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Register a new userCosmological perturbations in f(T) gravity
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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.
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We show that the f(T) gravitational paradigm, in which gravity is described by an arbitrary function of the torsion scalar, can provide a mechanism for realizing bouncing cosmologies, thereby avoiding the Big Bang singularity. After constructing the simplest version of an f(T) matter bounce, we investigate the scalar and tensor modes of cosmological perturbations. Our results show that metric perturbations in the scalar sector lead to a background-dependent sound speed, which is a distinguishable feature from Einstein gravity. Additionally, we obtain a scale-invariant primordial power spectrum, which is consistent with cosmological observations, but suffers from the problem of a large tensor-to-scalar ratio. However, this can be avoided by introducing extra fields, such as a matter bounce curvaton.
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.
We use a combination of observational data in order to reconstruct the free function of f(T) gravity in a model-independent manner. Starting from the data-driven determined dark-energy equation-of-state parameter we are able to reconstruct the f(T) form. The obtained function is consistent with the standard {Lambda}CDM cosmology within 1{sigma} confidence level, however the best-fit value experiences oscillatory features. We parametrise it with a sinusoidal function with only one extra parameter comparing to {Lambda}CDM paradigm, which is a small oscillatory deviation from it, close to the best-fit curve, and inside the 1{sigma} reconstructed region. Similar oscillatory dark-energy scenarios are known to be in good agreement with observational data, nevertheless this is the first time that such a behavior is proposed for f(T) gravity. Finally, since the reconstruction procedure is completely model-independent, the obtained data-driven reconstructed f(T) form could release the tensions between {Lambda}CDM estimations and local measurements, such as the H0 and {sigma}8 ones.
We calculate the deflection angle, as well as the positions and magnifications of the lensed images, in the case of covariant $f(T)$ gravity. We first extract the spherically symmetric solutions for both the pure-tetrad and the covariant formulation of the theory, since considering spherical solutions the extension to the latter is crucial, in order for the results not to suffer from frame-dependent artifacts. Applying the weak-field, perturbative approximation we extract the deviations of the solutions comparing to General Relativity. Furthermore, we calculate the deflection angle and then the differences of the positions and magnifications in the lensing framework. This effect of consistent $f(T)$ gravity on the lensing features can serve as an observable signature in the realistic cases where $f(T)$ is expected to deviate only slightly from General Relativity, since lensing scales in general are not restricted as in the case of Solar System data, and therefore deviations from General Relativity could be observed more easily.
Modifications of general relativity provide an alternative explanation to dark energy for the observed acceleration of the universe. We review recent developments in modified gravity theories, focusing on higher dimensional approaches and chameleon/f(R) theories. We classify these models in terms of the screening mechanisms that enable such theories to approach general relativity on small scales (and thus satisfy solar system constraints). We describe general features of the modified Friedman equation in such theories. The second half of this review describes experimental tests of gravity in light of the new theoretical approaches. We summarize the high precision tests of gravity on laboratory and solar system scales. We describe in some detail tests on astrophysical scales ranging from ~kpc (galaxy scales) to ~Gpc (large-scale structure). These tests rely on the growth and inter-relationship of perturbations in the metric potentials, density and velocity fields which can be measured using gravitational lensing, galaxy cluster abundances, galaxy clustering and the Integrated Sachs-Wolfe effect. A robust way to interpret observations is by constraining effective parameters, such as the ratio of the two metric potentials. Currently tests of gravity on astrophysical scales are in the early stages --- we summarize these tests and discuss the interesting prospects for new tests in the coming decade.
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