Action functional of the Cardassian universe

It is known that the Cardassian universe is successful in describing the accelerated expansion of the universe, but its dynamic equations are hard to get from the action principle. In this paper, we establish the connection between the Cardassian universe and $f(T,\mathcal{T})$ gravity, where $T$ is the torsion scalar and $\mathcal{T}$ is the trace of the matter energy-momentum tensor. For dust matter, we find that the modified Friedmann equations from $f(T,\mathcal{T})$ gravity can correspond to those of Cardassian models, and thus, a possible origin of Cardassian universe is given. We obtain the original Cardassian model, the modified polytropic Cardassian model, and the exponential Cardassian model from the Lagrangians of $f(T,\mathcal{T})$ theory. Furthermore, by adding an additional term to the corresponding Lagrangians, we give three generalized Cardassian models from $f(T,\mathcal{T})$ theory. Using the observation data of type Ia supernovae, cosmic microwave background radiation, and baryon acoustic oscillations, we get the fitting results of the cosmological parameters and give constraints of model parameters for all of these models.

Figure 1

Constraints on ${\mathrm{\Omega }}_{m0}$ and $n$ from the $1\sigma$ to the $3\sigma$ confidence levels by using JLA SNe $\mathrm{Ia}+\text{CMB}+\mathrm{BAO}$ for model I, while other parameters take their best fitting values.

Figure 2

Constraints on ${\mathrm{\Omega }}_{m0}$ and $n$ from the $1\sigma$ to the $3\sigma$ confidence levels by using JLA SNe $\mathrm{Ia}+\text{CMB}+\mathrm{BAO}$ for model II, while other parameters take their best fitting values.

Figure 3

Constraints on ${\mathrm{\Omega }}_{m0}$ and $n$ from the $1\sigma$ to the $3\sigma$ confidence levels by using JLA SNe $\mathrm{Ia}+\text{CMB}+\mathrm{BAO}$ for model III, while other parameters take their best fitting values.