Towards realistic $f(T)$ models with nonminimal torsion-matter coupling extension

Using the observation data of type Ia supernovae, cosmic microwave background, and baryon acoustic oscillations, we establish two concrete $f(T)$ models with a 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 and its large-scale structure and evolution. In other words, these models do not change the successful aspects of the $\mathrm{\Lambda }\mathrm{CDM}$ scenario under the error band of fitting values as describing the evolution history of the Universe including the radiation-dominated era, the 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 $\mathrm{\Lambda }\mathrm{CDM}$. A joint analysis is performed by using the data of cosmic microwave $\text{background}+\text{baryon}$ acoustic $\text{oscillations}+\text{joint}$ light-curve analysis, which leads to ${\mathrm{\Omega }}_{m0}=0.255\pm 0.010$, ${\mathrm{\Omega }}_{b0}{h}^2=0.0221\pm 0.0003$ and $H_0=68.54\pm 1.27$ for model I and ${\mathrm{\Omega }}_{m0}=0.306\pm 0.010$, ${\mathrm{\Omega }}_{b0}{h}^2=0.0225\pm 0.0003$ and $H_0=60.97\pm 0.44$ for model II at $1\sigma$ confidence level. The evolution of the decelaration parameter $q(a)$ and the effective equation of state $w_{DE}(a)$ are displayed. Furthermore, the resulting 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 and model II result in a de Sitter accelerating phase and a power-law one, respectively, even though $w_{DE0}<-1$ makes model I look like a phantom at the present time.

Figure 1

Evolution of the equation of state with different parameter values for model I. In the upper panel, $A=0.188$, and in the bottom panel, ${\mathrm{\Omega }}_{m0}=0.255$.

Figure 2

Evolution of the equation of state with different parameter values for model II.

Figure 3

Constraints on ${\mathrm{\Omega }}_{m0}$ and $A$ from $1\sigma$ to $3\sigma$ confidence level obtained by using JLA $\mathrm{SNeIa}+\mathrm{CMB}+\mathrm{BAO}$ for model I, while other parameters take their best fitting values.

Figure 4

The evolution of the deceleration parameter. The solid line is for model I, and the dot-dashed line is for model II.

Figure 5

The evolutions of the scale factor in the future of the Universe. The dotted line is for $\mathrm{\Lambda }\mathrm{CDM}$, the solid line is for model I, and the dot-dashed line is for model II.