'Swiss-cheese' inhomogeneous cosmology and the dark energy problem

We study an exact Swiss-cheese model of the universe, where inhomogeneous LTB patches are embedded in a. at FLRW background, in order to see how observations of distant sources are affected. We focus mainly on the redshift, both perturbatively and non-perturbatively: the net effect given by one patch is suppressed by ( L/R-H)(3) ( where L is the size of one patch and RH is the Hubble radius). We disentangle this effect from the Doppler term ( which is much larger and has been used recently ( Biswas et al 2007 J. Cosmol. Astropart. Phys. JCAP12( 2007) 017 [ astro-ph/ 0606703]) to try to fit the SN curve without dark energy) by making contact with cosmological perturbation theory. Then, the correction to the angular distance is discussed analytically and estimated to be larger, O( L/R-H)(2), perturbatively and non-perturbatively ( although it should go to zero after angular averaging).