Using the observation data of SNeIa, CMB and BAO, we establish two concrete f (T ) models with nonminimal torsion-matter coupling extension. We study in detail the cosmological implication of our models and find they are successful in describing the observation of the Universe, its large scale structure and evolution. In other words, these models do not change the successful aspects of ΛCDM scenario under the error band of fitting values as describing the evolution history of the Universe including radiation-dominated era, matter-dominated era and the present accelerating expansion. Meanwhile, the significant advantage of these models is that they could avoid the cosmological constant problem of ΛCDM. A joint analysis is performed by using the data of CMB+BAO+JLA, which leads to Ωm0 = 0.255 ± 0.010, Ω b0 h 2 = 0.0221 ± 0.0003 and H0 = 68.54 ± 1.27 for model I and Ωm0 = 0.306 ± 0.010, Ω b0 h 2 = 0.0225 ± 0.0003 and H0 = 60.97 ± 0.44 for model II at 1σ confidence level. The evolution of the decelaration parameter q(a) and the effective equation of state wDE(a) are displayed. Furthermore, The resulted age of the Universe from our models is consistent with the ages of the oldest globular clusters. As for the fate of the Universe, model I results in a de Sitter accelerating phase while model II appears a power-law one, even though wDE0 < −1 makes model I look like a phantom at present time.PACS numbers: 04.50. Kd, 95.36.+x arXiv:1511.07935v1 [gr-qc]

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In the previous paper, we have constructed two f (T ) models with non-minimal torsion-matter coupling extension, which are successful in describing the evolution history of the Universe including the radiation-dominated era, the matter-dominated era, and the present accelerating expansion. Meantime, the significant advantage of these models is that they could avoid the cosmological constant problem of CDM. However, the non-minimal coupling between matter and torsion will affect the tests of the Solar system. In this paper, we study the effects of the Solar system in these models, including the gravitation redshift, geodetic effect and perihelion precession. We find that Model I can pass all three of the Solar system tests. For Model II, the parameter is constrained by the uncertainties of the planets' estimated perihelion precessions.

We investigate the nonrotating neutron stars in f(T) gravity with $$f(T)=T+\alpha {T}^2$$ f ( T ) = T + α T 2 , where T is the torsion scalar in the teleparallel formalism of gravity. In particular, we utilize the SLy and BSk family of equations of state for perfect fluid to describe the neutron stellar matter and search for the effects of the f(T) modification on the models of neutron stars. For positive $$\alpha $$ α , the modification results in a smaller stellar mass in comparison to general relativity, while the neutron stars will contain larger amount of matter for negative $$\alpha $$ α . Moreover, there seems to be an upper limit for the central density of the neutron stars with $$\alpha >0$$ α > 0 , beyond which the effective f(T) fluid would have a steplike phase transition in density and pressure profiles, collapsing the numerical system. We obtain the mass–radius relations of the realistic models of neutron stars and subject them to the joint constraints from the observed massive pulsars PSR J0030+0451, PSR J0740+6620, and PSR J2215+5135, and gravitational wave events GW170817 and GW190814. For the neutron star model in f(T) gravity to be able to accommodate all the mentioned data, the model parameter $$\alpha $$ α needs to be smaller than $$-\,4.295$$ - 4.295 , $$-\,6.476$$ - 6.476 , $$-\,4.4$$ - 4.4 , and $$-\,2.12$$ - 2.12 (in the unit of $${G}^2M_\odot ^2/c^4$$ G 2 M ⊙ 2 / c 4 ) for SLy, BSk19, BSk20, and BSk21 equations of state, respectively. If one considers the unknown compact object in the event GW190814 not to be a neutron star and hence excludes this dataset, the constraints can be loosened to $$\alpha <-\,0.594$$ α < - 0.594 , $$-\,3.5$$ - 3.5 , 0.4 and 1.9 (in the unit of $${G}^2M_\odot ^2/c^4$$ G 2 M ⊙ 2 / c 4 ), respectively.