In this paper we consider a third quantized cosmological model with varying speed of light $c$ and varying gravitational constant $G$ both represented by non-minimally coupled scalar fields. The third quantization of such a model leads to a scenario of the doubleverse with the two components being quantum mechanically entangled. We calculate the two parameters describing the entanglement, namely: the energy and the entropy of entanglement where the latter appears to be a proper measure of the entanglement. We consider a possibility that the entanglement can manifests itself as an effective perfect fluid characterized by the time dependent barotropic index $w_{eff}$, which for some specific case corresponds to the fluid of cosmic strings. It seems that such an entanglement induced effective perfect fluid may generate significant backreaction effect at early times.
Scalar fields coupled to gravity via $ξR Φ^2$ in arbitrary Friedmann-Robertson-Walker backgrounds can be represented by an effective flat space field theory. We derive an expression for the scalar energy density where the effective scalar mass becomes an explicit function of $ξ$ and the scale factor. The scalar quartic self-coupling gets shifted and can vanish for a particular choice of $ξ$. Gravitationally induced symmetry breaking and de-stabilization are possible in this theory.
We present an analysis of the phase space of cosmological models based on a non minimal coupling between the geometry and a fermionic condensate. We obtain that the strong constraint coming from the Dirac equations allows a detailed design of the cosmology of these models and at the same time guarantees an evolution towards a state indistinguishable from General Relativistic cosmological models. In this light, we show how the use of some specific potentials is able to reproduce naturally two de Sitter phases separated by a power law expansion which could be an interesting model for the unifica…
We discuss non-minimally coupled cosmologies involving different geometric invariants. Specifically, actions containing a non-minimally coupled scalar field to gravity described, in turn, by curvature, torsion and Gauss--Bonnet scalars are considered. We show that couplings, potentials and kinetic terms are determined by the existence of Noether symmetries which, moreover, allows to reduce and solve dynamics. The main finding of the paper is that different non-minimally coupled theories, presenting the same Noether symmetries, are dynamically equivalent. In other words, Noether symmetries are …
Recent works showing that homogeneous and isotropic cosmologies involving scalar fields correspond to geodesics of certain augmented spaces are generalized to the non-minimal coupling case. As the Maupertuis-Jacobi principle in classical mechanics, this result allows us, in principle, to infer some of the dynamical properties of the cosmologies from the geometry of the associated augmented spaces.
We compare theoretical predictions with observations for a class of cosmological models in which the dark energy component is modeled as a fermionic condensate, non-minimally coupled with the gravitational field and characterized by some specific self-interaction potentials. Our analysis is based on the Markov Chain Monte Carlo Method (MCMC) and employs different data sets. It turns out that with an appropriate choice of parameters our models are fully compatible with several observed data. We combine these parameter values with phase space analysis to deduce the features of the entire cosmic …
We show that the scalar-tensor $σ$-model action is conformally equivalent to general relativity with a minimally coupled wavemap with a particular target metric. Inflation on the source manifold is then shown to occur in a natural way due both to the arbitrary curvature couplings and the wavemap self-interactions.
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 consider gravity theory with varying speed of light and varying gravitational constant. Both constants are represented by non-minimally coupled scalar fields. We examine the cosmological evolution in the near curvature singularity regime. We find that at the curvature singularity the speed of light goes to infinity while the gravitational constant vanishes. This corresponds to the Newton's Mechanics limit represented by one of the vertex of the Bronshtein-Zelmanov-Okun cube. The cosmological evolution includes both the pre-big-bang and post-big-bang phases separated by the curvature singula…
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 study a toy model for phantom cosmology recently introduced in the literature and consisting of two oscillators, one of which carries negative kinetic energy. The results are compared with the exact phase space picture obtained for similar dynamical systems describing, respectively, a massive canonical scalar field conformally coupled to the spacetime curvature, and a conformally coupled massive phantom. Finally, the dynamical system describing exactly a minimally coupled phantom is studied and compared with the toy model.
We examine theories of gravity which include finitely many coupled scalar fields with arbitrary couplings to the curvature (wavemaps). We show that the most general scalar-tensor $σ$-model action is conformally equivalent to general relativity with a minimally coupled wavemap with a particular target metric. Inflation on the source manifold is then shown to occur in a novel way due to the combined effect of arbitrary curvature couplings and wavemap self-interactions. A new interpretation of the conformal equivalence theorem proved for such `wavemap-tensor' theories through brane-bulk dynamics …
The scalar field degree of freedom in Einstein's plus Matter field equations is decoupled for Bianchi type I and V general cosmological models. The source, apart from the minimally coupled scalar field with arbitrary potential V(Phi), is provided by a perfect fluid obeying a general equation of state p =p(rho). The resulting ODE is, by an appropriate choice of final time gauge affiliated to the scalar field, reduced to 1st order, and then the system is completely integrated for arbitrary choices of the potential and the equation of state.
We investigate the Universe at the late stage of its evolution and inside the cell of uniformity 150-370 Mpc. We consider the Universe to be filled at these scales with dust like matter, a minimally coupled Galileon field and radiation. We use the mechanical approach. Therefore, the peculiar velocities of the inhomogeneities as well as the fluctuations of the other perfect fluids can be considered nonrelativistic. Such fluids are said to be coupled because they are concentrated around the inhomogeneities. We investigate the conditions under which the physical Galileon field, i.e. compatible wi…
This thesis contributes to the field of gravitational lensing (GL) and observational cosmology. We discuss the use of gravitational lensing as a tool in search of exotic objects in the Universe. In the next chapter the concordance of an alternative cosmological model with the current gravitational lensing observations is explored and also a non-minimally coupled effective gravity theory that supports non-topological solitonic solutions is considered. In the last chapter we study propagation of light in strong gravitational field. Using geometrical optics approach we show that massless particle…
We study the spherical collapse model in dark energy cosmologies, in which dark energy is modelled as a minimally coupled scalar field. We first follow the standard assumption that dark energy does not cluster on the scales of interest. Investigating four different popular potentials in detail, we show that the predictions of the spherical collapse model depend on the potential used. We also investigate the dependence on the initial conditions. Secondly, we investigate in how far perturbations in the quintessence field affect the predictions of the spherical collapse model. In doing so, we ass…
This paper generalizes two previously known techniques for generating minimally coupled Einstein-scalar field solutions in 4 dimensions; the Buchdahl and Fonarev transformations. By applying this solution generation technique, minimally coupled Einstein-scalar field solutions can be generated from vacuum solutions with arbitrary cosmological constant in arbitrary dimension. The only requirement to a seed solution is that it posesses a hypersurface-orthogonal Killing vector field. The generalization that allows us to use seed solutions with arbitrary cosmological constant uncovers a new class o…
In the context of averaged cosmologies, the effective equations can be written in the form of "regional" Friedmannian equations with additional sources arising from the so-called backreaction of inhomogeneities. We propose a mean field description of this backreaction in terms of a regionally homogeneous scalar field: this provides a physical motivation to the phenomenological scalar fields generically called quintessence fields. We explicitly reconstruct the potential of the scalar field for a one-parameter family of scaling solutions to the backreaction problem, showing that it entails most …
Although the standard cosmological model explains most of the observed phenomena it still struggles with the problem of initial singularity. An interesting scenario in which the problem of the initial singularity is somehow circumvented was proposed in the context of string theory where the canonical quantisation procedure was additionally applied. A similar effect can be achieved in the context of the canonically quantized theory with varying speed of light and varying gravitational constant where both quantities are represented by non-minimally coupled scalar fields. Such theory contains bot…
By using a bottom-up reconstruction technique for non-minimally coupled scalar-tensor theories, we realize the Einstein frame attractor cosmologies in the $Ω(ϕ)$-Jordan frame. For our approach, what is needed for the reconstruction method to work is the functional form of the non-minimal coupling $Ω(ϕ)$ and of the scalar-to-tensor ratio, and also the assumption of the slow-roll inflation in the $Ω(ϕ)$-Jordan frame. By appropriately choosing the scalar-to-tensor ratio, we demonstrate that the observational indices of the attractor cosmologies can be realized directly in the $Ω(ϕ)$-Jordan frame.…
The total canonical (Liouville-Henneaux-Gibbons-Hawking-Stewart) measure is finite for completely nonsingular Friedmann-Lemaitre-Robertson-Walker classical universes with a minimally coupled massive scalar field and a positive cosmological constant. For a cosmological constant very small in units of the square of the scalar field mass, most of the measure is for nearly de Sitter solutions with no inflation at a much more rapid rate. However, if one restricts to solutions in which the scalar field energy density is ever more than twice the equivalent energy density of the cosmological constant,…
We investigate the stability against inhomogeneous perturbations and the appearance of ghost modes in Gauss-Bonnet gravitational theories with a non-minimally coupled scalar field, which can be regarded as either the dilaton or a compactification modulus in the context of string theory. Through cosmological linear perturbations we extract four no-ghost and two sub-luminal constraint equations, written in terms of background quantities, which must be satisfied for consistency. We also argue that, for a general action with quadratic Riemann invariants, homogeneous and inhomogeneous perturbations…
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…
The problem of dark energy can be roughly stated as the proposition and validation of a cosmological model that can explain the phenomenon of the accelerated expansion of the Universe. This problem is an open discussion topic in modern physics. One of the most common approaches is that of the "Dark Energy" (DE), a matter component still unknown, with repulsive character (to explain the accelerated expansion), which fills about 2/3 of the total content of the Universe. In this thesis are investigated two cosmological models, a non-minimally coupled quintessence field, based on a Scalar-Tensor T…
Scalar-tensor Cosmologies can be dealt under the standard of the Hojman conservation theorem that allows to fix the form of the coupling $F(ϕ)$, of the potential $V(ϕ)$ and to find out exact solutions for related cosmological models. Specifically, the existence of a symmetry transformation vector for the equations of motion gives rise to a Hojman conserved quantity on the corresponding minisuperpace and exact solutions for the cosmic scale factor $a$ and the scalar field $ϕ$ can be achieved. In particular, we take advantage of the fact that minimally coupled solutions, previously obtained in t…
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…
In this article, we summarize two agnostic approaches in the framework of spatially curved Friedmann-Robertson-Walker (FRW) cosmologies discussed in detail in (Kerachian et al., 2020, 2019). The first case concerns the dynamics of a fluid with an unspecified barotropic equation of state (EoS), for which the only assumption made is the non-negativity of the fluid's energy density. The second case concerns the dynamics of a non-minimally coupled real scalar field with unspecified positive potential. For each of these models, we define a new set of dimensionless variables and a new evolution para…
Assuming that curvature perturbations and gravitational waves originally arise from vacuum fluctuations in a matter-dominated phase of contraction, we study the dynamics of the cosmological perturbations evolving through a nonsingular bouncing phase described by a generic single scalar field Lagrangian minimally coupled to Einstein gravity. In order for such a model to be consistent with the current upper limits on the tensor-to-scalar ratio, there must be an enhancement of the curvature fluctuations during the bounce phase. We show that, while it remains possible to enlarge the amplitude of c…
