In the mathematically rigorous analysis of semiclassical Einstein's equations, the renormalisation of the stress-energy tensor plays a crucial role. We address such a topic in the case of a scalar field with both arbitrary mass and coupling with gravity in the hypothesis that the underlying algebraic quantum state is of Hadamard type. Particularly, if we focus on highly symmetric solutions of the semiclassical Einstein's equations, the envisaged method displays a de Sitter type behaviour even without an a priori introduced cosmological constant. As a further novel result we shall show that these solutions turn out to be stable.
The scalar background field and its consequences are discussed for the Friedmann type cosmological solutions of the scalar-tensor theory of gravity with the Higgs field of the Standard Model as the scalar gravitational field.
A scalar field non-minimally coupled to certain geometric [or matter] invariants which are sourced by [electro]vacuum black holes (BHs) may spontaneously grow around the latter, due to a tachyonic instability. This process is expected to lead to a new, dynamically preferred, equilibrium state: a scalarised BH. The most studied geometric [matter] source term for such spontaneous BH scalarisation is the Gauss-Bonnet quadratic curvature [Maxwell invariant]. This phenomenon has been mostly analysed for asymptotically flat spacetimes. Here we consider the impact of a positive cosmological constant,…
We proved that strictly stationary Einstein-Maxwell-axion-dilaton spacetime with negative cosmological constant could not support a nontrivial configuration of complex scalar fields. We considered the general case of the arbitrary number of U(1) gauge fields in the theory under consideration.
In the present article we analyze the phenomenon of particle creation in a cosmological anisotropic universe when a constant electric field is present. We compute, via the Bogoliubov transformations, the density number of particles created.
We perform a detailed analysis on the dynamics of a Chiral-like cosmological model where the scalar fields can have negative kinetic terms. In particular, we study the asymptotic dynamics for the gravitational field equations for four different models in a spatially flat Friedmann--Lema\^ıtre--Robertson--Walker background space. When one of the scalar fields is phantom, we calculated that the cosmological fluid can evolves such that the parameter for the equation of state crosses twice the phantom divide line without the appearance of ghosts. Moreover, the cosmological viability of these four …
We study a model of scalar field with kinetic terms non-minimally coupled to to the curvature, and the scalar field coupled to the Gauss Bonnet 4-dimensional invariant. A variety of solutions are found, giving rise to different cosmological scenarios. A unified description of early time matter (radiation) dominance with transitions to late time quintessence and phantom phases have been made. Among others, we found solutions unifying asymptotically the early power law behavior and late time cosmological constant. Solutions of Chaplygin gas and generalized Chaplygin gas cosmologies have also bee…
A specific Horndeski scalar-gravity mimetic model is investigated within a FLWR space-time. The mimetic scalar field is implemented via a Lagrangian multiplier, and it is shown that the model has equations of motion formally similar to the original simpler mimetic matter model of Chamseddine-Mukhanov-Vikman. Several exact solutions describing inflation, bounces, future time singularities are presented and discussed.
In this contribution, classes of shear-free cosmological dust models with irrotational fluid flows will be investigated in the context of scalar-tensor theories of gravity. In particular, the integrability conditions describing a consistent evolution of the linearised field equations of quasi-Newtonian universes are presented. We also derive the covariant density and velocity propagation equations of such models and analyse the corresponding solutions to these perturbation equations.
In this paper we study how to include the cosmological constant in geometric scalar theory of gravity (GSG). Firstly we show that the cosmological constant could not be modeled by a matter field, unlike in General Relativity. We also show that a spherically symmetric matter distribution, over the de Sitter vacuum, does not produce the Kottler solution and no black hole. To circumvent this problem we introduce an coupling term between the scalar field and the vacuum curvature in way to provide the Kottler solution. We also apply the original (GSGI) and the modified (GSGII) geometric scalar theo…
We consider cosmological models driven by several canonical or noncanonical scalar fields. We show how the superpotential method enables one to construct twinlike models for a particular canonical model from some noncanonical ones. We conclude that it is possible to construct twinlike models for multi-field cosmological models, even when the spatial curvature is nonzero. This work extends the discussions of [D. Bazeia and J. D. Dantas, Phys. Rev. D, 85 (2012) 067303] to cases with multi scalar fields and with non-vanished spatial curvature, by using a different superpotential method.
In this paper, we study various cosmological parameters and quantities in scalar-tensor gravity from inflation and swampland conjecture. Therefore, by selecting different models such as power-law, exponential, and logarithmic in the framework of scalar-tensor theory, we obtain potential, tensor-to-scalar ratio, and the scalar spectral index. Next, we examine new constraints and compare the corresponding results with the latest observable data. Here, we take advantage of the obtained results and determine the compatibility or incompatibility of the corresponding model with the swampland conject…
We present arguments for the existence of both globally regular and black hole solutions of the Einstein equations with a conformally coupled scalar field, in the presence of a negative cosmological constant, for space-time dimensions greater than or equal to four. These configurations approach asymptotically anti-de Sitter spacetime and are indexed by the central value of the scalar field. We also study the stability of these solutions, and show that, at least for all the solutions studied numerically, they are linearly stable.
On the basis of the relativistic kinetic theory the mathematical model of cosmological plasmas with an attraction of the like charged scalar particles is formulated. It is shown, that cosmological the model, based on a classical scalar field with an attraction, is unsatisfactory, that leads to necessity of attraction of phantom models of a scalar field for systems with an attraction.
We investigate cosmological perturbations generated during de Sitter inflation in the three-coupled scalar theory. This theory is composed of three coupled scalars ($ϕ_p,p=1,2,3$) to give a sixth-order derivative scalar theory for $ϕ_3$, in addition to tensor. Recovering the power spectra between scalars from the LCFT correlators in momentum space indicates that the de Sitter/logarithmic conformal field theory (dS/LCFT) correspondence works in the superhorizon limit. We use LCFT correlators derived from the dS/LCFT differentiate dictionary to compare cosmological correlators (power spectra) an…
We construct a scalar field based cosmological model, possessing a cosmological singularity characterized by a finite value of the cosmological radius and an infinite scalar curvature. Using the methods of the qualitative theory of differential equations, we give a complete description of the cosmological evolutions in the model under consideration. There are four classes of evolutions, two of which have finite lifetimes, while the other two undergo an infinite expansion.
We couple a neutral scalar field and a Majorana fermion field to Einstein gravity represented by the Robertson-Walker metric and find a class of exact cosmological solutions.
On the basis of Hamilton a formalism the dynamic equations of movement scalar charged particles in a classical scalar field are formulated. Unlike earlier published works of the author the model with zero own weight of particles is considered. Linear integrals of movement are found and ambiguity of communication between kinematic speed and an impulse of particles is specified.
In this paper, we investigate the Noether symmetries of a generalized scalar-tensor, Brans-Dicke type cosmological model, in which we consider explicit scalar field dependent couplings to the Ricci scalar, and to the scalar field kinetic energy, respectively. We also include the scalar field self-interaction potential into the gravitational action. From the condition of the vanishing of the Lie derivative of the gravitational cosmological Lagrangian with respect to a given vector field we obtain three cosmological solutions describing the time evolution of a spatially flat Friedman-Robertson-W…
Simple scalar field cosmological models are considered describing gravity assisted crossing of the phantom divide line. This crossing or (de)-phantomization characterized by the change of the sign of the kinetic term of the scalar field is smooth and driven dynamically by the Einstein equations. Different cosmological scenarios, including the phantom phase of matter are sketched.
The paper provides a qualitative and numerical analysis-based investigation of cosmological models founded on an asymmetrical scalar doublet comprising of a classical and a phantom scalar fields. Presence of a phantom scalar field allows one to consider also classical scalar fields with attraction of like-charged particles which significantly extends a diversity of cosmological models' behaviours. It is shown that a cosmological model based on an asymmetric scalar doublet in the case of minimal interaction has 9 singular points 2 of which are attractive and the rest are non-stable saddle ones.…
On the basis of the relativistic kinetic theory the relativistic statistical systems with scalar interaction particles are investigated. The self-consistent system of the equations describing self-gravitating plasma with interpartial scalar interaction is formulated, macroscopical laws of preservation are received. The closed system of the equations describing cosmological models to which the matter is presented by plasma with interpartial scalar interaction is received.
We study cosmological perturbations in models with a single non-local scalar field originating from the string field theory description of the rolling tachyon dynamics. We construct the equation for the energy density perturbations of the non-local scalar field and explicitly prove that for the free field it is identical to a system of local cosmological perturbation equations in a particular model with multiple (maybe infinitely many) local free scalar fields.
We study the procedure of the reconstruction of phantom-scalar field potentials in two-field cosmological models. It is shown that while in the one-field case the chosen cosmological evolution defines uniquely the form of the scalar potential, in the two-field case one has an infinite number of possibilities. The classification of a large class of possible potentials is presented and the dependence of cosmological dynamics on the choice of initial conditions is investigated qualitatively and numerically for two particular models.
In a subclass of scalar-tensor theories, it has been shown that standard general relativity solutions of neutron stars and black holes with trivial scalar field profiles are unstable. Such an instability leads to solutions which are different from those of general relativity and have non-trivial scalar field profiles, in a process called scalarization. In the present work we focus on scalarization due to a non-minimal coupling of the scalar field to the Gauss-Bonnet curvature invariant. The coupling acts as a tachyonic mass for the scalar mode, thus leading to the instability of general relati…
The Machian cosmological solution satisfying $ϕ=O(ρ/ω)$ in the generalized scalar-tensor theory of gravitation with the varying cosmological constant is summarized. The scalar field $ϕ$ with the exponential potential is introduced as dark matter and the barotropic evolution of matter in the universe is discussed. As the universe expands, the coefficient $γ$ of the equation of state approaches to -1/3 and the coupling function $ω(ϕ)$ diverges to $-\infty $.
The use of Lagrange multipliers in the context of quintessence/phantom scalar fields allows to constrain the behavior of the scalar field, which provides a powerful tool, not only for the reconstruction of cosmological solutions but also for the study of some problems in cosmology and gravitational physics. In the present paper, we focus on the reconstruction of cosmological solutions capable of controlling the cosmological constant value by imposing a constraint on the scalar field, providing a relaxation mechanism of the value of the cosmological constant. The formalism is also extended to t…
The Klein-Gordon equations were recently solved in general relativity for the case of a plane-symmetric static massless scalar field with cosmological constant. By analytic continuation, time-dependent solutions can be obtained that correspond to cosmologies. These spacetimes are studied here, and include among them a solution exhibiting both early inflation and later continued rapid expansion that matches well with the Concordance Model.
A generalized scalar-tensor theory is investigated whose cosmological term depends on both a scalar field and its time derivative. A correspondence with solutions of five-dimensional Space-Time-Matter theory is noted. Analytic solutions are found for the scale factor, scalar field and cosmological term. Models with free parameters of order unity are consistent with recent observational data and could be relevant to both the dark-matter and cosmological-"constant" problems.
We demonstrate the existence of static, spherically symmetric globally regular, i.e. solitonic solutions of a shift-symmetric scalar-tensor gravity model with negative cosmological constant. The norm of the Noether current associated to the shift symmetry is finite in the full space-time. We also discuss the corresponding black hole solutions and demonstrate that the interplay between the scalar-tensor coupling and the cosmological constant leads to the existence of new branches of solutions. To linear order in the scalar-tensor coupling, the asymptotic space-time corresponds to an Anti-de Sit…
We study cosmological dynamics of a canonical bulk scalar field in the DGP setup within a superpotential approach. We show that the normal branch of this DGP-inspired model realizes a late-time de Sitter expansion on the brane. We extend this study to the case that the bulk contains a phantom scalar field. Our detailed study in the supergravity-style analysis reveals some yet unexplored aspects of cosmological dynamics of bulk scalar field in the normal DGP setup. Some clarifying examples along with numerical analysis of the model parameter space are presented in each case.
We consider thermal effects in the propagation of gravitational waves on a cosmological background. In particular, we consider scalar field cosmologies and study gravitational modes near cosmological singularities. We point out that the contribution of thermal radiation can heavily affect the dynamics of gravitational waves giving enhancement or dissipation effects both at quantum and classical level.These effects are considered both in General Relativity and in modified theories like $F(R)$ gravity which can be easily reduced to scalar-tensor cosmology. The possible detection and disentanglem…
A mathematical model of the evolution of plane perturbations in the cosmological statistical system of completely degenerated scalar-charged fermions with the Higgs scalar interaction is formulated. A complete closed system of differential equations describing the unperturbed state of a homogeneous and isotropic system and a system of self-consistent equations describing the evolution of small perturbations are constructed.
We study the cosmological evolution and singularity crossing in the Bianchi-I universe filled with a conformally coupled scalar field and compare them with those of the Bianchi-I universe filled with a minimally coupled scalar field. We also write down the solution for the Bianchi-I Universe in the induced gravity cosmology.
The exact solutions of Einstein - Yang - Mills and interacting with SO (3) - Yang-Mills field nonlinear scalar field equations in a class of spatially homogeneous cosmological Friedmann models are obtained.
The method of consistent potentials is used to explain how a minimally coupled (classical) scalar field can suppress Mixmaster oscillations in the approach to the singularity of generic cosmological spacetimes.
In this paper we present the study of the scalar cosmological perturbations of a single field inflationary model up to first order in deviation. The Christoffel symbols and the tensorial quantities are calculated explicitly in function of the cosmic time t. The Einstein equations are solved up-to first order in deviation and the scalar perturbations equation is derived.
The solutions of the field equations of the conformal theory of gravitation with Dirac scalar field in Weyl-Cartan spacetime in very early universe are obtained. In this theory dark energy (describing by an effective cosmological constant) is a function of the Dirac scalar field $β$. These solutions describe the exponential decreasing of $β$ at the first exponential stage of inflation. One of these solutions has a limit to a constant value of the dark energy at large time that can give a way to solving the fundamental cosmological constant problem as a consequence of the fields dynamics in the…
A mathematical model is formulated for the evolution of plane perturbations in a cosmological two-component statistical system of completely degenerate scalarly charged fermions with an asymmetric scalar Higgs interaction. A complete closed system of differential equations describing the unperturbed state of a homogeneous and isotropic system and a system of self-consistent evolution equations of small perturbations are constructed.
Based on the mathematical model of a statistical system with scalar interaction of fermions formulated earlier, a cosmological model based on a two-component statistical system of scalar charged degenerate fermions interacting with an asymmetric scalar doublet, canonical and phantom scalar fields, is investigated. The asymptotic and limiting properties of the cosmological model are investigated, and it is shown that among all models there is a class of models with a finite lifetime. The asymptotic behavior of models near the corresponding singularities is investigated and numerical implementat…
In this paper we investigate the asymptotic behavior of the cosmological model based on phantom scalar field on the ground of qualitative analysis of the system of the cosmological model's differential equations and show that as opposed to models with classical scalar field, such models have stable asymptotic solutions with constant value of the potential both in infinite past and infinite future. We also develop numerical models of the cosmological evolution models with phantom scalar field in this paper. {\bf keywords}: cosmological model, phantom scalar field, quality analysis, asymptotic b…
We study evolution of cosmological models filled with the scalar field and barotropic matter. We consider the scalar field minimally and non-minimally coupled to gravity. We demonstrated the growth of degree of complexity of evolutional scenario through the description of matter content in terms of the scalar field. In study of all evolutional paths for all initial conditions methods of dynamical systems are used. Using linearized solutions we present simple method of derivation corresponding form of the Hubble function of the scale factor $H(a)$.
We present new cosmological parameter constraints for general Horndeski scalar-tensor theories, using CMB, redshift space distortion, matter power spectrum and BAO measurements from the Planck, SDSS/BOSS and 6dF surveys. We focus on theories with cosmological gravitational waves propagating at the speed of light, $c_{\rm GW} = c$, implementing and discussing several previously unaccounted for aspects in the constraint derivation for such theories, that qualitatively affect the resulting constraints. In order to ensure our conclusions are robust, we compare results for three different parametri…
Scalar-tensor gravitational theories are important extensions of standard general relativity, which can explain both the initial inflationary evolution, as well as the late accelerating expansion of the Universe. In the present paper we investigate the cosmological solution of a scalar-tensor gravitational theory, in which the scalar field $ϕ$ couples to the geometry via an arbitrary function $F(ϕ$). The kinetic energy of the scalar field as well as its self-interaction potential $V(ϕ)$ are also included in the gravitational action. By using a standard mathematical procedure, the Lie group app…
In this paper, we analyze a simple class of Horndeski scalar-tensor theory. We investigate several cosmological solutions for inflation, bounce scenario and finite future-time singuarities. Perturbations respect to Friedmann-Robertson-Walker metric are studied and discussed in the context of inflation.
Based on the proposed earlier by the Author approach to macroscopic description of scalar interaction, this paper develops the macroscopic model of relativistic plasma with a fantom scalar interaction of elementary particles. In the article the macroscopic equations for a statistical system with scalar interaction of particles are obtained and the complete set of macroscopic equations describing cosmological models is built.
We provide the correspondence between the variables in the Jordan frame and those in the Einstein frame in scalar-tensor gravity and consider the frame-(in)dependence of the cosmological observables. In particular, we show that the cosmological observables/relations (redshift, luminosity distance, temperature anisotropies) are frame-independent. We also study the frame-dependence of curvature perturbations and find that the curvature perturbations are conformal invariant if the perturbation is adiabatic and the entropy perturbation between matter and the Brans-Dicke scalar is vanishing. The re…
The equations of the conformal field theory of gravitation with the Dirac's scalar field in Weyl-Cartan spacetime have been received. Exact solutions for Dirac's scalar field for an early Universe have been derived. Intensive decrease of physical vacuum energy (dark energy) is obtained with the Dirac's scalar field as the effective cosmological "constant".
We explore dynamics of cosmological models with bounce solutions evolving on a spatially flat Friedmann-Lemaitre-Robertson-Walker background. We consider cosmological models that contain the Hilbert-Einstein curvature term, the induced gravity term with a negative coupled constant, and even polynomial potentials of the scalar field. Bounce solutions with non-monotonic Hubble parameters have been obtained and analyzed. The case when the scalar field has the conformal coupling and the Higgs-like potential with an opposite sign is studied in detail. In this model the evolution of the Hubble param…
Continuing the investigation of the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity we study an influence of the cosmological constant on the behaviour of trajectories in closed minisuperspace Friedmann-Robertson-Walker model. The transition from chaotic to regular behaviour for large values of cosmological constant is discussed. Combining numerical calculations with qualitative analysis both in configuration and phase space we present a convenient classification of trajectories.
We study whether it is possible to design a "classical" spatially flat bouncing cosmology or a static, spherically symmetric asymptotically flat Lorentzian wormhole in cubic Galileon theories interacting with an extra scalar field. We show that bouncing models are always plagued with gradient instabilities, while there are always ghosts in wormhole backgrounds.
The possibility that the universe may have a fundamental and positive cosmological constant has motivated an interesting cosmological model, in which initially the universe is in a cosmological constant sea, then the local quantum fluctuations violating the null energy condition create some islands with matter and radiation, which under certain conditions might corresponds to our observable universe. We in this note study the perturbation spectra of scalar fields not affecting the evolution of background during the fluctuation. We will examine whether they can be interesting, and responsible f…
In order to give the standard scenario of the astrophysics, we study the Einstein theory with minimally coupled scalar field and the cosmological term by considering the scalar field as a candidate of the dark matter. We obtained the exact solution in the cosmological scale and the approximate gravitational potential in the galactic or solar scale. We find that the scalar field plays the role of the dark matter in some sense in the cosmological scale but it does not play the role of the dark matter in the galactic or solar scale within our approximation.
We study the qualitative properties of cosmological models in scalar-tensor theories of gravity by exploiting the formal equivalence of these theories with general relativity minimally coupled to a scalar field under a conformal transformation and field redefinition. In particular, we investigate the asymptotic behaviour of spatially homogeneous cosmological models in a class of scalar-tensor theories which are conformally equivalent to general relativistic Bianchi cosmologies with a scalar field and an exponential potential whose qualitative features have been studied previously. Particular a…
