Constraints on Dirac-Born-Infeld type dark energy models from varying alpha

We study the variation of the effective fine-structure constant alpha for Dirac-Born-Infeld (DBI) type dark energy models. The DBI action based on string theory naturally gives rise to a coupling between gauge fields and a scalar field responsible for accelerated expansion of the universe. This leads to the change of alpha due to a dynamical evolution of the scalar field, which can be compatible with the recently observed cosmological data around the redshift $\tilde{z}\lesssim 3$. We place constraints on several different DBI models including exponential, inverse power-law and rolling massive scalar potentials. We find that these models can satisfy the varying alpha constraint provided that mass scales of the potentials are fine-tuned. When we adopt the mass scales which are motivated by string theory, both exponential and inverse power-law potentials give unacceptably large change of alpha, thus ruled out from observations. On the other hand the rolling massive scalar potential is compatible with the observationally allowed variation of alpha. Therefore the information of varying alpha provides a powerful way to distinguish between a number of string-inspired DBI dark energy models.

Figure 1

The variation of $\Delta \alpha /\alpha$ as a function of the redshift $\tilde{z}$ for the exponential potential (30) with $\mu =8.65\times {10}^{-3}{H}_0$. Initial conditions are chosen to be $x_i-1=-1.0\times {10}^{-12}$, $y_i=2.5\times {10}^{-10}$, $z_i=0.99$ and $\lambda =5.0\times {10}^{-3}$ at $\tilde{z}={10}^6$. The present epoch ($\tilde{z}=0$) corresponds to ${\Omega }_{\varphi }\simeq 0.7$ and ${\Omega }_m\simeq 0.3$.

Figure 2

The evolution of the energy densities ${\rho }_{\varphi }$, ${\rho }_r$ and ${\rho }_m$ for the exponential potential (30) with $\mu =8.65\times {10}^{-3}{H}_0$. Initial conditions are the same as in Fig. 1.

Figure 3

The mass scale $M/M_p$ determined by the varying alpha constraint in terms of the function of the power $n$. Each case corresponds to (a) $|\Delta \alpha /\alpha |={10}^{-5}$, (b) $|\Delta \alpha /\alpha |={10}^{-6}$, and (c) $|\Delta \alpha /\alpha |={10}^{-7}$ at $\tilde{z}=1$. The curve (d) is the bound which is determined by the condition for accelerated expansion, see Eq. (45).

Figure 4

The evolution of ${\Omega }_{\varphi }$, ${\Omega }_m$ and ${\Omega }_r$ as a function of the redshift $\tilde{z}$ for the inverse power-law potential with $n=1$ and $M=3.79\times {10}^{-19}{M}_p$. This case satisfies ${\Omega }_{\varphi }=0.7$ and ${\varphi }_{0}M=1.50\times {10}^{42}$ at $\tilde{z}=0$. This cosmological evolution corresponds to the case (a) in which the slow-roll condition $ϵ\ll 1$ is satisfied for $\tilde{z}>\mathcal{O}(1)$.

Figure 5

The evolution of the slow-roll parameter $ϵ$ for the inverse power-law potential with $n=1$ and $M=3.79\times {10}^{-19}{M}_p$. Each case corresponds to (a) ${\varphi }_{0}M=1.50\times {10}^{42}$ and (b) ${\varphi }_{0}M=3.98\times {10}^{36}$ at $\tilde{z}=0$. In the case (a) $ϵ$ is nearly constant with $ϵ\ll 1$. Meanwhile $ϵ$ becomes smaller than $1$ only near to the present in the case (b).

Figure 6

The variation of alpha as a function of the redshift $\tilde{z}$ with same model parameters and initial conditions as in Fig. 5. The case (a) shows a small variation of alpha, whereas the case (b) gives large values of $|\Delta \alpha /\alpha |$.