We investigate the cosmological applications of $F(T,T_G)$ gravity, which is a novel modified gravitational theory based on the torsion invariant $T$ and the teleparallel equivalent of the Gauss-Bonnet term $T_{G}$. $F(T,T_{G})$ gravity differs from
both $F(T)$ theories as well as from $F(R,G)$ class of curvature modified gravity, and thus its corresponding cosmology proves to be very interesting. In particular, it provides a unified description of the cosmological history from early-times inflation to late-times self-acceleration, without the inclusion of a cosmological constant. Moreover, the dark energy equation-of-state parameter can be quintessence or phantom-like, or experience the phantom-divide crossing, depending on the parameters of the model.
The $f(T,T_G)$ class of gravitational modification, based on the quadratic torsion scalar $T$, as well as on the new quartic torsion scalar $T_G$ which is the teleparallel equivalent of the Gauss-Bonnet term, is a novel theory, different from both $f
(T)$ and $f(R,G)$ ones. We perform a detailed dynamical analysis of a spatially flat universe governed by the simplest non-trivial model of $f(T,T_G)$ gravity which does not introduce a new mass scale. We find that the universe can result in dark-energy dominated, quintessence-like, cosmological-constant-like or phantom-like solutions, according to the parameter choices. Additionally, it may result to a dark energy - dark matter scaling solution, and thus it can alleviate the coincidence problem. Finally, the analysis at infinity reveals that the universe may exhibit future, past, or intermediate singularities depending on the parameters.
We investigate the cosmological implications of the recently constructed 5-dimensional braneworld cosmology with gravitating Nambu-Goto matching conditions. Inserting both matter and radiation sectors, we first extract the analytical cosmological sol
utions. Additionally, we use observational data from Type Ia Supernovae (SNIa) and Baryon Acoustic Oscillations (BAO), along with requirements of Big Bang Nucleosynthesis (BBN), in order to impose constraints on the parameters of the model. We find that the scenario at hand is in very good agreement with observations, and thus a small departure from the standard Randall-Sundrum scenario is allowed.
We perform a combined perturbation and observational investigation of the scenario of non-minimal derivative coupling between a scalar field and curvature. First we extract the necessary condition that ensures the absence of instabilities, which is f
ulfilled more sufficiently for smaller coupling values. Then using Type Ia Supernovae (SNIa), Baryon Acoustic Oscillations (BAO), and Cosmic Microwave Background (CMB) observations, we show that, contrary to its significant effects on inflation, the non-minimal derivative coupling term has a negligible effect on the universe acceleration, since it is driven solely by the usual scalar-field potential. Therefore, the scenario can provide a unified picture of early and late time cosmology, with the non-minimal derivative coupling term responsible for inflation, and the usual potential responsible for late-time acceleration. Additionally, the fact that the necessary coupling term does not need to be large, improves the model behavior against instabilities.
