Relating the cosmological constant and slow roll to conformal symmetry   breaking
  We show that a theory with conformal invariance, which is explicitly broken by small terms, provides a solution to the fine tuning problem of the cosmological constant. In the absence of the symmetry breaking terms, the cosmological constant is zero. Its value in the full theory is controlled by the symmetry breaking terms. The symmetry breaking terms also provide the slow roll conditions, which may be useful in constructing a model of inflation. 
Pankaj Jain and Gopal Kashyap
astro-ph.CO gr-qc hep-ph