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-averaged systems have the same asymptotic behavior. Numerical simulations are presented as evidence of such behavior. Moreover, the asymptotic behavior of the solutions is independent of the coupling function.
We find the group of symmetry transformations generated by interacting fluids in spatially flat Friedmann-Robertson-Walker (FRW) spacetime which links cosmologies with the same scale factor {\it (identity)} or with scale factors $a$ and $a^{-1}$ {\it (duality)}. There exists a duality between contracting and superaccelerated expanding scenarios associated with {\it (phantom)} cosmologies. We investigate the action of this symmetry group on self-interacting minimally(conformally) coupled quintessence and $k$-essence cosmologies.
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 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 paper we show that by considering a universe dominated by two interacting components a superaccelerated expansion can be obtained from a decelerated one by applying a dual transformation that leaves the Einstein's field equations invariant.
Exact models for Bianchi VI0 spacetimes with multiple scalar fields with exponential potentials have been derived and analysed. It has been shown that these solutions, when they exist, attract neighbouring solutions in the two cases corresponding to interacting and non-interacting fields. Unlike the results obtained in a previous work dealing with the late-time inflationary behaviour of Bianchi VI0 cosmologies, the knowledge of exact solutions has made possible to study in detail the occurrence of inflation before the asymptotic regime. As happened in preceding works, here as well inflation is…
It is well known that Kasner-type cosmologies provide a useful framework for analyzing the three-dimensional anisotropic expansion because of the simplification of the anisotropic dynamics. In this paper relativistic multi-fluid Kasner-type scenarios are studied. We first consider the general case of a superposition of two ideal cosmic fluids, as well as the particular cases of non-interacting and interacting ones, by introducing a phenomenological coupling function $q(t)$. For two-fluid cosmological scenarios there exist only cosmological scaling solutions, while for three-fluid configuration…
It is shown that the dynamics of cosmologies sourced by a mixture of perfect fluids and self-interacting scalar fields are described by the non-linear, Ermakov-Pinney equation. The general solution of this equation can be expressed in terms of particular solutions to a related, linear differential equation. This characteristic is employed to derive exact cosmologies in the inflationary and quintessential scenarios. The relevance of the Ermakov-Pinney equation to the braneworld scenario is discussed.
For space-times with two spacelike isometries, we present infinite hierarchies of exact solutions of the Einstein and Einstein--Maxwell equations as represented by their Ernst potentials. This hierarchy contains three arbitrary rational functions of an auxiliary complex parameter. They are constructed using the so called `monodromy transform' approach and our new method for the solution of the linear singular integral equation form of the reduced Einstein equations. The solutions presented, which describe inhomogeneous cosmological models or gravitational and electromagnetic waves and their in…
We study the dynamics near finite-time singularities of flat isotropic universes filled with two interacting but otherwise arbitrary perfect fluids. The overall dynamical picture reveals a variety of asymptotic solutions valid locally around the spacetime singularity. We find the attractor of all solutions with standard decay, and for `phantom' matter asymptotically at early times. We give a number of special asymptotic solutions describing universes collapsing to zero size and others ending at a big rip singularity. We also find a very complicated singularity corresponding with a logarithmic …
We present a phase-space analysis of the qualitative dynamics cosmologies where dark matter exchanges energy with the vacuum component. We find fixed points corresponding to power-law solutions where the different components remain a constant fraction of the total energy density and given an existence condition for any fixed points with nonvanishing energy transfer. For some interaction models we find novel fixed points in the presence of a third noninteracting fluid with constant equation of state, such as radiation, where the interacting vacuum+matter tracks the evolution of the third fluid,…
We investigate the case of two interacting fluids in homogeneous and isotropic cosmologies with a non-linear interaction term. The interaction term avoids the unrealistic form generally used in the literature, beginning with Tolman, in which the interaction is zero when the Hubble parameter vanishes. A variety of exact solutions for the scale factor are found and describe a range of new behaviors. We also extend the analysis of possible cosmological solutions with interacting fluids when curvature is taken into consideration. We use an example of energy exchange between radiation and scalar fi…
In this paper we explore possible extensions of Interacting Dark Energy cosmologies, where Dark Energy and Dark Matter interact non-gravitationally with one another. In particular, we focus on the neutrino sector, analyzing the effect of both neutrino masses and the effective number of neutrino species. We consider the Planck 2018 legacy release data combined with several other cosmological probes, finding no evidence for new physics in the dark radiation sector. The current neutrino constraints from cosmology should be therefore regarded as robust, as they are not strongly dependent on the da…
We define the flatness and quasi-flatness problems in cosmological models. We seek solutions to both problems in homogeneous and isotropic Brans-Dicke cosmologies with varying speed of light. We formulate this theory and find perturbative, non-perturbative, and asymptotic solutions using both numerical and analytical methods. For a particular range of variations of the speed of light the flatness problem can be solved. Under other conditions there exists a late-time attractor with a constant value of Ωthat is smaller than, but of order, unity. Thus these theories may solve the quasi-flatness p…
We study Bianchi I type brane cosmologies with scalar matter self-interacting through combinations of exponential potentials. Such models correspond in some cases to inflationary universes. We discuss the conditions for accelerated expansion to occur, and pay particular attention to the influence of extra dimensions and anisotropy. Our results show that the associated effects evolve in such a way that they become negligible in the late time limit, those related to the anisotropy disappearing earlier. This study focuses mainly on single field models, but we also consider a generalization yieldi…
We study the observational viability of coupled quintessence models with their expansion and growth histories matched to modified gravity cosmologies. We find that for a Dvali-Gabadadze-Porrati model which has been fitted to observations, the matched interacting dark energy models are observationally disfavoured. We also study the distinguishability of interacting dark energy models matched to scalar-tensor theory cosmologies and show that it is not always possible to find a physical interacting dark energy model which shares their expansion and growth histories.
Up-to-date cosmological data analyses have shown that \textit{(a)} a closed universe is preferred by the Planck data at more than $99\%$ CL, and \textit{(b)} interacting scenarios offer a very compelling solution to the Hubble constant tension. In light of these two recent appealing scenarios, we consider here an interacting dark matter-dark energy model with a non-zero spatial curvature component and a freely varying dark energy equation of state in both the quintessential and phantom regimes. When considering Cosmic Microwave Background data only, a phantom and closed universe can perfectly …
We present a new generating algorithm to construct exact non static solutions of the Einstein field equations with two-dimensional inhomogeneity. Infinite dimensional families of $G_1$ inhomogeneous solutions with a self interacting scalar field, or alternatively with perfect fluid, can be constructed using this algorithm. Some families of solutions and the applications of the algorithm are discussed.
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…
We investigate in detail the qualitative behaviour of the class of Bianchi type B spatially homogeneous cosmological models in which the matter content is composed of two non-interacting components; the first component is described by a barotropic fluid having a gamma-law equation of state, whilst the second is a non-interacting scalar field (phi) with an exponential potential V=Lambda exp(k phi). In particular, we study the asymptotic properties of the models both at early and late times, paying particular attention on whether the models isotropize (and inflate) to the future, and we discuss …
Several isotropic, homogeneous cosmological models containing a self-interacting minimally coupled scalar field, a perfect fluid source and cosmological constant are solved. New exact, asymptotically stable solutions with an inflationary regime or a final Friedmann stage are found for some simple, interesting potentials. It is shown that the fluid and the curvature may determine how these models evolve for large times.
We present the study of exact inhomogeneous cosmological solutions to a four-dimensional low energy limit of string theory containing non-minimal interacting electromagnetic, dilaton and axion fields. We analyze Einstein-Rosen solutions of Einstein-Maxwell-dilaton-axion equations and show, by explicitly taken the asymptotic limits, that they have asymptotically velocity-term dominated (AVTD) singularities.
The dynamics of a universe dominated by a self-interacting nonminimally coupled scalar field are considered. The structure of the phase space and complete phase portraits are given. New dynamical behaviors include superinflation ($\dot{H}>0$), avoidance of big bang singularities through classical birth of the universe, and spontaneous entry into and exit from inflation. This model is promising for describing quintessence as a nonminimally coupled scalar field.
We present solution generating techniques which permit to construct exact inhomogeneous and anisotropic cosmological solutions to a four-dimensional low energy limit of string theory containing non-minimally interacting electromagnetic and dilaton fields. Some explicit homogeneous and inhomogeneous cosmological solutions are constructed. For example, inhomogeneous exact solutions presenting Gowdy - type EMD universe are obtained. The asymptotic behaviour of the solutions is investigated. The asymptotic form of the metric near the initial singularity has a spatially varying Kasner form. The cha…
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…
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 illustrate how form-invariance transformations can be used for constructing phantom cosmologies from standard scalar field universes. First, we discuss how to relate two flat Friedmann-Robertson-Walker cosmologies with different barotropic indexes $γ$ and $\bar γ$. Then, we consider the particular case $\bar γ=-γ$, and we show that if the matter content is interpreted in terms of self-interacting scalar fields, then the corresponding transformation provides the link between a standard and a phantom cosmology. After that, we illustrate the method by considering models with exponential potent…
Starting from the inhomogeneous shear--free Nariai metric we show, by solving the Einstein--Klein--Gordon field equations, how a self--interacting scalar field plus a material fluid, a variable cosmological term and a heat flux can drive the universe to its currently observed state of homogeneous accelerated expansion. A quintessence scenario where power-law inflation takes place for a string-motivated potential in the late--time dominated field regime is proposed.
In this article we investigate and develop specific aspects of Friedmann-Robertson-Walker (FRW) scalar field cosmologies related to the interpretation that canonical and phantom scalar field sources may be interpreted as cosmological configurations with a mixture of two interacting barotropic perfect fluids: a matter component $ρ_1(t)$ with a stiff equation of state ($p_1=ρ_1$), and an "effective vacuum energy" $ρ_2(t)$ with a cosmological constant equation of state ($p_2=-ρ_2$). An important characteristic of this alternative equivalent formulation in the framework of interacting cosmologies …
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…
We find various asymptotic limits of universes containing two interacting fluids which interact and exchange energy. We study the finite-time singularities that may develop in these cosmologies and obtain the asymptotic behaviours of the solutions near such blow up regimes.
We consider the general behaviour of cosmologies in Brans-Dicke theory where the dilaton is self-interacting via a potential $V(Φ)$. We show that the general radiation universe is a two-dimensional dynamical system whereas the dust or false vacuum universe is three-dimensional. This is in contrast to the non-interacting dilaton which has uniformly a two-dimensional phase space. We find the phase spaces in each case and the general behaviour of the cosmologies.
We prove the cosmic no-hair conjecture for all orthogonal Bianchi cosmologies with matter in the $R+βR^2$ theory using the conformally equivalent Einstein field equations, with the scalar field having the full self-interacting potential, in the presence of the conformally related matter fields. We show, in particular, that the Bianchi IX universe asymptotically approaches de Sitter space provided that initially the scalar three-curvature does not exceed the potential of the scalar field associated with the conformal transformation. Our proof relies on rigorous estimates of the possible bounds …
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 …
A non-perturbative canonical quantization of Gowdy $T^3$ polarized models carried out recently is considered. This approach profits from the equivalence between the symmetry reduced model and 2+1 gravity coupled to a massless real scalar field. The system is partially gauge fixed and a choice of internal time is performed, for which the true degrees of freedom of the model reduce to a massless free scalar field propagating on a 2-dimensional expanding torus. It is shown that the symplectic transformation that determines the classical dynamics cannot be unitarily implemented on the correspondin…
We analyse a classical model of gravitation coupled to a self interacting scalar field. We show that, within the context of this model for Robertson-Walker cosmologies, there exist solutions in the spatially non-flat cases exhibiting transitions from a Euclidean to a Lorentzian spacetime. We then discuss the conditions under which these signature changing solutions to Einstein's field equations exist. In particular, we find that an upper bound for the cosmological constant exists and that close to the signature changing hypersurface, both the scale factor and the scalar field have to be consta…
It has been pointed out that non-singular cosmological solutions in second-order scalar-tensor theories generically suffer from gradient instabilities. We extend this no-go result to second-order gravitational theories with an arbitrary number of interacting scalar fields. Our proof follows directly from the action of generalized multi-Galileons, and thus is different from and complementary to that based on the effective field theory approach. Several new terms for generalized multi-Galileons on a flat background were proposed recently. We find a covariant completion of them and confirm that t…
It is shown that any spatially flat and isotropic universe undergoing accelerated expansion driven by a self-interacting scalar field can be directly related to a contracting, decelerating cosmology. The duality is made manifest by expressing the scale factor and Hubble parameter as functions of the scalar field and simultaneously interchanging these two quantities. The decelerating universe can be twinned with a cosmology sourced by a phantom scalar field by inverting the scale factor and leaving the Hubble parameter invariant. The accelerating model can be related to the same phantom univers…
We shall present a complete (compactified) dynamical systems analysis of the Quintom model comprised of an interacting quintessence scalar field and a phantom. We find a range for the model parameters $κ, λ$ such that there are expanding Quintom cosmologies that undergo two inflationary periods, and this behaviour is not destabilized by spatial curvature. We also discuss a class of bouncing cosmologies. Finally, the linear cosmological perturbations are studied.
The accelerated expansion of the universe is a rather established fact in cosmology and many different models have been proposed as a viable explanation. Many of these models are based on the standard general relativistic framework of non-interacting fluids or more recently of coupled (interacting) dark energy models, where dark energy (the scalar field) is coupled to the dark matter component giving rise to a fifth-force. An interesting alternative is to couple the scalar field directly to the gravity sector via the Ricci scalar. These models are dubbed non-minimally coupled models and give r…
We study non-linear structure formation in an interacting model of the dark sector of the Universe in which the dark energy density decays linearly with the Hubble parameter, $ρ_Λ \propto H$, leading to a constant-rate creation of cold dark matter. We derive all relevant expressions to calculate the mass function and the cluster number density using the Sheth-Torman formalism and show that the effect of the interaction process is to increase the number of bound structures of large masses ($M \gtrsim 10^{14} M_{\odot}h^{-1}$) when compared to the standard $Λ$CDM model. Since these models are no…
We study how the constants $G$ and $Λ$ may vary in different theoretical models (general relativity with a perfect fluid, scalar cosmological models (\textquotedblleft quintessence\textquotedblright) with and without interacting scalar and matter fields and a scalar-tensor model with a dynamical $Λ$) in order to explain some observational results. We apply the program outlined in section II to study three different geometries which generalize the FRW ones, which are Bianchi \textrm{V}, \textrm{VII}$_{0}$ and \textrm{IX}, under the self-similarity hypothesis. We put special emphasis on calculat…
Electrodynamics for self-interacting scalar fields in spatially flat Friedmann-Robertson-Walker space-times is studied. The corresponding one-loop field equation for the expectation value of the complex scalar field in the conformal vacuum is derived. For exponentially expanding universes, the equations for the Bogoliubov coefficients describing the coupling of the scalar field to gravity are solved numerically. They yield a non-local correction to the Coleman-Weinberg effective potential which does not modify the pattern of minima found in static de Sitter space. Such a correction contains a …
New exact solutions of Einstein's gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar fields. Solutions are obtained for a Friedmann-Robertson-Walker geometry both for the cases of zero and non-zero curvatures, and a variety of interesting features are found. It is shown that one class of solutions tends asymptotically to a power-law inflationary behaviour $S(t)\sim t^p$ with $p>1$, while another class exhibits a late time approach to the $S(…
We propose additional conditions (beyond those considered in our previous papers) that should be imposed on Wick products and time-ordered products of a free quantum scalar field in curved spacetime. These conditions arise from a simple ``Principle of Perturbative Agreement'': For interaction Lagrangians $L_1$ that are such that the interacting field theory can be constructed exactly--as occurs when $L_1$ is a ``pure divergence'' or when $L_1$ is at most quadratic in the field and contains no more than two derivatives--then time-ordered products must be defined so that the perturbative solutio…
We derive the effective equations for the out of equilibrium time evolution of the order parameter and the fluctuations of a scalar field theory in spatially flat FRW cosmologies.The calculation is performed both to one-loop and in a non-perturbative, self-consistent Hartree approximation.The method consists of evolving an initial functional thermal density matrix in time and is suitable for studying phase transitions out of equilibrium. The renormalization aspects are studied in detail and we find that the counterterms depend on the initial state. We investigate the high temperature expansion…
A non-singular cosmological bounce in the Einstein frame can only take place if the Null Energy Condition (NEC) is violated. We explore situations where a single scalar field drives the NEC violation and derive the constraints imposed by demanding tree level unitarity on a cosmological background. We then focus on the explicit constraints that arise in P(X) theories and show that constraints from perturbative unitarity make it impossible for the NEC violation to occur within the region of validity of the effective field theory without also involving irrelevant operators that arise at a higher …
We consider self-interacting, perturbative quantum field theory in a curved spacetime background with a Killing vector field. We show that the action of this spacetime symmetry on interacting field operators can be implemented by a Noether charge which arises as a surface integral over the time-component of the interacting Noether current-density associated with the Killing field. The proof of this involves the demonstration of a corresponding set of Ward identities. Our work is based on the perturbative construction by Brunetti and Fredenhagen (Commun.Math.Phys. 208 (2000) 623-661) of self-in…
We present a perturbative construction of interacting quantum field theories on any smooth globally hyperbolic manifold. We develop a purely local version of the Stueckelberg-Bogoliubov-Epstein-Glaser method of renormalization using techniques from microlocal analysis. As byproducts, we describe a perturbative construction of local algebras of observables, present a new definition of Wick polynomials as operator-valued distributions on a natural domain, and we find a general method for the extension of distributions which were defined on the complement of some surfaces.
We study the asymptotic behavior at late times of Friedmann-Robertson-Walker (uniform density) cosmological models within scalar-tensor theories of gravity. Particularly, we analyze the late time behavior in the present (matter dominated) epoch of the universe. The result of Damour and Nordtvedt that for a massless scalar in a flat cosmology the Universe evolves towards a state indistinguishable from general relativity is generalized. We first study a massless scalar field in an open universe. It is found that, while the universe tends to approach a state with less scalar contribution to gravi…
It has been shown that the observed dark matter (DM) abundance can be produced by amplification of quantum fluctuations of an energetically subdominant scalar field during inflation. In this paper, we study the robustness of this "spectator dark matter" scenario to changes in the expansion rate of the early Universe. Compared to the standard radiation-dominated (RD) scenario, two aspects will change: the DM energy density evolves differently as a function of time, and also the DM isocurvature perturbation spectrum will be different from the result in the RD case. These can impose sizeable chan…
We study curved isotropic cosmologies filled with two interacting fluids near their time singularities. We find that a number of these universes asymptote to flat limits in the sense that their asymptotic properties become indistinguishable from those of flat Friedmann-Robertson-Walker models on approach to the singularity along any asymptotic direction. In particular, there are no essential singularities in these models. We discuss connections of this result with possible extensions of the cosmic no hair theorem to the case of two interacting fluids, and also provide links to a quantum cosmol…
The problem of cosmological production of gravitational waves is discussed in the framework of an expanding, spatially homogeneous and isotropic FRW type Universe with time-evolving vacuum energy density. The gravitational wave equation is established and its modified time-dependent part is analytically resolved for different epochs in the case of a flat geometry. Unlike the standard $Λ$CDM cosmology (no interacting vacuum), we show that gravitational waves are produced in the radiation era even in the context of general relativity. We also show that for all values of the free parameter, the h…
The nonlinear, cubic Schrodinger (NLS) equation has numerous physical applications, but in general is very difficult to solve. Nonetheless, under certain circumstances parameters quantifying the width, momentum and energy of the wavefunction evolve under a closed set of ordinary differential equations. It is shown that for the case of the radial, two dimensional NLS equation, such evolution equations may be mapped directly onto the cosmological Friedmann equations for a spatially flat and isotropic universe sourced by a self-interacting scalar field and a barotropic perfect fluid. Consequently…
