Does the Planck Mass Run on the Cosmological-Horizon Scale?

Einstein’s theory of general relativity contains a universal value of the Planck mass. However, one may envisage that in alternative theories of gravity the effective value of the Planck mass (or Newton’s constant), which quantifies the coupling of matter to metric perturbations, can run on the cosmological-horizon scale. In this Letter, we study the consequences of a glitch in the Planck mass from subhorizon to superhorizon scales. We show that current cosmological observations severely constrain this glitch to less than 1.2%.

Figure 1

Top: Observational constraints on the UV/IR Planck mass mismatch parameter $\alpha$ from 3 years of WMAP data alone [24] (red, dashed line), and our compilation (see the text) of cosmological observations (black straight line). Bottom: Transition between the IR and UV regimes for the effective Planck mass (in units of $M_{p,\mathrm{UV}}$) defined in Eq. (8) for the quadratic Cuscuton with $\alpha =-0.05$ (red, solid line). The transition for a canonical scalar field model ($c_s^2=1$) is depicted in green (dashed line). For $c_s^2\gtrsim 10$, the transitions virtually coincide with the quadratic Cuscuton (for which $c_s^2=\infty$).