Multi-field TDiff theories: the mixed regime case

Abstract

We study theories breaking diffeomorphism (Diff) invariance down to the subgroup of transverse diffeomorphisms (TDiff), consisting of multiple scalar fields in a cosmological background. In particular, we focus on models involving a field dominated by its kinetic term and a field dominated by its potential, coupled to gravity through power-law functions of the metric determinant. The Diff symmetry breaking results in the individual energy-momentum tensors not being conserved, although the total conservation-law is satisfied. Consequently, an energy exchange takes place between the fields, acting as an effective interaction between them. With this in mind, we consider the covariantized approach to describe the theory in a Diff invariant way but with an additional field, and discuss the phenomenological consequences of these models when it comes to the study of the dark sector.

Figures (7)

• Figure 1: Effective EoS parameter $w_\mathrm{eff,1}$ for the potentially driven field under the kinetic field domination regime in terms of the potential coupling exponent $\alpha_1$ and the EoS parameter for the kinetic field $w_2$.
• Figure 2: Effective EoS parameter for both components in terms of the scale factor for the case with $\alpha_1<0$ ($\alpha_1=-1/2$, $C_1=7/10$). Dark energy exhibits phantom behavior and asymptotically tends to a cosmological constant in the future.
• Figure 3: Evolution of the DM and DE energy densities in terms of the scale factor $a$ for $\alpha_1<0$ ($\alpha_1=-1/2$, $C_1=7/10$). DE presents phantom behavior and asymptotically tends to a cosmological constant in the future.
• Figure 4: Equation of state of the dark sector in terms of the scale factor $a$ for $\alpha_1<0$ ($\alpha_1=-1/2$, $C_1=7/10$). $w_\mathrm{DS}$ smoothly transitions from 0 in the past (DM domination) to $-1$ in the future (DE domination).
• Figure 5: Effective EoS parameter for both components in terms of the scale factor for the case with $0<\alpha_1<1$ ($\alpha_1=1/20$, $C_1=700$). $\phi_1$ exhibits phantom quintessence behavior with $-1<w_{\mathrm{eff},1}(a)<-1/3$ under $\phi_2$ domination in the past and tracks $\phi_2$ in the future.