De Sitter and scaling solutions in a higher-order modified teleparallel theory

Abstract

The existence and the stability conditions for some exact relativistic solutions of special interest are studied in a higher-order modified teleparallel gravitational theory. The theory with the use of a Lagrange multiplier is equivalent with that of General Relativity with a minimally coupled noncanonical field. The conditions for the existence of de Sitter solutions and ideal gas solutions in the case of vacuum are studied as also the stability criteria. Furthermore, in the presence of matter the behaviour of scaling solutions is given. Finally, we discuss the degrees of freedom of the field equations and we reduce the field equations in an algebraic equation, where in order to demonstrate our result we show how this noncanonical scalar field can reproduce the Hubble function of Λ-cosmology.PACS numbers: 98.80.-k, 95.35.+d, 95.36.+x

Exact Spherically Symmetric Solutions in Modified Teleparallel Gravity

“…In [25,37] the authors found that there is one extra gravitational polarization mode in this theory, as in f (R) gravity. It has been found that f (T, B) cosmology can explain dark energy without evoking a cosmological constant and also that this theory can describe a transition from a matter dominated era to two different accelerated eras, one of which describes a de Sitter universe [38][39][40].…”

Cartan symmetries and global dynamical systems analysis in a higher-order modified teleparallel theory

“…Assuming that the non-holonomic frame is inherent in the structure of spacetime we have at our disposal n 2 new parameters h µ i which can be used for the definition of dark energy. We associate with dark energy the scalar field of geometric origin and noncanonical kinetic term with energy momentum tensor [45,46]…”

“…In this article, we work in the context of the TEGR by considering a higher-order theory of gravity which introduces a scalar field with a noncanonical kinetic term as a dark-energy component [45,46] 1 . Another well-known scalar field which is related with a modified theory is the field in the O'Hanlon theory which describes the geometrodynamic degrees of freedom in f (R) −gravity.…”

Generalised nonminimally gravity-matter coupled theory

“…If we replace the above equation and also use the Friedmann constraint (63), the remaining three Eqs. (48), (53) and (54) gives us the following set of equations,…”