Scale Invariance as a Solution to the Cosmological Constant Problem
  We show that scale invariance provides a solution to the fine tuning problem
of the cosmological constant. We construct a generalization of the standard
model of particle physics which displays exact quantum scale invariance. The
matter action is invariant under global scale transformations in arbitrary
dimensions. However the gravitational action breaks scale invariance
explicitly. The scale symmetry is broken spontaneously in the matter sector of
the theory. We show that the contribution to the vacuum energy and hence the
cosmological constant is identically zero from the matter sector within the
full quantum theory. However the gravitational sector may give non-zero
contributions to the cosmological constant at loop orders. No fine tuning may
be required at loop orders since the matter sector gives zero contribution to
the cosmological constant. We also show that we do not require full scale
invariance in order to constrain the vacuum energy from the matter sector. We
only require invariance under pseudoscale transformations. Using this idea and
motivated by the concept of unimodular gravity we propose an alternative model.
In this case also we show that matter sector gives exactly zero contribution to
the vacuum energy.
