We consider an original variational approach for building new models of quintessence interacting with dark or baryonic matter. The coupling is introduced at the Lagrangian level using a variational formulation for relativistic fluids, where the interacting term generally depends on both the dynamical degrees of freedom of the theory and their spacetime derivatives. After deriving the field equations from the action, we consider applications in the context of cosmology. Two simple models are studied using dynamical system techniques showing the interesting phenomenology arising in this framework. We find that these models contain dark energy dominated late time attractors with early time matter dominated epochs and also obtain a possible dynamical crossing of the phantom barrier. The formulation and results presented here complete and expand the analysis exposed in the first part of this work, where only algebraic couplings, without spacetime derivatives, were considered.
We investigate cosmological scenarios with a non-minimal derivative coupling between the scalar field and the curvature, examining both the quintessence and the phantom cases in zero and constant potentials. In general, we find that the universe transits from one de Sitter solution to another, determined by the coupling parameter. Furthermore, according to the parameter choices and without the need for matter, we can obtain a Big Bang, an expanding universe with no beginning, a cosmological turnaround, an eternally contracting universe, a Big Crunch, a Big Rip avoidance and a cosmological boun…
We present a new approach to build models of quintessence interacting with dark or baryonic matter. We use a variational approach for relativistic fluids to realize an effective description of matter fields at the Lagrangian level. The coupling is introduced directly in the action by considering a single function mixing the dynamical degrees of freedom of the theory. The resulting gravitational field equations are derived by variations with respect to the independent variables. New interesting phenomenology can be obtained at both small scales, where new screening mechanisms for scalar fields …
The rapid oscillating scalar field is considered as the quintessence in the framework of nonminimal kinetic coupling model. The scalar field behaves like a perfect fluid with a variable equation of state parameter which can be expressed as a function of the Hubble parameter. This feature enables us to study its evolution via continuity equation. The scalar field may behave as dark energy in the present epoch, while it behaves like dark matter in the future. This characteristic allows the occurrence of a decelerated expansion after the present acceleration, without invoking any interaction. The…
We demonstrate analytically and numerically the existence of geodesically complete singularities in quintessence and scalar tensor quintessence models with scalar field potential of the form $V(ϕ)\sim \vert ϕ\vert^n$ with $0<n<1$. In the case of quintessence, the singularity which occurs at $ϕ=0$, involves divergence of the third time derivative of the scale factor (Generalized Sudden Future Singularity (GSFS)), and of the second derivative of the scalar field. In the case of scalar-tensor quintessence with the same potential and with a linear minimal coupling ($F(ϕ)=1-λϕ$), the singularity is…
We present a family of consistent quantum field theories of monodromy quintessence in strong coupling, which can serve as benchmarks in modeling dark energy different from cosmological constant. These theories have discrete gauge symmetries which can protect them from quantum field theory and quantum gravity corrections, both perturbative and nonperturbative. The strong coupling effects, at scales $\ga {\rm mm}^{-1}$, flatten the potential and activate operators with higher powers of derivatives. The predicted equation of state is close to, but not exactly equal to $-1$, thus being within reac…
The string theory swampland proposes that there is no UV-completion for an effective field theory with an exact (metastable) de Sitter vacua, thereby ruling out standard $Λ$CDM cosmology if the conjecture is taken seriously. The swampland criteria have also been shown to be in sharp tension with quintessence models under current and forthcoming observational bounds. As a logical next step, we introduce higher derivative self-interactions in the low-energy effective Lagrangian and show that one can satisfy observational constraints as well as the swampland criteria for some specific models. In …
A cosmic scalar field evolving very slowly in time can account for the observed dark energy of the Universe. Unlike a cosmological constant, an evolving scalar field also has local spatial gradients due to gravity. If the scalar field has a minimal derivative coupling to electromagnetism, it will cause modifications of Maxwell's equations. In particular, in the presence of a scalar field gradient generated by Earth's gravity, regions with a magnetic field appear to be electrically charged and regions with a static electric field appear to contain electric currents. We propose experiments to de…
In the framework of teleparallel equivalent of general relativity, we study a gravity theory where a scalar field beyond its minimal coupling, is also coupled with the vector torsion through a non-minimal derivative coupling. After a suitable choice of auxiliary variables that allows us to perform the phase-space analysis of the model we obtain the critical points and their stability. While there is no scaling attractor in non-interacting scenario, by considering an interaction between dark energy and dark matter, we find scaling attractors in which the fractional densities of dark energy and …
In this paper, we apply the new Gedanken experiment to investigate the weak cosmic censorship conjecture for Reissner-Nordström AdS black holes surrounded by quintessence. Since the perturbation of matter fields doesn't affect the spacetime geometry, we propose the stability condition and assume the process of matter fields falling into the black hole satisfies the null energy condition. Based on Iyer-Wald formalism we can derive the first order and second-order variational identities. From the two identities and the above two conditions lead to the first-order and second-order perturbation in…
We derive an interacting quintessence model on the framework of a recently introduced new class of geometrical scalar-tensor theories of gravity formulated on a Weyl-Integrable geometry, where the gravitational sector is described by both a scalar and a tensor metric field. By using a Palatini variational principle we construct a scalar-tensor action invariant under the Weyl symmetry group of the background geometry, which in the Einstein-Riemann frame leads to a gravitoelectromagnetic theory. We use the gauge freedom of the theory and the fact that the Weyl scalar field couples with matter fi…
We examine the behavior of dark energy models in the plane defined by w (the equation of state parameter for the dark energy) and w' (the derivative of w with respect to the logarithm of the scale factor). For non-phantom barotropic fluids with positive squared sound speed, we find that w' < 3w(w+1), the opposite of the bound on quintessence models previously derived by Caldwell and Linder. Thus, these barotropic models and quintessence models for the dark energy occupy disjoint regions in the w - w' plane. We also derive two new bounds for quintessence models in the w - w' plane: the first is…
We explore a class of effective field theory models of cosmic acceleration involving a metric and a single scalar field. These models can be obtained by starting with a set of ultralight pseudo-Nambu-Goldstone bosons whose couplings to matter satisfy the weak equivalence principle, assuming that one boson is lighter than all the others, and integrating out the heavier fields. The result is a quintessence model with matter coupling, together with a series of correction terms in the action in a covariant derivative expansion, with specific scalings for the coefficients. After eliminating higher …
We investigate the cosmological implications of a new class of modified gravity, where the field equations generically include higher-order derivatives of the matter fields, arising from the introduction of non-dynamical auxiliary fields in the action. Imposing a flat, homogeneous and isotropic geometry we extract the Friedmann equations, obtaining an effective dark-energy sector containing higher derivatives of the matter energy density and pressure. For the cases of dust, radiation, and stiff matter we analyze the cosmological behavior, finding accelerating, de Sitter, and non-accelerating p…
We study generic single-field dark energy models, by a parametrization of the most general theory of their perturbations around a given background, including higher derivative terms. In appropriate limits this approach reproduces standard quintessence, k-essence and ghost condensation. We find no general pathology associated to an equation of state w_Q < -1 or in crossing the phantom divide w_Q = -1. Stability requires that the w_Q < -1 side of dark energy behaves, on cosmological scales, as a k-essence fluid with a virtually zero speed of sound. This implies that one should set the speed of s…
We discuss the criteria that must be satisfied by a well-posed variational principle. We clarify the role of Gibbons-Hawking-York type boundary terms in the actions of higher derivative models of gravity, such as F(R) gravity, and argue that the correct boundary terms are the naive ones obtained though the correspondence with scalar-tensor theory, despite the fact that variations of normal derivatives of the metric must be fixed on the boundary. We show in the case of F(R) gravity that these boundary terms reproduce the correct ADM energy in the hamiltonian formalism, and the correct entropy f…
We construct $F(T,\left(\nabla{T}\right)^2,\Box {T})$ gravitational modifications, which are novel classes of modified theories arising from higher-derivative torsional terms in the action, and are different than their curvature analogue. Applying them in a cosmological framework we obtain an effective dark energy sector that comprises of the novel torsional contributions. We perform a detailed dynamical analysis for two specific examples, extracting the stable late-time solutions and calculating the corresponding observables. We show that the thermal history of the universe can be reproduced,…
We perform a dynamical analysis for the exponential scalar field with non-minimally derivative coupling. For the quintessence case, the stable fixed points are the same with and without the non-minimally derivative coupling. For the phantom case, the attractor with dark energy domination exists for the minimal coupling only. For the non-minimally derivative coupling without the standard canonical kinetic term, only the de-Sitter attractor exists, and the dark matter solution is unstable.
A method of calculation for the variational derivatives for gravitational actions in the pseudo-Riemannian case is proposed as a practical variant of the first order formalism with constraints. The method is then used to derive the metric field equations for a generic $f(R)$ model.
This investigation explores using the beta function formalism to calculate analytic solutions for the observable parameters in rolling scalar field cosmologies. The beta function in this case is the derivative of the scalar $ϕ$ with respect to the natural log of the scale factor $a$, $β(ϕ)=\frac{d ϕ}{d \ln(a)}$. Once the beta function is specified, modulo a boundary condition, the evolution of the scalar $ϕ$ as a function of the scale factor is completely determined. A rolling scalar field cosmology is defined by its action which can contain a range of physically motivated dark energy potentia…
We consider a cosmological scenario endowed with an interaction between the universe's dark components $-$ dark matter and dark energy. Specifically, we assume the dark matter component to be a pressure-less fluid, while the dark energy component is a quintessence scalar field with Lagrangian function modified by the quadratic Generalized Uncertainty Principle. The latter modification introduces new higher-order terms of fourth-derivative due to quantum corrections in the scalar field's equation of motion. Then we investigate asymptotic dynamics and general behaviour of solutions of the field …
Our main aim in this paper is to promote the coframe variational method as a unified approach to derive field equations for any given gravitational action containing the algebraic functions of the scalars constructed from the Riemann curvature tensor and its contractions. We are able to derive a master equation which expresses the variational derivatives of the generalized gravitational actions in terms of the variational derivatives of its constituent curvature scalars. Using the Lagrange multiplier method relative to an orthonormal coframe, we investigate the variational procedures for modif…
We study the greybody factor and Hawking radiation with a non-minimal derivative coupling between the scalar field and the curvature in the background of the slowly rotating Kerr-Newman black hole. Our results show that both the absorption probability and luminosity of Hawking radiation of the scalar field increase with the coupling. Moreover, we also find that for the weak coupling $η<η_c$, the absorption probability and luminosity of Hawking radiation decrease when the black hole's Hawking temperature decreases; while for stronger coupling $η>η_c$, the absorption probability and luminosity o…
A linear relationship between the Hubble expansion parameter and the time derivative of the scalar field is explored in order to derive exact cosmological, attractor-like solutions, both in Einstein's theory and in Brans-Dicke gravity with two fluids: a background fluid of ordinary matter, together with a self-interacting scalar field accounting for the dark energy in the universe. A priori assumptions about the functional form of the self-interaction potential or about the scale factor behavior are not necessary. These are obtained as outputs of the assumed relationship between the Hubble par…
A model is proposed, according to which the metric tensor field in the standard gravitational Lagrangian is decomposed into a projection (generally - with a non-zero covariant derivative) tensor field, orthogonal to an arbitrary 4-vector field and a tensor part along the same vector field. A theorem has been used, according to which the variation and the partial derivative, when applied to a tensor field, commute with each other if and only if the tensor field and its variation have zero covariant derivatives, provided also the connection variation is zero. Since the projection field obviously…
Spherically symmetric cosmological equations in the usual FLRW coordinates are explored, with different sources. The first couples a perfect fluid with a quintessence scalar field and the second couples a perfect fluid to a tachyonic scalar field. In both cases, in the inflationary regime, the scale factor a(t) and its first two time derivatives are positive definite. Both sources in the matter phase yield a scale factor and its first derivative as positive definite. In both cases and in each phase, the general solutions of the differential equations together with the algebraic and differentia…
We consider the interacting holographic dark energy with new infrared cutoff (involving Hubble parameter and its derivative) in non-flat universe. In this context, we obtain the equation of state parameter which evolutes the universe from vacuum dark energy region towards quintessence region for particular values of constant parameters. It is found that this model always remains unstable against small perturbations. Further, we establish the correspondence of this model having quintessential behavior with quintessence, tachyon, K-essence and dilaton scalar field models. The dynamics of scalar …
The prescription of Silva to derive superpotential equations from variational derivatives rather than from Lagrangian densities is applied to theories of gravity derived from Lovelock Lagrangians in the Palatini representation. Spacetimes are without torsion and isolated sources of gravity are minimally coupled. On a closed boundary of spacetime, the metric is given and the connection coefficients are those of Christoffel. We derive equations for the superpotentials in these conditions. The equations are easily integrated and we give the general expression for all superpotentials associated wi…
The usual interpretation of Weyl geometry is modified in two senses. First, both the additive Weyl connection and its variation are treated as (1, 2) tensors under the action of Weyl covariant derivative. Second, a modified covariant derivative operator is introduced which still preserves the tensor structure of the theory. With its help, the Riemann tensor in Weyl geometry can be written in a more compact form. We justify this modification in detail from several aspects and obtain some insights along the way. By introducing some new transformation rules for the variation of tensors under the …
The purpose of the paper is to develop further a projection variational approach in relativistic hydrodynamics. The approach, previously proposed in [gr-qc/9908032], is based on the variation of the vector field and the projection tensor (instead of the given metric tensor) and their first partial derivatives. The previously proved property of non-commutativity of the variation and the partial derivative in respect to the projection tensor has been used to find all the variations. Subsequently, motivated by some analogy with the well-known (3+1) ADM projection formalism, an assumption has been…
It is shown that when in a higher order variational principle one fixes fields at the boundary leaving the field derivatives unconstrained, then the variational principle (in particular the solution space) is not invariant with respect to the addition of boundary terms to the action, as it happens instead when the correct procedure is applied. Examples are considered to show how leaving derivatives of fields unconstrained affects the physical interpretation of the model. This is justified in particularl by the need of clarifying the issue for the purpose of applications to relativistic gravita…
This paper is aimed at a (mostly) pedagogical exposition of the derivation of the motion equations of certain modifications of general relativity. Here we derive in all detail the motion equations in the Brans-Dicke theory with the cubic self-interaction. This is a modification of the Brans-dicke theory by the addition of a term in the Lagrangian which is non-linear in the derivatives of the scalar field: it contains second-order derivatives. This is the basis of the so-called Brans-Dicke Galileon. We pay special attention to the variational principle and to the algebraic details of the deriva…
