Gravity with perturbative constraints: Dark energy without new degrees of freedom

Major observational efforts in the coming decade are designed to probe the equation of state of dark energy. Measuring a deviation of the equation-of-state parameter $w$ from $-1$ would indicate a dark energy that cannot be represented solely by a cosmological constant. While it is commonly assumed that any implied modification to the $\Lambda \mathrm{CDM}$ model amounts to the addition of new dynamical fields, we propose here a framework for investigating whether or not such new fields are required when cosmological observations are combined with a set of minimal assumptions about the nature of gravitational physics. In our approach, we treat the additional degrees of freedom as perturbatively constrained and calculate a number of observable quantities, such as the Hubble expansion rate and the cosmic acceleration, for a homogeneous universe. We show that current observations place our universe within the perturbative validity of our framework and allow for the presence of nondynamical gravitational degrees of freedom at cosmological scales.

Figure 1

Contours of constant values of the parameter ${\Omega }_m$ at the present epoch, for different values of the cosmological constant $\Lambda$ and the parameter ${\mu }^4$ of the action of the gravitational field. The normalization constant ${\rho }_{m,0}$ is the density of matter at the present epoch. The hatched area shows the region of the parameter space where the calculation of ${\Omega }_m$ is not perturbatively valid.

Figure 2

Same as Fig. 1 for the deceleration parameter $q_0$ at the present epoch. Only negative values of $q_0$ are shown, which correspond to universes that are currently accelerating.

Figure 3

Same as Fig. 1 for the equivalent equation-of-state parameter $w_X$ of a XCDM model with the same cosmological expansion at the present epoch.