We study future singularity in teleparallel dark energy models, particularly its behavior and its (non)occurrence in the observationally viable models. For the models with a general self-potential of the scalar field, we point out that both at early times and in the future near the singularity the behavior of dark energy can be described by the analytic solutions of the scalar field we obtained for the model with no self-potential. As to the (non)occurrence in the viable models, we consider a natural binding-type self-potential, the quadratic potential, when fitting observational data, and illustrate the constraining region up to the $3σ$ confidence level as well as the region where a singularity will occur. As a result, the singularity region is outside the $3σ$ constraint. Thus, although the future singularity problem potentially exists in teleparallel dark energy models, the observationally viable models may not suffer this problem.
Recently, Geng et al. proposed to allow a non-minimal coupling between quintessence and gravity in the framework of teleparallel gravity, motivated by the similar one in the framework of General Relativity (GR). They found that this non-minimally coupled quintessence in the framework of teleparallel gravity has a richer structure, and named it "teleparallel dark energy". In the present work, we note that there might be a deep and unknown connection between teleparallel dark energy and Elko spinor dark energy. Motivated by this observation and the previous results of Elko spinor dark energy, we…
We study the post-Newtonian limit in the teleparallel equivalent of General Relativity with a scalar field which non-minimally couples to gravity. The metric perturbation is obtained from the vierbein field expansion with respect to the Minkowski background. Due to the structure of the teleparallel gravity Lagrangian, the potential of the scalar field shows no effect to the parametrized post-Newtonian parameters, and compatible results with Solar System observations are found.
It has been proposed recently the existence of a non-minimal coupling between a canonical scalar field (quintessence) and gravity in the framework of teleparallel gravity, motivated by similar constructions in the context of General Relativity. The dynamics of the model, known as teleparallel dark energy, has been further developed, but no scaling attractor has been found. Here we consider a model in which the non-minimal coupling is ruled by a dynamically changing coefficient $α\equiv f_{,ϕ}/\sqrt{f}$, with $f(ϕ)$ an arbitrary function of the scalar field $ϕ$. It is shown that in this case th…
We propose the simplest model of teleparallel dark energy with purely a non-minimal coupling to gravity but no self-potential, a single model possessing various interesting features: simplicity, self-potential-free, the guaranteed late-time cosmic acceleration driven by the non-minimal coupling to gravity, tracker behavior of the dark energy equation of state at earlier times, a crossing of the phantom divide at a late time, and the existence of a finite-time future singularity. We find the analytic solutions of the dark-energy scalar field respectively in the radiation, matter, and dark energ…
A nonminimally coupled quintessence dark energy in teleparallel model of gravity is considered. It is clarified how a matter dominated universe with initial negligible dark energy density can evolve to a late time de Sitter space-time via the $Z_2$ symmetry breaking.
Within this work, we propose a new generalised quintom dark energy model in the teleparallel alternative of general relativity theory, by considering a non-minimal coupling between the scalar fields of a quintom model with the scalar torsion component $T$ and the boundary term $B$. In the teleparallel alternative of general relativity theory, the boundary term represents the divergence of the torsion vector, $B=2\nabla_μT^μ$, and is related to the Ricci scalar $R$ and the torsion scalar $T$, by the fundamental relation: $R=-T+B$. We have investigated the dynamical properties of the present qui…
We use data from Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) observations to constrain the recently proposed teleparallel dark energy scenario based on the teleparallel equivalent of General Relativity, in which one adds a canonical scalar field, allowing also for a nonminimal coupling with gravity. Using the power-law, the exponential and the inverse hyperbolic cosine potential ansatzes, we show that the scenario is compatible with observations. In particular, the data favor a nonminimal coupling, and although the scalar field is canoni…
We study the growth rate of matter perturbations in the context of teleparallel dark energy in a flat universe. We investigate the dynamics of different theoretical scenarios based on specific forms of the scalar field potential. Allowing for non-minimal coupling between torsion scalar and scalar field, we perform a phase-space analysis of the autonomous systems of equations through the study of critical points. We thus analyze the stability of the critical points, and discuss the cosmological implications searching for possible attractor solutions at late times. Furthermore, combing the growt…
In this paper we propose a new dark energy model in the teleparallel alternative of general relativity, by considering a generalized non--minimal coupling of a tachyonic scalar field with the teleparallel boundary term. Within the framework of teleparallel gravity, the boundary coupling term is associated with the divergence of the torsion vector. Considering the linear stability technique for various potentials and couplings, we have analyzed the dynamical properties of the present tachyonic dark energy model in the phase space, uncovering the corresponding essential dynamical features. Our s…
Using the "teleparallel" equivalent of General Relativity as the gravitational sector, which is based on torsion instead of curvature, we add a canonical scalar field, allowing for a nonminimal coupling with gravity. Although the minimal case is completely equivalent to standard quintessence, the nonminimal scenario has a richer structure, exhibiting quintessence-like or phantom-like behavior, or experiencing the phantom-divide crossing. The richer structure is manifested in the absence of a conformal transformation to an equivalent minimally-coupled model.
We study the cosmological perturbations in teleparallel dark energy models in which there is a dynamical scalar field with a non-minimal coupling to gravity. We find that the propagating degrees of freedom are the same as in quintessence cosmology despite that variables of the perturbed vierbein field are greater than those in metric theories. We numerically show some evident discrepancy from general relativity in the evolutions of the perturbations on all scales of the universe. We also demonstrate that the gravitational interactions are enhanced during the unique tracker evolutions in these …
We analyze the common four types of the finite-time singularities using a generic framework of the phase portrait geometric approach. This technique requires that the Friedmann system to be written as a one dimensional autonomous system. We employ a scale factor that has been used widely in literature to realize the four finite-time singularity types, then we show a detailed discussion for each case showing possible novel models. Moreover, we show how different singularity types can play essential roles in different cosmological scenarios. Among several modified gravity theories, we show that …
Realization of quintom dark energy after DESI DR2 in Nieh-Yan modified teleparallel gravity
University of Science and Technology of China（中国科学技术大学）；Interdisciplinary Center for Theoretical Study, University of Science and Technology of China（中国科学技术大学交叉理论研究中心）；Peng Huanwu Center for Fundamental Theory（彭桓武基础理论中心）
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,…
The present paper represents an attempt for a very generic string inspired theory of gravitation, based on a stringy action in the teleparallel gravity which includes a specific functional which depends on the scalar field and its kinetic energy, as well as the torsion and boundary terms, embedding also possible effects from the teleparallel Gauss--Bonnet invariants. We focus our study on FLRW cosmology. After we deduce the cosmological equations for the associated generic theory of gravitation, we focus on string inspired couplings which are studied by considering different analytical techniq…
We present a novel reconstruction method of $f(T)$ teleparallel gravity from phenomenological parameterizations of the deceleration parameter or other alternatives. This can be used as a toolkit to produce viable modified gravity scenarios directly related to cosmological observations. We test two parameterizations of the deceleration parameter considered in recent literatures in addition to one parametrization of the effective (total) equation of state (EoS) of the universe. We use the asymptotic behaviour of the matter density parameter as an extra constraint to identify the viable range of …
The fundamental nature and origin of dark energy are one of the premier mysteries of theoretical physics. In General Relativity Theory, the cosmological constant $Λ$ is the simplest explanation for dark energy. On the other hand, the cosmological constant $Λ$ suffers from a delicate issue so-called fine-tuning problem. This motivates one to modify the spacetime geometry of Einstein's GR. The $f(Q)$ gravity is a recently proposed modified theory of gravity in which the non-metricity scalar $Q$ drives the gravitational interaction. In this article, we consider a linear $f(Q)$ model, specifically…
We develop the reconstruction of a model of $f(T)$ gravity according to the holographic dark energy. $T$ is the torsion scalar and its initial value from the Teleparallel gravity is imposed for fitting the initial value of the function $f(T)$. The result shows a polynomial function for $f(T)$, and we also observe that, when $Ω_V\rightarrow 1$ at the future time, $ω_V$ may cross -1 for some values of the input parameter $b$. Another interesting aspect of the obtained model is that it provides the unification of the dark matter with the dark energy.
We discuss how dynamical dark energy universes with exotic singularities may be distinguished from the standard $Λ$CDM model on the basis of their redshift drift signal, for which measurements both in the acceleration phase and in the deep matter era will be provided by forthcoming astrophysical facilities. Two specific classes of exotic singularity models are studied: sudden future singularity models and finite scale factor singularity models. In each class we identify the models which can mimic $Λ$CDM and play the role of dark energy as well as models for which redshift drift signals are sig…
Using the fluid representation, we formulate the conditions for the appearance of all four types finite-time future singularity in modified gravity in accelerating FRW universe. It stressed that number of standard quintessence/phantom DE theories (including scalar, fluid, DBI ones, etc) brings the accelerating cosmology to future singularity precisely in the same way as singular modified gravity DE. The viable non-singular modified gravity unifying the early-time inflation with late-time acceleration is considered. It is shown that adding such non-singular theory to another realistic singular …
We discuss various types of exotic (non-standard) singularities in the Universe: a Big-Rip (BR or type I), a Sudden Future Singularity (SFS or type II), a Generalized Sudden Future Singularity, a Finite Scale Factor singularity (FSF or type III), a Big-Separation (BS or type IV) and a $w$-singularity. They are characterized by violation of all or some of the energy conditions which results in a blow-up of all or some of the physical quantities: the scale factor, the energy density, the pressure, and the barotropic index. We relate the emergence of these singularities with physical theories (su…
The knowledge of the universe future is of fundamental importance for any advanced civilization. We study the future of singular dark universe where thermal effects due to the Hawking radiation on the apparent horizon of the FRW universe are taken in consideration. It is shown that dark universe which ends up at finite-time Type I and Type III singularity or infinite-time Little Rip singularity transits to finite-time Type II singularity due to account of thermal effects. On the same time, the Type II and IV singular universe does not change its qualitative behavior. The combined account of qu…
The fundamental problem of the occurrence/removal of finite-time future singularity in the universe evolution for coupled dark energy (DE) is addressed. It is demonstrated the existence of the (instable or local minimum) de Sitter space solution which may cure the Type II or Type IV future singularity for DE coupled with DM as the result of tuning the initial conditions. In case of phantom DE, the corresponding coupling may help to resolve the coincidence problem but not the Big Rip (Type I) singularity issue. We show that modified gravity of special form or inhomogeneous DE fluid may offer th…
Current observational evidence does not yet exclude the possibility that dark energy could be in the form of phantom energy. A universe consisting of a phantom constituent will be driven toward a drastic end known as the `Big Rip' singularity where all the matter in the universe will be destroyed. Motivated by this possibility, other evolutionary scenarios have been explored by Barrow, including the phenomena which he called Sudden Future Singularities (SFS). In such a model it is possible to have a blow up of the pressure occurring at sometime in the future evolution of the universe while the…
It is investigated the cosmological dynamics of scalar-torsion $f(T,ϕ)$ gravity as a dark energy model, where $T$ is the torsion scalar of teleparallel gravity and $ϕ$ is a canonical scalar field. In this context, we are concerned with the phenomenology of the class of models with non-linear coupling to gravity and exponential potential. We obtain the critical points of the autonomous system, along with the stability conditions of each one of them and their cosmological properties. Particularly, we show the existence of new attractors with accelerated expansion, as well as, new scaling solutio…
The future finite-time singularities emerging in alternative gravity dark energy models are classified and studied in Jordan and Einstein frames. It is shown that such singularity may occur even in flat spacetime for the specific choice of the effective potential. The conditions for the avoidance of finite-time singularities are presented and discussed. The problem is reduced to the study of a scalar field evolving on an effective potential by using the conformal transformations. Some viable modified gravity models are analyzed in detail and the way to cure singularity is considered by introdu…
The Born-Infeld determinantal gravity has been recently proposed as a way to smooth the Big Bang singularity. This theory is formulated on the Weitzenbock space-time and the teleparallel representation is used instead of the standard Riemannian representation. We find that although this theory is shown to be singularity-free for certain region of the parameter space in which the divergence of the Hubble rate at the high energy regime is substituted by a de-Sitter stage or a bounce in a Friedmann-Lemaitre-Robertson-Walker universe, cosmological singularities such as Big Rip, Big Bang, Big Freez…
In this paper, we study the $f(T,\mathcal{T})$ gravity model in the presence of the bulk viscosity by the flat-FRW metric. The field equation is obtained by teleparallel gravity with tetrad field. The universe components are considered as matter and dark energy which the dark energy component associates from the viscous $f(T,\mathcal{T})$ gravity. After calculating the Friedmann equations, we obtain the energy density, the pressure and the EoS of dark energy in terms of the redshift parameter. Afterward, we plot the corresponding cosmological parameters versus the redshift parameter and examin…
The question of the origin of the recent acceleration of the Universes expansion is still pending. What is making the situation even worst, it is impossible to distinguish the vast majority of the proposed models of the dynamical dark energy and modified gravity from the $ΛCDM$ in view of recent geometrical and dynamical, observational data. On the other hand on scales much smaller than the present Hubble scale, there are differences in the growth of the matter perturbations for different modes of the perturbations in the $ΛCDM$. In the view of the new planned observations that will give insig…
In this paper bulk viscosity is introduced to describe the effects of cosmic non-perfect fluid on the cosmos evolution and to build the unified dark energy (DE) with (dark) matter models. Also we derive a general relation between the bulk viscosity form and Hubble parameter that can provide a procedure for the viscosity DE model building. Especially, a redshift dependent viscosity parameter $ζ\proptoλ_{0}+λ_{1}(1+z)^{n}$ proposed in the previous work by X.H.Meng and X.Dou in 2009\cite{md} is investigated extensively in this present work. Further more we use the recently released supernova data…
The current observational data imply that the universe would end with a cosmic doomsday in the holographic dark energy model. However, unfortunately, the big-rip singularity will ruin the theoretical foundation of the holographic dark energy scenario. To rescue the holographic scenario of dark energy, we employ the braneworld cosmology and incorporate the extra-dimension effects into the holographic theory of dark energy. We find that such a mend could erase the big-rip singularity and leads to a de Sitter finale for the holographic cosmos. Therefore, in the holographic dark energy model, the …
