Local and global phase-space descriptions and averaging methods are used to find qualitative features of solutions for the FLRW and the Bianchi I metrics in the context of scalar field cosmologies with arbitrary potentials and arbitrary couplings to matter. The stability of the equilibrium points in a phase-space as well as the dynamics in the regime where the scalar field diverges are studied. Equilibrium points that represent some solutions of cosmological interest such as: several types of scaling solutions, a kinetic dominated solution representing a stiff fluid, a solution dominated by an effective energy density of geometric origin, a quintessence scalar field dominated solution, the vacuum de Sitter solution associated to the minimum of the potential, and a non-interacting matter dominated solution are obtained. All reveal a very rich cosmological phenomenology.
We show that several integrable (i.e., exactly solvable) scalar cosmologies considered by Fré, Sagnotti and Sorin (Nuclear Physics \textbf{B 877}(3) (2013), 1028--1106) can be generalized to include cases where the spatial curvature is not zero and, besides a scalar field, matter or radiation are present with an equation of state $p^{(m)} = w\, ρ^{(m)}$; depending on the specific form of the self-interaction potential for the field, the constant $w$ can be arbitrary or must be fixed suitably.
Phase-space descriptions are used to find qualitative features of the solutions of generalized scalar field cosmologies with arbitrary potentials and arbitrary couplings to matter. Previous results are summarized and new ones are presented as theorems, which include the previous ones as corollaries. Examples of these results are presented as well as counterexamples when the hypotheses of the theorems are not fulfilled. Potentials with small cosine-like corrections motivated by inflationary loop-quantum cosmology are discussed. Finally, the Hubble-normalized formulation for the FRW metric and f…
A frame representation is used to derive a first order quasi-linear symmetric hyperbolic system for a scalar field minimally coupled to gravity. This procedure is inspired by similar evolution equations introduced by Friedrich to study the Einstein-Euler system. The resulting evolution system is used to show that small nonlinear perturbations of expanding Friedman-Lemaître-Robertson-Walker backgrounds, with scalar field potentials satisfying certain future asymptotic conditions, decay exponentially to zero, in synchronous time.
In this paper, we use both local and global phase-space descriptions and averaging methods to find qualitative features of solutions for the FLRW and Bianchi I metrics in the context of scalar field cosmologies with arbitrary potentials and arbitrary couplings to matter. We prove new theorems and also retrieve previous results that can be seen as corollaries of the present results. We study the stability of the equilibrium points in a phase-space, as well as the dynamics in the regime where the scalar field diverges. We obtain equilibrium points that represent some solutions of cosmological in…
Scalar field cosmologies with a generalized harmonic potential are investigated in flat and negatively curved Friedmann-Lemaître-Robertson-Walker and Bianchi I metrics. An interaction between the scalar field and matter is considered. Asymptotic methods and averaging theory are used to obtain relevant information about the solution space. In this approach, the Hubble parameter plays the role of a time-dependent perturbation parameter which controls the magnitude of the error between full-system and time-averaged solutions as it decreases. Our approach is used to show that full and time-average…
We investigate a mechanism that generates the exact solutions of scalar field cosmologies in a unified way. The procedure investigated here permits to recover allmost all known solutions, and allows one to derive new solutions as well. In particular, we derive and discuss one novel solution defined in terms of the Lambert function. The solutions are organized in a classification which depends on the choice of a generating function which we have denoted by $x(ϕ)$ that reflects the underlying thermodynamics of the model. We also analyse and discuss the existence of form invariances and dualities…
We analyse spacetimes with a conformal scalar field source, a cosmological constant and a quartic self-interaction term for the scalar field. We also consider additional matter contents in the form of Maxwell and Yang-Mills fields or radiation fluids. Existence theorems for weakly asymptotically flat spacetimes are given. We give a generalisation of Bekenstein's result [Ann. Phys. 82, 535 (1974)] and use it to derive existence theorems for spacetimes that contain an isotropic singularity. The results are combined to suggest a mathematical setup for Penrose's CCC scenario using a conformal scal…
We revisit a general minisuperspace (MSS) formalism for scalar-tensor (ST) FLRW type cosmological models in arbitrary frame with perfect fluid source. We discuss how to impose Cauchy data on the corresponding dynamical system in order to reconstruct standard (ΛCDM) cosmological model. So far, the integrability of such models has been extensively studied in the Einstein or Jordan frames mainly. We extend these studies to arbitrary frame taking into account non-minimal coupling between matter and gravity. To this aim we explore a gauge freedom associated with a choice of lapse function. We show …
We study general dynamical equations describing homogeneous isotropic cosmologies coupled to a scalaron $ψ$. For flat cosmologies ($k=0$), we analyze in detail the gauge-independent equation describing the differential, $χ(α)\equivψ^\prime(α)$, of the map of the metric $α$ to the scalaron field $ψ$, which is the main mathematical characteristic locally defining a `portrait' of a cosmology in `$α$-version'. In the `$ψ$-version', a similar equation for the differential of the inverse map, $\barχ(ψ)\equiv χ^{-1}(α)$, can be solved asymptotically or for some `integrable' scalaron potentials $v(ψ)$…
Scalar-tensor theories are frequently only consistent with fifth force constraints in the presence of a screening mechanism, namely in order to suppress an otherwise unacceptably large coupling between the scalar and ordinary matter. Here we investigate precisely which subsets of Horndeski theories do not give rise to and/or require such a screening mechanism. We investigate these subsets in detail, deriving their form and discussing how they are restricted upon imposing additional bounds from the speed of gravitational waves, solar system tests and cosmological observables. Finally, we also i…
In this work we investigate the duality linking standard and tachyon scalar field cosmologies. We determine the transformation between standard and tachyon scalar fields and between their associated potentials, corresponding to the same background evolution. We show that, in general, the duality is broken at a perturbative level, when deviations from a homogeneous and isotropic background are taken into account. However, we find that for slow-rolling fields the duality is still preserved at a linear level. We illustrate our results with specific examples of cosmological relevance, where the co…
We study the two particular models of g-essence with Yukawa type interactions between a scalar field $ϕ$ and a classical Dirac field $ψ$. For the homogeneous, isotropic and flat Friedmann-Robertson-Walker universe filled with the such g-essence, some exact solutions of these models are found. Moreover, we reconstruct the corresponding scalar and fermionic potentials.
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for the Locally Rotationally Symmetric (LRS) Bianchi I and flat Friedmann-Lemaître-Robertson-Walker (FLRW) metrics are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, the simplest time-averaged system determines the future asymptotic behavior. Depending on the values of $γ$, th…
We propose a new reconstruction method for scalar--tensor gravity based on the use of conformal transformations. The new method allows the derivation of a set of interesting exact cosmological solutions in brans Dicke gravity as well as other extensions of General Relativity.
We discuss the particle horizon problem in the framework of spatially homogeneous and isotropic scalar cosmologies. To this purpose we consider a Friedmann-Lemaitre-Robertson-Walker (FLRW) spacetime with possibly non-zero spatial sectional curvature (and arbitrary dimension), and assume that the content of the universe is a family of perfect fluids, plus a scalar field that can be a quintessence or a phantom (depending on the sign of the kinetic part in its action functional). We show that the occurrence of a particle horizon is unavoidable if the field is a quintessence, the spatial curvature…
We calculate the running of the scalar index in the ekpyrotic and matter bounce cosmological scenarios, and find that it is typically negative for ekpyrotic models, while it is typically positive for realizations of the matter bounce where multiple fields are present. This can be compared to inflation, where the observationally preferred models typically predict a negative running. The magnitude of the running is expected to be between $10^{-4}$ and up to $10^{-2},$ leading in some cases to interesting expectations for near-future observations.
We solve isotropic, homogeneous cosmological models containing a self-interacting scalar field. Calculations are performed in four and two-dimensional spacetimes. We find several exact solutions that have an inflationary regime or has a final Friedmann stage. Also their asymptotically stability is studied.
In this contribution we summarize two recent applications of a correspondence between backreaction terms in averaged inhomogeneous cosmologies and an effective scalar field (the `morphon'). Backreaction terms that add to the standard sources of Friedmannian kinematical laws and that emerge from geometrical curvature invariants built from inhomogeneities, can be interpreted in terms of a minimally coupled scalar field in the case of a dust matter source. We consider closure conditions of the averaged equations that lead to different evolution scenarii: a) the standard Chaplygin equation of stat…
Scalar field cosmologies with a generalized harmonic potential and a matter fluid with a barotropic Equation of State (EoS) with barotropic index $γ$ for Locally Rotationally Symmetric (LRS) Bianchi III metric and open Friedmann-Lemaître-Robertson-Walker (FLRW) metric are investigated. Methods from the theory of averaging of nonlinear dynamical systems are used to prove that time-dependent systems and their corresponding time-averaged versions have the same late-time dynamics. Therefore, simple time-averaged systems determine the future asymptotic behavior. Depending on values of barotropic in…
We derive a set of equations monitoring the evolution of covariant and gauge-invariant linear scalar perturbations of Friedman-Lemaître-Robertson-Walker models with multiple interacting non-linear scalar fields. We use a dynamical systems' approach in order to perform a stability analysis for some classes of scalar field potentials. In particular, using a recent approximation for the inflationary dynamics of the background solution, we derive conditions under which homogenization occurs for chaotic (quadratic and quartic potentials) and new inflation. We also prove a cosmic no-hair result for …
We analyse spatially homogenous cosmological models of locally rotationally symmetric Bianchi type III with a massive scalar field as matter model. Our main result concerns the future asymptotics of these spacetimes and gives the dominant time behaviour of the metric and the scalar field for all solutions for late times. This metric is forever expanding in all directions, however in one spatial direction only at a logarithmic rate, while at a power-law rate in the other two. Although the energy density goes to zero, it is matter dominated in the sense that the metric components differ qualitat…
Regular bouncing solutions in the framework of a scalar-tensor gravity model were found in a recent work. We reconsider the problem in the Einstein frame (EF) in the present work. Singularities arising at the limit of physical viability of the model in the Jordan frame (JF) are either of the Big Bang or of the Big Crunch type in the EF. As a result we obtain integrable scalar field cosmological models in general relativity (GR) with inverted double-well potentials unbounded from below which possess solutions regular in the future, tending to a de Sitter space, and starting with a Big Bang. The…
We build a number of integrable one--scalar spatially flat cosmologies, which play a natural role in inflationary scenarios, examine their behavior in several cases and draw from them some general lessons on this type of systems, whose potentials involve combinations of exponential functions, and on similar non--integrable ones. These include the need for the scalar to emerge from the initial singularity while climbing up sufficiently steep exponential potentials ("climbing phenomenon") and the inevitable collapse in a big Crunch whenever the scalar tries to settle at negative extrema of the p…
