Cuscuton cosmology: Dark energy meets modified gravity

Abstract

In a companion paper [1], we have introduced a model of scalar field dark energy, Cuscuton, which can be realized as the incompressible (or infinite speed of sound) limit of a k-essence fluid. In this paper, we study how Cuscuton modifies the constraint sector of Einstein gravity. In particular, we study Cuscuton cosmology and show that even though Cuscuton can have an arbitrary equation of state, or time dependence, and is thus inhomogeneous, its perturbations do not introduce any additional dynamical degree of freedom and only satisfy a constraint equation, amounting to an effective modification of gravity on large scales. Therefore, Cuscuton can be considered to be a minimal theory of evolving dark energy, or a minimal modification of a cosmological constant, as it has no internal dynamics. Moreover, this is the only modification of Einstein gravity to our knowledge, that does not introduce any additional degrees freedom (and is not conformally equivalent to the Einstein gravity). We then study two simple Cuscuton models, with quadratic and exponential potentials. The quadratic model has the exact same expansion history as ΛCDM, and yet contains an early dark energy component with constant energy fraction, which is constrained to ΩQ < ∼ 2%, mainly from WMAP Cosmic Microwave Background (CMB) and SDSS Lyman-α forest observations. The exponential model has the same expansion history as the DGP self-accelerating braneworld model, but generates a much smaller integrated Sachs-Wolfe (ISW) effect, and is thus consistent with the CMB observations. Finally, we show that the evolution is local on super-horizon scales, implying that there is no gross violation of causality, despite Cuscuton's infinite speed of sound.

Tachyacoustic cosmology: An alternative to inflation

“…This can be identified as exactly the cuscuton Lagrangian, suggested by Afshordi, et al as a candidate for dark energy [29,34,35]. Similarly, the n ¼ 0 solution considered in Sec.…”

Inhomogeneity simplified

“…have been proposed in the context of dark energy [20,21]. The same action arose in the context of holography for Ricci flat backgrounds: the holographic fluid on a timelike hypersurface outside a Rindler horizon has properties consistent with a hydrodynamic expansion around a φ = t background solution of the cuscuton model [22,23].…”

Probing dark energy anisotropy

“…Standard inhomogeneous perturbations, from a low sound speed for example, do not suffice. The pressure perturbations may be decoupled though from the density ones by adopting an infinite sound speed such as in the cuscuton model [48]. Large surveys give strong constraints but must be subdivided into patches to compare the equation of state along different lines of sight, diluting their effective volume.…”