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Register a new userSpin connection and cosmological perturbations in $f(T)$ gravity
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In this paper we study cosmological perturbations in teleparallel gravity. We discuss problems which appear in standard approach to $f(T)$ gravity, and find that these problems may be solved within covariant formulation of teleparallel gravity, which take into account spin connection. We calculate spin connection which symmetrize equation for perturbation and split diagonal and non-diagonal part of equation of motion. We demonstrate that there is minimal solution for spin connection, which lead to zero slip, however, in this case one additional equation appears, so the system may become over-determined. After that, we show that a more general solution exists, which is incompatible with zero slip, but allows to write down the equations of motion for cosmological perturbation in a self-consistent way without additional equations to be satisfied.
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We investigate the cosmological perturbations in f(T) gravity. Examining the pure gravitational perturbations in the scalar sector using a diagonal vierbien, we extract the corresponding dispersion relation, which provides a constraint on the f(T) ansatzes that lead to a theory free of instabilities. Additionally, upon inclusion of the matter perturbations, we derive the fully perturbed equations of motion, and we study the growth of matter overdensities. We show that f(T) gravity with f(T) constant coincides with General Relativity, both at the background as well as at the first-order perturbation level. Applying our formalism to the power-law model we find that on large subhorizon scales (O(100 Mpc) or larger), the evolution of matter overdensity will differ from LCDM cosmology. Finally, examining the linear perturbations of the vector and tensor sectors, we find that (for the standard choice of vierbein) f(T) gravity is free of massive gravitons.
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.
In this paper we study cosmological solutions of the $f(T,B)$ gravity using dynamical system analyses. For this purpose we consider cosmological viable functions of $f(T,B)$ that are capable of reproducing the dynamics of the Universe. We present three specific models of $f(T,B)$ gravity which have a general form of the solutions by writing the equations of motion as an autonomous system. Finally, we study its hyperbolic critical points and general trajectories in the phase space of the resulting dynamical variables which are compatible with the current late-time observations.
The recent article entitled Cosmological inviability of $f(R,T)$ gravity [Phys. Rev. D 95 (2017) 123536], by H. Velten and T.R.P. Caram^es, claims that the reference A transition from a decelerated to an accelerated phase of the universe expansion from the simplest non-trivial polynomial function of T in the f(R,T) formalism by P.H.R.S. Moraes, G. Ribeiro and R.A.C. Correa [Astrophys. Space Sci. 361 (2016) 227] has problematic points concerning its mathematical approach and observable consequences. Velten and Caram^es argue that the equation of the scale factor evolution in time in the $f(R,T)=R+alpha T+beta T^{2}$ cosmology was erroneously calculated. One crucial consequence of the supposed corrected version of such an equation, presented by the authors in [Phys. Rev. D 95 (2017) 123536], would be the absence of the transition from a decelerated to an accelerated phase of the expansion of the universe, an outcome originally predicted by Moraes, Ribeiro and Correa. We show that the above claim is incorrect and that there are no inconsistencies with the results by Moraes, Ribeiro and Correa in the referred work. In particular, we show that Velten and Caram^es have incorrectly performed their calculations, invalidating all their mathematical and physical criticism regarding the article by Moraes, Ribeiro and Correa. In addition, we quote that the solutions obtained by Velten and Caram^es are unfeasible in view of their mathematical misunderstanding.
We study cosmological perturbation theory within the framework of unimodular gravity. We show that the Lagrangian constraint on the determinant of the metric required by unimodular gravity leads to an extra constraint on the gauge freedom of the metric perturbations. Although the main equation of motion for the gravitational potential remains the same, the shift variable, which is gauge artifact in General Relativity, cannot be set to zero in unimodular gravity. This non-vanishing shift variable affects the propagation of photons throughout the cosmological evolution and therefore modifies the Sachs-Wolfe relation between the relativistic gravitational potential and the microwave temperature anisotropies. However, for adiabatic fluctuations the difference between the result in General Relativity and unimodular gravity is suppressed on large angular scales. Thus, no strong constraints on the theory can be derived.
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