Antonio Enea Romano, Pisin Chen
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. We compute the Taylor expansion for the luminosity distance in a LTB solution with non vanishing cosmological constant. We then apply it to derive a relation between the apparent and the true value of the cosmological constant, i.e. the one appearing in the LTB solution. The assumption to be at the center of a spherically symmetric inhomogeneous matter distribution corresponds to effectively calculate the monopole contribution of the large scale structure around us, which we expect to be the dominant one, because of other observations such as the cosmic microwave background radiation supporting a high level of isotropy of the Universe around us.
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http://arxiv.org/abs/1207.5572
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