Agravity

TL;DR

agravity proposes a scale-free, renormalizable theory of gravity in which all mass scales arise dynamically, notably generating the Planck scale via a scalar that acts as the Higgs of gravity. The authors compute the full one-loop RGEs for adimensional gravity coupled to a generic matter sector, deriving conditions under which a vanishing cosmological constant and a Planck-scale vacuum emerge, and show that inflation is a generic outcome with slow-roll parameters tied to the theory's $\beta$-functions. Identifying the inflaton with the gravity-related scalar predicts $n_s = 1 - \frac{2}{N}$ and $r = \frac{8}{N}$, e.g. $n_s \approx 0.967$ and $r \approx 0.13$ for $N\approx60$; a concrete mirror-SM model yields $r \approx 0.128$ and an inflaton mass around $10^{13}$ GeV. The framework also argues that quadratically divergent Higgs corrections can vanish, allowing the weak scale to be natural without low-energy new physics, provided the gravitational couplings are suitably small, thereby linking Planck- and weak-scale physics through quantum corrections.

Abstract

We explore the possibility that the fundamental theory of nature does not contain any scale. This implies a renormalizable quantum gravity theory where the graviton kinetic term has 4 derivatives, and can be reinterpreted as gravity minus an anti-graviton. We compute the super-Planckian RGE of adimensional gravity coupled to a generic matter sector. The Planck scale and a flat space can arise dynamically at quantum level provided that a quartic scalar coupling and its $β$ function vanish at the Planck scale. This is how the Higgs boson behaves for $M_h\approx 125$ GeV at $M_t\approx 171$ GeV. Within agravity, inflation is a generic phenomenon: the slow-roll parameters are given by the $β$-functions of the theory, and are small if couplings are perturbative. The predictions $n_s\approx 0.967$ and $r\approx 0.13$ arise if the inflaton is identified with the Higgs of gravity. Furthermore, quadratically divergent corrections to the Higgs mass vanish: a small weak scale is natural and can be generated by agravity quantum corrections.

Figures (3)

• Figure 1: Gravitational corrections to the running of the gauge couplings.
• Figure 2: Gravitational corrections to the running of the Yukawa couplings.
• Figure 3: Running of the quartic Higgs coupling in the SM NNLO. Agravity corrections can increase $\beta_{\lambda_H} = d\lambda_H/d\ln\bar{\mu}$ and thereby $\lambda_H$ at scales above $M_{0,2}$. Parameterizing the effective potential as $V_{\rm eff}(h) \equiv \lambda_{\rm eff}(h) h^4/4$, the $\beta$ function of $\lambda_{\rm eff}$ vanishes at a scale a factor of few higher than the $\beta$ function of $\lambda_H$.