Teleparallel theory of gravity and its modifications have been studied extensively in literature. However, gravitational waves has not been studied enough in the framework of teleparallelism. In the present study, we discuss gravitational waves in general theories of teleparallel gravity containing the torsion scalar T, the boundary term B and a scalar field . The goal is to classify possible new polarizations generalizing results presented in Bamba et al. (Phys Lett B 727:194–198, arXiv:1309.2698, 2013). We show that, if the boundary term is minimally coupled to the torsion scalar and the scalar field, gravitational waves have the same polarization modes of General Relativity.

In the present study, we consider an extended form of teleparallel Lagrangian f (T, φ, X), as function of a scalar field φ, its kinetic term X and the torsion scalar T . We use linear perturbations to obtain the equation of matter density perturbations on sub-Hubble scales. The gravitational coupling is modified in scalar modes with respect to the one of General Relativity, albeit vector modes decay and do not show any significant effects. We thus extend these results by involving multiple scalar field models. Further, we study conformal transformations in teleparallel gravity and we obtain the coupling as the scalar field is non-minimally coupled to both torsion and boundary terms. Finally, we propose the specific model f (T, φ, X) = T + ∂µφ ∂ µ φ + ξT φ 2 . To check its goodness, we employ the observational Hubble data, constraining the coupling constant, ξ, through a Monte Carlo technique based on the Metropolis-Hastings algorithm. Hence, fixing ξ to its best-fit value got from our numerical analysis, we calculate the growth rate of matter perturbations and we compare our outcomes with the latest measurements and the predictions of the ΛCDM model. one way to tackle the dark energy problem is to consider new dynamical degrees of freedom inside the teleparallel scheme. For example, theories in which one replaces the Lagrangian by f (T ) functions, i.e. where the torsion scalar is replaced by a nonlinear function f (T ) [16][17][18][19][20][21], represent a viable framework naively inspired by f (R)gravity. This prescription can be even extended by a more general form based on f (T, B) functions in order to include both torsion and the boundary term [22,23]. This leads to a generalization of both f (R) and f (T ) classes of models and have been also studied as f (R, T ) in [24].In addition, one can use a scalar field responsible for the expansion, providing a scalar-tensor teleparallel dark energy acting as solution to the cosmic acceleration problem [26][27][28][29][30][31] and analogous to [25]. In this picture, the scalar field should be non-minimally coupled to gravity. This has been proved by working on renormalization of scalar-tensor theory and in the context of quantum corrections on curved spacetime [32][33][34][35][36][37][38].The most common way is to include a single scalar field, although this choice is not unique. Indeed, even though the use of single field models is consistent with data, the idea to consider multiple field models during inflation and the late-time expansion [39] is still possible. The multi-field can also be non-minimally coupled to gravity.

Abstract. Multiple field models of inflation exhibit new features than single field models.In this work, we study the hierarchy of parameters based on Hubble expansion rate in curved field space and derive the system of flow equations that describe their evolutions. Then we focus on obtaining derivatives of number of e-folds with respect to scalar fields during inflation and at hypersurface of the end of inflation.

This work is devoted to drive an energy-momentum complex (due to matter and fields including gravity) in the realm of modified teleparallel gravity. For this purpose, the Lagrangian of teleparallel theory is extended to a more general form by replacing the torsion scalar with an arbitrary function of it. Furthermore, considering cosmological perturbations, we explicitly calculate energy distribution associated with the Friedmann-Lemaitre-Robertson-Walker spacetime. Finally, we discuss also the coupling case between matter and gravity in the context of teleparallel modified theory.

We reconsider the stochastic gravitational wave background spectrum produced during the first order hadronization process, in presence of ultraviolet cutoffs suggested by the generalized uncertainty principle as a promising signature towards the Planck scale physics. Unlike common perception that the dynamics of QCD phase transition and its phenomenological consequences are highly influenced by the critical temperature, we find that the underlying Planck scale modifications can affect the stochastic gravitational spectrum arising from the QCD transition without a noteworthy change in the relevant critical temperature. Our investigation shows that incorporating the natural cutoffs into MIT bag equation of state and background evolution leads to a growth in the stochastic gravitational power spectrum, while the relevant redshift of the QCD era, remains unaltered. These results have double implications from the point of view of phenomenology. Firstly, it is expected to enhance the chance of detecting the stochastic gravitational signal created by such a transition in future observations. Secondly, it gives a hint on the decoding from the dynamics of QCD phase transition.