Truman Tapia, Clara Rojas
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.
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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.
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.
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.
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 $.
Charged, rotating black hole solutions of Einstein's gravitational equations are investigated in the presence of a cosmological constant. A pair of wave equations governing the electromagnetic and gravitational perturbations are derived.
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.
Adiabatic perturbations propagate in the expanding universe like scalar massless fields in some effective Robertson-Walker space-time.
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 investigate the large scale cosmological perturbation in the Universe with multiple perfect fluids. Using the long-wavelength approximation with Hamilton-Jacobi method, we derive the formula for the gauge invariant comoving curvature perturbation. As an application of our approach, we examine the large scale perturbation in a brane 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.
Evolution of spherical perturbations in the cosmological environment of the Higgs scalar field and an ideal scalar charged fluid
本文构建含希格斯标量相互作用的宇宙学理想标量荷流体球对称扰动模型，揭示奇点处扰动特性及稳定性对扰动形态的影响，数值模拟验证分层晕形成。
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…
We present the dynamical analysis for interacting quintessence, considering linear cosmological perturbations. Matter perturbations improve the background analysis and viable critical points describing the transition of the three cosmological eras are found. The stability of those fixed points are similar to previous studies in the literature, for both coupled and uncoupled cases, leading to a late-time attractor.
In this paper, a specific solution to the second-order cosmological perturbation theory is given. Perturbations are performed around any FLRW spacetime filled with dust and with a positive cosmological constant. In particular, with a possibly non-vanishing spatial curvature. The adopted symmetry condition allows us to simplify the equations, leaving us with a great deal of freedom to choose the density distribution. In the result, we get a relatively simple metric of an inhomogeneous cosmological model, which will give a perfect tool for studying the influence of the local inhomogeneities onto…
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 construct explicit solutions for scalar, vector and tensor perturbations in a less known setting, a flat universe filled by an isotropic elastic solid with pressure and shear modulus proportional to energy density. The solutions generalize the well known formulas for cosmological perturbations in a universe filled by ideal fluid.
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 describe the fully gauge invariant cosmological perturbation equations in braneworld teleparallel gravity. In this theory, perturbations are the result of small fluctuations in the pentad field. We derive the gauge invariant 'potentials' for both geometric and matter variables. Unlike the metric fluctuations in general relativity, pentad perturbations can only contain scalar and vector modes. As a result, in teleparallel gravity, tensor modes including gravitational waves, come from the contortion tensor.
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".
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.
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…
We develop a technique for the reconstruction of the potential for a scalar field or a tachyon field, reproducing a given cosmological evolution in a closed and open isotropic cosmological models. Such potentials are explicitly written down for the cases of the evolutions driven by a generic barotropic fluid and by radiation plus a cosmological constant, for the case of a scalar field. For tachyon and pseudo-tachyon fields the potentials are reconstructed for some special cases, corresponding to particular values of the barotropic index.
The global behavior of scalar field cosmological models with very hard potential walls is investigated via the simple example of an exponentially steep potential well. It is found that the solutions exhibit a non-trivial oscillatory behavior in the approach to an initial space-time singularity. This behavior can be interpreted as being due to the inability of the scalar field to negotiate the walls of the steep potential well.
A complete cosmological evolution model of the classical scalar field with a Higgs potential is studied and simulated on a computer without the assumption that the Hubble constant is nonnegative. It is shown that with most initial conditions, the cosmological model goes from the expansion stage to the compression stage. Thus, cosmological models based on the classical Higgs field are unstable to finite perturbations.
In this brief note we present a set of equations describing the evolution of perturbed scalar fields in a cosmological spacetime with multiple scalar fields. We take into account of the simultaneously excited full metric perturbations in the context of the uniform-curvature gauge which is known to be the best choice. The equations presented in a compact form will be useful for handling the structure formation processes under the multiple episodes of inflation.
Reconstruction the scalar-torsion gravity version from the frame of exact cosmological solutions
本文研究了基于标量-扭力引力的宇宙学模型，通过观测约束确定了扭力与标量场的非最小耦合类型，并证明此类暴胀模型可通过观测验证。
Cosmological perturbations on a manifold admitting signature change are studied. The background solution consists in a Friedmann-Lemaitre-Robertson- Walker (FLRW) Universe filled by a constant scalar field playing the role of a cosmological constant. It is shown that no regular solution exist satisfying the junction conditions at the surface of change. The comparison with similar studies in quantum cosmology is made.
In this paper we generalize our previous results on spin connection for the linear scalar cosmological perturbation in $f(T)$ theory to wider class of theories which includes a scalar field $Φ$ non-minimally coupled to torsion, and allows $Φ$-dependence of the function $f$. The case of $f_{TT}=0$, with a scalar field non-minimally coupled to torsion needs a special treatment. In both considered cases we derive self-consistent equations of motion for cosmological perturbation using a solution for non-trivial spin connection.
The 2+1-dimensional geodesic circularly symmetric solutions of Einstein-massless-scalar field equations with negative cosmological constant are found and their local and global properties are studied. It is found that one of them represents gravitational collapse where black holes are always formed.
This is the fourth paper in a series of four in which we use space adiabatic methods in order to incorporate backreactions among the homogeneous and between the homogeneous and inhomogeneous degrees of freedom in quantum cosmological perturbation theory. In this paper, we finally consider the gauge invariant scalar (Mukhanov-Sasaki) and tensor (primordial gravitational wave) inhomogeneous perturbations of General Relativity coupled to an inflaton field which arise from a careful constraint analysis of this system up to second order in the perturbations. The simultaneous quantisation of the hom…
Renormalized cosmological models based on the general-relativistic second-order perturbation theory were proposed in the previous papers to solve a tension on the observed Hubble constants. The cosmological random adiabatic fluctuations were found to play an important role as the first-order perturbations. The second-order metric perturbations in a previous paper are revised in the present paper. It is shown as a result that two types of Hubble constants (the kinematic constant H_kin and the dynamic constant H_dyn) are derived, and their values are found to be comparable, and larger than the b…
The article represents a research of the cosmological evolution of fermion statistical systems with fantom scalar interaction where "kinetic" term's contribution to the total energy of a scalar field is negative. As a result of analytical and numerical simulation of such systems it has been revealed a existence of four possible scenarios depending on parameters of the system and initial conditions. Among these scenarios there are scenarios with an early, intermediate and late non-relativistic stages of the cosmological evolution, all of which also have necessary inflation stage.
The solution to the current extending Universe problem, and the description of all stages of evolution compels scientists to consider various cosmological models. Scalar - tensor models are rather simple and also allow us to clearly define the separate stages of evolution. Furthermore, other cosmological models are reduced. Our work takes into consideration the non-minimally interacted scalar field and the spinor field. The spinor field has been considered to establish a better understanding of the stages of evolution in our Universe.
The stability of the cosmological event horizons (CEHs) of a class of non-static global cosmic strings is studied against perturbations of gravitational waves and massless scalar field. It is found that the perturbations of gravitational waves always turn the CEHs into non-scalar weak spacetime curvature singularities, while the ones of massless scalar field turn the CEHs either into non-scalar weak singularities or into scalar ones depending on the particular cases considered. The perturbations of test massless scalar field is also studied, and it is found that they do not always give the cor…
Scalar and tensor cosmological perturbations during an inflationary universe scenario in the context of the a generalized gravity theory are studied. This analyze is carried out considering an ansatz on the variables associated to scalar and tensor perturbation ($z_s$ and $z_t$) in the Jordan frame. In this context, we analyze two different Ansatze for the ratio $z_s/z_t$, and we study in great detail the analytical and exact solutions for the cosmological perturbations together with the corresponding reconstruction of the background variables. Recent observational data from the Planck 2018 re…
We present a gauge invariant argument that a nonlocal measure of second-order metric and matter perturbations dominate that of linear fluctuations in its effect on the gravitational field in 'slow-rolling' spacetimes.
We investigate the simplest cosmological model with the massive real scalar non-interacting inflaton field minimally coupled to gravity. The classification of trajectories in closed minisuperspace Friedmann-Robertson-Walker model is presented.The fractal nature of a set of infinitely bounced trajectories is discussed. The results of numerical calculations are compared with those obtained byperturbative analytical calculations around the exactly solvable minisuperspace cosmological model with massless scalar field.
On the basis of the qualitative analysis and numerical simulation of cosmological models with classical and phantom scalar fields with self-action there have been revealed and refined such models' distinctive features and potential possibilities for their usage as basic models in cosmology.
We reconstruct the field potentials in case of (non)phantom fields for different models resulting from parametrization of q(t), a(t) or H(t). In addition we carry out similar procedure for tachyonic field. We also discuss specific form of parametrization for reconstruction of scalar field potential.
We study the scalar curvature of spacelike hypersurfaces in the family of cosmological models known as generalized Robertson-Walker spacetimes, and give several rigidity results under appropriate mathematical and physical assumptions. On the other hand, we show that this family of spacetimes provides suitable models obeying the null convergence condition to explain accelerated expanding universes.
In this paper we present a new formulation of the change of gauge formulas in second order cosmological perturbation theory which unifies and simplifies known results. Our approach is based on defining new second order scalar perturbation variables by adding a multiple of the square of the corresponding first order variables to each second order variable. A bonus is that these new perturbation variables are of broader significance in that they also simplify the analysis of second order scalar perturbations in the super-horizon regime in a number of ways, and lead to new conserved quantities.
The solution of the field equations of the conformal theory of gravitation with Dirac scalar field in Cartan-Weyl spacetime at the very early Universe is obtained. In this theory dark energy (describing by an effective cosmological constant) is a function of the Dirac scalar field $β$. This solution describes the exponential decreasing of $β$ at the inflation stage and has a limit to a constant value of the dark energy at large time. This can give a way to solving the fundamental cosmological constant problem as a consequence of the fields dynamics in the early Universe.
We consider a scalar field with a negative kinetic term minimally coupled to gravity. We obtain an exact non-static spherically symmetric solution which describes a wormhole in cosmological setting. The wormhole is shown to connect two homogeneous spatially flat universes expanding with acceleration. Depending on the wormhole's mass parameter $m$ the acceleration can be constant (the de Sitter case) or infinitely growing.
We investigate cosmological models in a recently proposed geometrical theory of gravity, in which the scalar field appears as part of the space-time geometry. We extend the previous theory to include a scalar potential in the action. We solve the vacuum field equations for different choices of the scalar potential and give a detailed analysis of the solutions. We show that in some cases a cosmological scenario is found that seems to suggest the appearance of a geometric phase transition. We build a toy model, in which the accelerated expansion of the early universe is driven by pure geometry.
With the help of our own software package DifEqTools, numerical modeling of the cosmological evolution of a system consisting of an asymmetric scalar doublet of nonlinear, minimally interacting scalar fields, a classical field and a phantom field, has been performed. Peculiarities of the behavior of the model near zeroenergy hypersurfaces have been revealed.
We study the influence of reheating on super-horizon density perturbations and gravitational waves. We correct wrong claims [L. P. Grishchuk Phys. Rev. D 50, 7154 (1994) and gr-qc/9801011] about the joining of perturbations at cosmological transitions and about the quantization of cosmological perturbations.
Perturbation theory within Newtonian approximation is presented for cosmological models with varying physical constants. Analytical solutions for perturbations dynamics are obtained for each Gurzadyan-Xue model with pressureless matter and radiation. We found that perturbations grow during entire expansion within GX models, including curvature- and vacuum-dominated stage when they cease to grow in the standard cosmological model.
Cosmological solutions of Einstein's equations for equilibrium statistical systems of particles with scalar interaction are investigated. It is shown that the scalar field can effectively change the state equation of a statistical system, that leads to the possibility of secondary acceleration of the cosmological expansion.
The background dynamical evolution of a universe filled with matter and a cosmological scalar field is analyzed employing dynamical system techniques. After the phenomenology of a canonical scalar field with exponential potential is revised, square and square root kinetic corrections to the scalar field canonical Lagrangian are considered and the resulting dynamics at cosmological distances is obtained and studied. These noncanonical cosmological models imply new interesting phenomenology including early time matter dominated solutions, cosmological scaling solutions and late time phantom domi…
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.
Using the existence of a covariant conserved quantity on large perturbation scales in a spatially flat perfect fluid or scalar field universe, we present a general formula for gauge-invariantly defined comoving energy density perturbations which encodes the entire linear perturbation dynamics in a closed time integral. On this basis we discuss perturbation modes in different cosmological epochs.
The averaging problem in cosmology is of considerable importance for the correct interpretation of cosmological data. A rigorous mathematical definition of averaging in a cosmological model is necessary. In general, a spacetime is completely characterized by its scalar curvature invariants, and this suggests a particular spacetime averaging scheme based entirely on scalars. We clearly identify the problems of averaging in a cosmological model. We then present a precise definition of a cosmological model, and based upon this definition, we propose an averaging scheme in terms of scalar curvatur…
We study the pure and thermal states of quantized scalar and tensor perturbations in various epochs of Universe evolution. We calculate the density matrix of non-relativistic particles in an environment of these perturbations. We show that particle's motion can be described by a stochastic equation with a noise coming from the cosmological environment. We investigate the squeezing of Gaussian wave packets in different epochs and its impact upon the noise of quantized cosmological perturbations.
We show that at second order in cosmological perturbation theory vorticity generation is sourced by entropy gradients. This is an extension of Crocco's theorem to a cosmological setting.
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