On the cosmological viability of the Hu-Sawicki type modified induced gravity

It has been shown recently that the normal branch of a DGP braneworld scenario self-accelerates if the induced gravity on the brane is modified in the spirit of f(R) modified gravity. Within this viewpoint, we investigate cosmological viability of the Hu-Sawicki type modified induced gravity. Firstly, we present a dynamical system analysis of a general f(R)-DGP model. We show that in the phase space of the model, there exist three standard critical points; one of which is a de Sitter point corresponding to accelerating phase of the universe expansion. The stability of this point depends on the effective equation of state parameter of the curvature fluid. If we consider the curvature fluid to be a canonical scalar field in the equivalent scalar-tensor theory, the mentioned de Sitter phase is unstable, otherwise it is an attractor, stable phase. We show that the effective equation of state parameter of the model realizes an effective phantom-like behavior. A cosmographic analysis shows that this model, which admits a stable de Sitter phase in its expansion history, is a cosmologically viable scenario.     

Cosmological solutions of time varying speed of light theories

We consider scalar–tensor theory for describing varying speed of light in a spatially flat FRW space–time. We find some exact solutions in the metric and Palatini formalisms. Also we examine the dynamics of this theory by dynamical system method assuming a ΛCDM background and we find some exact solutions by considering the character of critical points of the theory in both formalisms. We show that for any attractor the form of non-minimal coupling coefficient is quadratic in terms of the scalar field Ψ. Also we show that only attractors of the de Sitter era satisfy the horizon criteria.     

Dark Energy Model with Canonical Scalar Field and Non-Linear Born–Infeld Type Scalar Field

In this paper, we propose the non-linear Born–Infeld scalar field and canonical scalar field dark energy models with the potential , which admits late time de Sitter attractor solution. The attractor solution corresponds to an equation of state ω_φ → − 1 and a cosmic density parameter Ω_φ → 1, which are important features for a dark energy model that can meet the current observations. dark energy; canonical scalar field, non-linear Born–Infeld type scalar field, attractor solution. PACS number(s):98.80.-k; 98.80.Cq; 98.80.Es.     

A new vacuum state in de Sitter space

We present a new vacuum state which can be defined in a region of de Sitter space. This region corresponds to a K=?1 Robertson-Walker coordinatization of de Sitter space. The renormalized expectation value of the stress tensor for the conformally invariant massless scalar field in this vacuum is evaluated, and is found to differ from the corresponding result in the usual de Sitter-invariant vacuum by the absence of a pure radiation term. We also indicate that this can be accounted for by regarding the de Sitter-invariant vacuum as a thermal state relative to the new vacuum.     

Quasi-resonant Modes of Massive Scalar Fields in Schwarzschild–de Sitter Space-Time

Recent research of massive fields quasinormal modes suggested that the arbitrary long living modes can be exist. Using different orders of WKB method, we study the massive scalar fields quasinormal modes of Schwarzschild–de Sitter black holes. It is shown that the WKB method can not applied for large massive scalar fields directly in asymptotic flat space-time but can fit well in de Sitter space-time. We prove the non-existence of QRMs in de Sitter space-time and find that the real parts of QNMs increase linearly and the imaginary parts approach to special values as the mass of scalar fields increase.     

Dynamical system approach to scalar–vector–tensor cosmology

Using scalar–vector–tensor Brans Dicke (VBD) gravity (Ghaffarnejad in Gen Relativ Gravit 40:2229, 2008; Gen Relativ Gravit 41:2941, 2009) in presence of self interaction BD potential \(V(\phi )\) and perfect fluid matter field action we solve corresponding field equations via dynamical system approach for flat Friedmann Robertson Walker metric (FRW). We obtained three type critical points for \(\Lambda CDM\) vacuum de Sitter era where stability of our solutions are depended to choose particular values of BD parameter \(\omega \). One of these fixed points is supported by a constant potential which is stable for \(\omega <0\) and behaves as saddle (quasi stable) for \(\omega \ge 0\). Two other ones are supported by a linear potential \(V(\phi )\sim \phi \) which one of them is stable for \(\omega =0.27647\). For a fixed value of \(\omega \) there is at least 2 out of 3 critical points reaching to a unique critical point. Namely for \(\omega =-0.16856(-0.56038)\) the second (third) critical point become unique with the first critical point. In dust and radiation eras we obtained one critical point which never become unique fixed point. In the latter case coordinates of fixed points are also depended to \(\omega \). To determine stability of our solutions we calculate eigenvalues of Jacobi matrix of 4D phase space dynamical field equations for de Sitter, dust and radiation eras. We should point also potentials which support dust and radiation eras must be similar to \(V(\phi )\sim \phi ^{-\frac{1}{2}}\) and \(V(\phi )\sim \phi ^{-1}\) respectively. In short our study predicts that radiation and dust eras of our VBD–FRW cosmology transmit to stable de Sitter state via non-constant potential (effective variable cosmological parameter) by choosing \(\omega =0.27647\).     

Casimir Effect for Moving Branes in Static dS4+1 Bulk

In this paper we study the Casimir effect for conformally coupled massless scalar fields on background of Static dS₄₊₁ spacetime. We will consider the general plane–symmetric solutions of the gravitational field equations and boundary conditions of the Dirichlet type on the branes. Then we calculate the vacuum energy-momentum tensor in a configuration in which the boundary branes are moving by uniform proper acceleration in static de Sitter background. Static de Sitter space is conformally related to the Rindler space, as a result we can obtain vacuum expectation values of energy-momentum tensor for conformally invariant field in static de Sitter space from the corresponding Rindler counterpart by the conformal transformation.     

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.     

Dynamics of quintessential inflation

In this paper, we study a realistic model of quintessential inflation with radiation and matter. By the analysis of the dynamical system and numerical work about the evolution of the equation of state and cosmic density parameter, we show that this model is a good match for the current astronomical observation. The conclusion we obtain is in favour of the model where the modular part of the complex field plays the role of the inflaton whereas the argument part is the quintessence field. Numerical calculation shows that a heteroclinic orbit (solution of the dynamical system) is interpolated between early-time de Sitter phase (an unstable critical point) and a late-time de Sitter attractor.     

Stability Properties and Asymptotics for N Nonminimally Coupled Scalar Fields Cosmology

We consider here the dynamics of some homogeneous and isotropic cosmological models with N interacting classical scalar fields nonminimally coupled to the spacetime curvature, as an attempt to generalize some recent results obtained for one and two scalar fields. We show that a Lyapunov function can be constructed under certain conditions for a large class of models, suggesting that chaotic behavior is ruled out for them. Typical solutions tend generically to the empty de Sitter (or Minkowski) fixed points, and the previous asymptotic results obtained for the one field model remain valid. In particular, we confirm that, for large times and a vanishing cosmological constant, even in the presence of the extra scalar fields, the universe tends to an infinite diluted matter dominated era.     

The physical meaning of the de Sitter invariants

We study the Lie algebras of the covariant representations transforming the matter fields under the de Sitter isometries. We point out that the Casimir operators of these representations can be written in closed forms and we deduce how their eigenvalues depend on the field’s rest energy and spin. For the scalar, vector and Dirac fields, which have well-defined field equations, we express these eigenvalues in terms of mass and spin obtaining thus the principal invariants of the theory of free fields on the de Sitter spacetime. We show that in the flat limit we recover the corresponding invariants of the Wigner irreducible representations of the Poincaré group.     

The fields of uniformly accelerated charges in de Sitter spacetime

The scalar and electromagnetic fields of charges uniformly accelerated in de Sitter spacetime are constructed. They represent the generalization of the Born solutions describing fields of two particles with hyperbolic motion in flat spacetime. In the limit Lambda-->0, the Born solutions are retrieved. Since in the de Sitter universe the infinities I+/- are spacelike, the radiative properties of the fields depend on the way in which a given point of I+/- is approached. The fields must involve both retarded and advanced effects: Purely retarded fields do not satisfy the constraints at the past infinity I-.     

Scalar particles mass spectrum and localization on FRW branes embedded in a 5D de Sitter bulk

In this paper, we study the scalar fields evolving on a FRW brane embedded in a five-dimensional de Sitter bulk. The scale function and the warp factor, solutions of the Einstein equations, are employed in the five-dimensional Gordon equation describing the massive scalar field, whose wave function depends on the cosmic time and on the extra-dimension. We point out the existence of bounded states and find a minimum value of the effective four-dimensional mass. For the test (scalar) field envelope along the extra-dimension, we derive the corresponding Schrödinger-like equation which is formally that for the Pöschl-Teller potential. Accordingly, we have obtained the quantization law for the mass parameter of the tested scalar field.     

One-loop effective potential in gauged O(4) supergravity and the problem of the Λ term

We calculate the one-loop, off-shell, effective action in O(4) gauged supergravity assuming an (anti) de Sitter metric and constant scalar fields as a background. The problem of the large induced Λ term (present already for free matter fields) is stressed and the possibility of dynamical breakdown of local supersymmetry is pointed out. We illustrate our techniques and qualitative conclusions on a number of examples, including Ø⁴ theory and QED scalar potentials on a de Sitter background and an effective action in Einstein theory with a cosmological constant. Possible solutions of the Λ-term problem are also discussed.     

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.     

Open quantum system approach to the Gibbons-Hawking effect of de Sitter space-time

We analyze, in the paradigm of open quantum systems, the reduced dynamics of a freely falling two-level detector in de Sitter space-time in weak interaction with a reservoir of fluctuating quantized conformal scalar fields in the de Sitter-invariant vacuum. We find that the detector is asymptotically driven to a thermal state at the Gibbons-Hawking temperature, regardless of its initial state. Our discussion, therefore, shows that the Gibbons-Hawking effect of de Sitter space-time can be understood as a manifestation of thermalization phenomena that involves decoherence and dissipation in open quantum systems.     

Hawking-de Sitter Thermalization of Quasi-Minkowskian Massless Scalaron Production,Energy Density Content and Back-Reaction

Projecting the closed form expression of the de Sitter scalar field operator onto the Minkowskian positive frequency massless modes, we compute the corresponding Bogolubov coefficient which is associated to the (massless) quasiparticle creation during the stationary quasi-de Sitter stage of the Universe. Thereafter, we derive the expression of the thermalized energy density which reveals an interesting mixture of de Sitter false vacuum and dark-radiation, exotic dust and black body radiation. Setting the temperature to the value of the Hawking one for the de Sitter spacetime, we finally analyze the (straightforward) back-reaction of the newly created “matter” on the scale function. It basically points out three stages of highly continuous evolution represented by an initially short radiation-like era, a somewhat long-lasting connecting phase made of coherent massless oscillations, in its beginnings, ended up by the dark-radiation (i.e. curvature-like term) contribution and, finally, a much slower exponential expansion than the initial de Sitter one.     

Regular phantom black holes

We study self-gravitating, static, spherically symmetric phantom scalar fields with arbitrary potentials (favored by cosmological observations) and single out 16 classes of possible regular configurations with flat, de Sitter, and anti-de Sitter asymptotics. Among them are traversable wormholes, bouncing Kantowski-Sachs (KS) cosmologies, and asymptotically flat black holes (BHs). A regular BH has a Schwarzschild-like causal structure, but the singularity is replaced by a de Sitter infinity, giving a hypothetic BH explorer a chance to survive. It also looks possible that our Universe has originated in a phantom-dominated collapse in another universe, with KS expansion and isotropization after crossing the horizon. Explicit examples of regular solutions are built and discussed. Possible generalizations include k-essence type scalar fields (with a potential) and scalar-tensor gravity.     

A dynamical system approach to Bianchi III cosmology for Hu–Sawicki type <Emphasis Type="Italic">f</Emphasis>(<Emphasis Type="Italic">R</Emphasis>) gravity

The cosmological dynamics of spatially homogeneous but anisotropic Bianchi type-III space-time is investigated in presence of a perfect fluid within the framework of Hu–Sawicki model. We use the dynamical system approach to perform a detailed analysis of the cosmological behaviour of this model for the model parameters \(n=1, c_1=1\), determining all the fixed points, their stability and corresponding cosmological evolution. We have found stable fixed points with de Sitter solution along with unstable radiation like fixed points. We have identified a matter like point which act like an unstable spiral and when the initial conditions of a trajectory are very close to this point, it stabilizes at a stable accelerating point. Thus, in this model, the universe can naturally approach to a phase of accelerated expansion following a radiation or a matter dominated phase. It is also found that the isotropisation of this model is affected by the spatial curvature and that all the isotropic fixed points are found to be spatially flat.