Abstract
We study cosmological perturbations in bimetric theory with two fluids each of which is coupled to one of the two metrics. Focusing on a healthy branch of background solutions, we clarify the stability of the cosmological perturbations. For this purpose, we extend the condition for the absence of the so-called Higuchi ghost, and show that the condition is guaranteed to be satisfied on the healthy branch. We also calculate the squared propagation speeds of perturbations and derive the conditions for the absence of the gradient instability. To avoid the gradient instability, we find that the model parameters are weakly constrained.
Highlights
Background equations and solution brancheswe derive the equations of motion for the background FLRW universe, and discuss the branches of the background solutions
We have presented a linear analysis of cosmological perturbations in bimetric theory, in which two metrics are coupled through non-derivative coupling so that it does not yield BoulwareDeser ghost as prescribed in [10]
We consider perturbations around the background of two dynamical FLRW metrics sharing spatial isometries, each of which is minimally coupled to a different k-essence field
Summary
We derive the equations of motion for the background FLRW universe, and discuss the branches of the background solutions. In the low energy limit or in the pure gravity case, W in eq (3.17) with K = 0 is reduced to m2eff /2 − H2, where meff is the effective graviton mass defined in eq (3.13). This quantity must be positive for the absence of Higuchi ghost [17]. The positivity of W indicates that J = 0 is not realized except in the limit where H2 + K/a2 and W simultaneously vanish, provided that |K|/a2 < H2 in accord with observation In this low energy limit, the value of ξ converges to ξc, which is different from the zeros of J(ξ) in general. As long as the healthy branch solution continues to exist, the condition dρm/d ln ξ > 0 is maintained
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