Generalizing tensor-vector-scalar cosmology

I consider an extended version of Bekenstein’s Tensor-Vector-Scalar theory where the action of the vector field is of a general Einstein-Ether form. This work presents the cosmological equations of this theory, both at the background and perturbed level, for scalar, vector and tensor perturbation modes. By solving the background equations in the radiation era analytically, to an excellent approximation, I construct the primordial adiabatic perturbation for a general family of scalar field kinetic functions.

Figure 1

Exact numerical evolution (solid) and the analytical approximation (dashed) for $\overline{\varphi }$ (upper panel) and $\mu$ (lower panel). The initial condition for $\overline{\varphi }$ is ${10}^{-3}$. Both approximations are excellent in the radiation era and depart from the true solution once the Universe starts to enter the matter era. The radiation-matter equality is indicated by the vertical dotted lines.

Figure 2

Exact numerical evolution (solid) and the analytical approximation (dashed) for $\dot{\overline{\varphi }}$ (upper panel) and $\mu \dot{\overline{\varphi }}t$ (lower panel) for the same model in Fig. 1. Both approximations are excellent in the radiation era and depart from the true solution once the Universe starts to enter the matter era. The radiation-matter equality is indicated by the vertical dotted lines.

Figure 3

Exact numerical evolution (solid) and the analytical approximation (dashed) for $h$ (upper left panel), $v_{\nu }$ (upper right panel), ${\delta }_{\gamma }$ (lower left panel), and ${\sigma }_{\nu }$ (lower right panel), for the same model in Fig. 1. All approximations are excellent in the radiation era during tight-coupling and depart from the exact numerical solution once the Universe starts to enter the matter era and/or departs from tight-coupling.

Figure 4

Exact numerical evolution (solid) and the analytical approximation (dashed) for $\phi$ (upper left panel), $y$ (lower left panel), $u$ (upper right panel) and $E$ (lower right panel), for the same model as in Fig. 1. All approximations are excellent in the radiation era during tight-coupling and depart from the exact numerical solution once the Universe starts to enter the matter era and/or departs from tight-coupling.