Corrections to the apparent value of the cosmological constant due to
  local inhomogeneities
  Supernovae observations strongly support the presence of a cosmological
constant, but its value, which we will call apparent, is normally determined
assuming that the Universe can be accurately described by a homogeneous model.
Even in the presence of a cosmological constant we cannot exclude nevertheless
the presence of a small local inhomogeneity which could affect the apparent
value of the cosmological constant. Neglecting the presence of the
inhomogeneity can in fact introduce a systematic misinterpretation of
cosmological data, leading to the distinction between an apparent and true
value of the cosmological constant. We establish the theoretical framework to
calculate the corrections to the apparent value of the cosmological constant by
modeling the local inhomogeneity with a $\Lambda LTB$ solution. Our assumption
to be at the center of a spherically symmetric inhomogeneous matter
distribution correspond to effectively calculate the monopole contribution of
the large scale inhomogeneities surrounding us, which we expect to be the
dominant one, because of other observations supporting a high level of isotropy
of the Universe around us.
  By performing a local Taylor expansion we analyze the number of independent
degrees of freedom which determine the local shape of the inhomogeneity, and
consider the issue of central smoothness, showing how the same correction can
correspond to different inhomogeneity profiles. Contrary to previous attempts
to fit data using large void models our approach is quite general. The
correction to the apparent value of the cosmological constant is in fact
present for local inhomogeneities of any size, and should always be taken
appropriately into account both theoretically and observationally.
