Inflation from Broken Scale Invariance

We construct a model of inflation based on a low-energy effective theory of spontaneously broken global scale invariance. This provides a shift symmetry that protects the inflaton potential from quantum corrections. Since the underlying scale invariance is noncompact, arbitrarily large inflaton field displacements are readily allowed in the low-energy effective theory. A weak breaking of scale invariance by almost marginal operators provides a nontrivial inflaton minimum, which sets and stabilizes the final low-energy value of the Planck scale. The underlying scale invariance ensures that the slow-roll approximation remains valid over large inflaton displacements, and yields a scale invariant spectrum of perturbations, as required by the cosmic microwave background observations.

Figure 1

Values of $n_s$ and $r$ for $\epsilon \sqrt{\xi }\in [-0.5,0.5]$, for ${\phi }_0<⟨\phi ⟩=0$. The same results are obtained for ${\phi }_0>⟨\phi ⟩=0$, but with opposite signs for $\epsilon$. The points shown correspond to $\epsilon \sqrt{\xi }=-0.001,-0.01,-0.05,0.001,0.01,0.1,0,5$, and $\sqrt{2/3}$ in green for the Starobinsky model. The red and blue contours show the 68% and 95% confidence regions by Planck and BICEP2, respectively.

Figure 2

Line of values of $n_s$ and $r$ for $\epsilon \sqrt{\xi }\in (0,0.5]$, with points at $\epsilon \sqrt{\xi }=0.1,0.01$, for either sign of ${\phi }_0$. The same results are obtained for negative $\epsilon$. The red and blue contours show the 68% and 95% confidence regions by Planck and BICEP2, respectively.