponential potentials

We investigate some power-law solutions in inflationary cosmology, both by analytic and numerical means, considering first a simple model of a scalar field with an exponential field coupled to gravity. As has been pointed out recently by Yokoyama and Maeda, in power-law inflation viscous forces caused by couplings of the inflation to other particles can be important. We use numerical simulation to examine the effects of this viscosity on the inflation, for both a simple exponential potential and a more realistic potential motivated by particle physics. In general, the viscosity enhances the exponent of the power-law inflation, increasing the efficiency of inflation in power-law models, and we outline a specific inflationary model featuring viscosity.     

Higher derivatives in quantum cosmology: (I). The isotropic case

This paper is the first in a series that investigates the effects on cosmology of curvature-squared terms which are bound to appear in the effective action whether or not gravity is perturbatively finite, is cut off by nonperturbative effects, or is made renormalisable by the addition of curvature squared terms to the bare action. We examine how these terms affect the recent proposal that the quantum state of the universe is defined by a path integral over compact metrics. In this paper we consider a simple minisuperspace model of an isotropic universe. In such a model the C-squared term in the action plays no role while the R-squared term behaves like a massive scalar field. The wave function of the universe can be interpreted as corresponding in the classical limit to a family of solutions that start out with a long period of exponential expansion and then go over to a matter dominated era.     

Gauss–Bonnet term on vacuum decay

We study the effect of the Gauss–Bonnet term on vacuum decay process in the Coleman–De Luccia formalism. The Gauss–Bonnet term has an exponential coupling with the real scalar field, which appears in the low energy effective action of string theories. We calculate numerically the instanton solution, which describes the process of vacuum decay, and obtain the critical size of bubble. We find that the Gauss–Bonnet term has a nontrivial effect on the false vacuum decay, depending on the Gauss–Bonnet coefficient.     

The euclidean vacuum: Justification from quantum cosmology

We evaluate the wave function of the universe for a de Sitter minisuperspace with inhomogeneous matter perturbations from a massive scalar field. From the Wheeler-DeWitt equation, we derive Schrödinger equations for the matter modes. We show that the matter part of the Hartle-Hawking wave function is the euclidean vacuum state of quantum field theory in curved spacetime.     

Cosmological model with dynamical cancellation of vacuum energy and dark energy

We propose a model with a compensating scalar field whose back reaction to the cosmological curvature cancels possible vacuum energy density down to the terms of the order of the time-dependent critical energy density. Thus, the model simultaneously solves the mystery of the compensation of vacuum energy with an accuracy of 120 orders of magnitude and explains the existence of the observed dark energy. At an early stage, the suggested cosmological model might experience exponential expansion without an additional inflaton field. However, the solution found is unstable with respect to small perturbations. The stability can be ensured by introducing nonanalytical terms depending upon the absolute value of the curvature scalar R. Unfortunately, stable solutions do not describe realistic cosmology at the matter-dominated stage.     

Quantum Cosmology in Higher Derivative and Scalar-Tensor Gravity

The Bicknell theorem states that a non-linear Lagrangian can be recast in the form of a scalar-tensor theory, with a suitable potential, through a conformal transformation. In this paper, we first show that such classical equivalence remains valid at the level of the Wheeler—deWitt equation. Then, we consider a specific case, represented by a Lagrangian f(R) = R + l^–2(l²R)^4/3 whose vacuum cosmological solutions describe a non-singular Universe. The corresponding scalar-tensor theory and its cosmological solutions are written down. We find again non-singular solutions. The Wheeler—deWitt equation for this case is analyzed. The application of the Bicknell theorem leads to the interpretation of the behaviour of the scale factor in terms of the matter content, represented by the scalar field, and consequently to the energy conditions. The problem of classical and quantum regime is discussed and the classical behaviour is recovered, from the quantum solutions, near the maximum of the scale factor where the strong energy condition is satisfied.     

FRW cosmology from five dimensional vacuum Brans–Dicke theory

We follow the approach of induced-matter theory for a five-dimensional (5D) vacuum Brans–Dicke theory and introduce induced-matter and induced potential in four dimensional (4D) hypersurfaces, and then employ a generalized FRW type solution. We confine ourselves to the scalar field and scale factors be functions of the cosmic time. This makes the induced potential, by its definition, vanishes, but the model is capable to expose variety of states for the universe. In general situations, in which the scale factor of the fifth dimension and scalar field are not constants, the 5D equations, for any kind of geometry, admit a power–law relation between the scalar field and scale factor of the fifth dimension. Hence, the procedure exhibits that 5D vacuum FRW-like equations are equivalent, in general, to the corresponding 4D vacuum ones with the same spatial scale factor but a new scalar field and a new coupling constant, [(w)\tilde]{\tilde{\omega}} . We show that the 5D vacuum FRW-like equations, or its equivalent 4D vacuum ones, admit accelerated solutions. For a constant scalar field, the equations reduce to the usual FRW equations with a typical radiation dominated universe. For this situation, we obtain dynamics of scale factors of the ordinary and extra dimensions for any kind of geometry without any priori assumption among them. For non-constant scalar fields and spatially flat geometries, solutions are found to be in the form of power–law and exponential ones. We also employ the weak energy condition for the induced-matter, that gives two constraints with negative or positive pressures. All types of solutions fulfill the weak energy condition in different ranges. The power–law solutions with either negative or positive pressures admit both decelerating and accelerating ones. Some solutions accept a shrinking extra dimension. By considering non-ghost scalar fields and appealing the recent observational measurements, the solutions are more restricted. We illustrate that the accelerating power–law solutions, which satisfy the weak energy condition and have non-ghost scalar fields, are compatible with the recent observations in ranges −4/3 < ω ≤ −1.3151 for the coupling constant and 1.5208 ≤ n < 1.9583 for dependence of the fifth dimension scale factor with the usual scale factor. These ranges also fulfill the condition ${\tilde{\omega} > -3/2}${\tilde{\omega} > -3/2} which prevents ghost scalar fields in the equivalent 4D vacuum Brans–Dicke equations. The results are presented in a few tables and figures.