Phase portraits of generalf(T) cosmology

Journal of Cosmology and Astroparticle Physics, 2014

We present an extension of f (T) gravity, allowing for a general coupling of the torsion scalar T with the trace of the matter energy-momentum tensor T. The resulting f (T, T) theory is a new modified gravity, since it is different from all the existing torsion or curvature based constructions. Applied to a cosmological framework, it leads to interesting phenomenology. In particular, one can obtain a unified description of the initial inflationary phase, the subsequent non-accelerating, matter-dominated expansion, and then the transition to a late-time accelerating phase. Additionally, the effective dark energy sector can be quintessence or phantom-like, or exhibit the phantom-divide crossing during the evolution. Moreover, in the far future the universe results either to a de Sitter exponential expansion, or to eternal power-law accelerated expansions. Finally, a detailed study of the scalar perturbations at the linear level reveals that f (T, T) cosmology can be free of ghosts and instabilities for a wide class of ansatzes and model parameters.

Physical review, 2023

Physical Review D, 2011

Being based on the only assumption that the universe is homogenous and isotropic on large scales, cosmography is an ideal tool to investigate the cosmic expansion history in a almost modelindependent way. Fitting the data on the luminosity distance and Baryon Acoustic Oscillations allows to determine the confidence ranges for the cosmographic parameters hence giving some quantitative constraints that a whatever theory has to fulfill. As an application, we consider here the case of teleparallel gravity (TEGR) also referred to as f (T) gravity. To this end, we first work out analytical expressions to express the present day values of f (T) derivatives as a function of the cosmographic parameters which hold under quite general and physically motivated conditions. We then use the constraints coming from cosmography to find out the confidence ranges for f (T) derivatives up to the fifth order and show how these can be used to check the viability of given TEGR models without the need to explicitly solve the second order dynamic equations.

We investigate the main features of the flat Friedmann-Lemaître-Robertson-Walker cosmological models in the f (T ) modified gravity regime. In particular, a general approach to find out exact cosmological solutions in f (T ) gravity is discussed. Instead of taking into account phenomenological models, we consider as a selection criterion, the existence of Noether symmetries in the cosmological f (T ) point-like Lagrangian. We find that only the f (T ) = f0T n model admits extra Noether symmetries. The existence of extra Noether integrals can be used in order to simplify the system of differential equations (equations of motion) as well as to determine the integrability of the f (T ) = f0T n cosmological model. Within this context, we can solve the problem analytically and thus we provide the evolution of the main cosmological functions such as the scale factor of the universe, the Hubble expansion rate, the deceleration parameter and the linear matter perturbations. We show that the f (T ) = f0T n cosmological model suffers from two basic problems. The first problem is related to the fact that the deceleration parameter is constant which means that it never changes sign, and therefore the universe always accelerates or always decelerates depending on the value of n. Secondly, we find that the clustering growth rate remains always equal to unity implying that the recent growth data disfavor the f (T ) = f0T n gravity. Finally, we prove that the f (T ) = f0T n gravity can be cosmologically equivalent with the f (R) = R n gravity model and the time varying vacuum model Λ(H) = 3γH 2 (for n −1 = 1 − γ) because the above cosmological scenarios share exactly the same Hubble expansion, despite the fact that the three models have a different geometrical origin. Finally, some important differences with power-law f (R)-gravity are pointed out. 95.35.+d, 95.36.+x

arXiv (Cornell University), 2022

Journal of Cosmology and Astroparticle Physics, 2011

We investigate f (T ) cosmology in both the background, as well as in the perturbation level, and we present the general formalism for reconstructing the equivalent one-parameter family of f (T ) models for any given dynamical dark energy scenario. Despite the completely indistinguishable background behavior, the perturbations break this degeneracy and the growth histories of all these models differ from one another. As an application we reconstruct the f (T ) equivalent for quintessence, and we show that the deviation of the matter overdensity evolution is strong for small scales and weak for large scales, while it is negligible for large redshifts.

Astrophysics and Space Science, 2012

In this paper, we investigate the behavior of equation of state parameter and energy density for dark energy in the framework of f (T) gravity. For this purpose, we use anisotropic LRS Bianchi type I universe model. The behavior of accelerating universe is discussed for some well-known f (T) models. It is found that the universe takes a transition between phantom and non-phantom phases for f (T) models except exponential and logarithmic models. We conclude that our results are relativity analogous to the results of FRW universe.

International Journal of Geometric Methods in Modern Physics

In this paper, we considered the study of Friedmann–Robertson–Walker (FRW) model in the framework of [Formula: see text] gravity, an extension of symmetric teleparallel gravity, recently defined by Xu et al. [[Formula: see text] gravity, Eur. Phys. J. C 79 (2019) 708]. The nonlinear model [Formula: see text], where [Formula: see text] and [Formula: see text] are constants, is taken into account. The equation of state of perfect fluid is assumed and 31 points of Hubble data are used to constrain the value of model parameter. To explore the evolution of the universe, the numerical solutions of cosmological implications, such as Hubble parameter, deceleration parameter, apparent magnitude and luminosity distance, are determined and the energy conditions are examined. The theoretical results of Hubble parameter are compared with [Formula: see text]CDM model. Further, 57 Supernova data (42 from Supernova cosmology project and 15 from Calán/Tolono supernova survey) are also used to have c...

Cornell University - arXiv, 2022

We analyze the cosmological solutions of f (T, B) gravity using dynamical system analysis where T is the torsion scalar and B be the boundary term scalar. In our work, we assume two specific cosmological models. For first model, we consider f (T, B) = f 0 (B k + T m), where k and m are constants. For second model, we consider f (T, B) = f 0 T B. We generate an autonomous system of differential equations for each models by introducing new dimensionless variables. To solve this system of equations, we use dynamical system analysis. We also investigate the critical points and their natures, stability conditions and their behaviors of Universe expansion. For both models, we get four critical points. The phase plots of this system are analyzed in detail and study their geometrical interpretations also. In both model, we evaluated density parameters such as Ω r , Ω m , Ω Λ and ω ef f and deceleration parameter (q) and find their suitable range of the parameter λ for stability. For first model, we get ω ef f = −0.833, −0.166 and for second model, we get ω ef f = − 1 3. This shows that both the models are in quintessence phase. Further, we compare the values of EoS parameter and deceleration parameter with the observational values.

2012

In this paper, we intend to evaluate and analyze the statefinder parameters in f ðT Þ cosmology. Friedmann equation in f ðT Þ model is taken, and the statefinder parameters fr; sg are calculated. We consider a model of f ðT Þ which contains a constant, linear and non-linear form of torsion. We plot r and s in order to characterize this model in the fr; sg plane. We found that our model f ðT Þ ¼ 2C 1 ffiffiffiffiffiffiffi ÀT p þ T þ C 2 ; predicts the decay of dark energy in the far future while its special case namely teleparallel gravity predicts that dark energy will overcome over all the energy content of the Universe.