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Register a new userLuminosity distance in Swiss cheese cosmology with randomized voids: I. Single void size
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Recently there have been suggestions that the Type Ia supernova data can be explained using only general relativity and cold dark matter with no dark energy. In Swiss cheese models of the Universe, the standard Friedmann-Robertson-Walker picture is modified by the introduction of mass compensating spherical inhomogeneities, typically described by the Lemaitre-Tolman-Bondi metric. If these inhomogeneities correspond to underdense cores surrounded by mass-compensating overdense shells, then they can modify the luminosity distance-redshift relation in a way that can mimic accelerated expansion. It has been argued that this effect could be large enough to explain the supernova data without introducing dark energy or modified gravity. We show that the large apparent acceleration seen in some models can be explained in terms of standard weak field gravitational lensing together with insufficient randomization of void locations. The underdense regions focus the light less than the homogeneous background, thus dimming supernovae in a way that can mimic the effects of acceleration. With insufficient randomization of the spatial location of the voids and of the lines of sight, coherent defocusing can lead to anomalously large demagnification effects. We show that a proper randomization of the voids and lines of sight reduces the effect to the point that it can no longer explain the supernova data.
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In a recent work, it has been proposed that the recent cosmic passage to a cosmic acceleration era is the result of the existence of small anti-gravity sources in each galaxy and clusters of galaxies. In particular, a swiss-cheese cosmology model which relativistically integrates the contribution of all these anti-gravity sources on galactic scale has been constructed assuming the presence of an infrared fixed point for a scale dependent cosmological constant. The derived cosmological expansion provides explanation for both the fine tuning and the coincidence problem. The present work relaxes the previous assumption on the running of the cosmological constant and allows for a generic scaling around the infrared fixed point. Our analysis reveals in order to produce a cosmic evolution consistent with the best $Lambda$CDM model, the IR-running of the cosmological constant is consistent with the presence of an IR-fixed point.
Galaxy bias, the unknown relationship between the clustering of galaxies and the underlying dark matter density field is a major hurdle for cosmological inference from large-scale structure. While traditional analyses focus on the absolute clustering amplitude of high-density regions mapped out by galaxy surveys, we propose a relative measurement that compares those to the underdense regions, cosmic voids. On the basis of realistic mock catalogs we demonstrate that cross correlating galaxies and voids opens up the possibility to calibrate galaxy bias and to define a static ruler thanks to the observable geometric nature of voids. We illustrate how the clustering of voids is related to mass compensation and show that volume-exclusion significantly reduces the degree of stochasticity in their spatial distribution. Extracting the spherically averaged distribution of galaxies inside voids from their cross correlations reveals a remarkable concordance with the mass-density profile of voids.
We present a model of (modified) gravity on spacetimes with fractal structure based on packing of spheres, which are (Euclidean) variants of the Packed Swiss Cheese Cosmology models. As the action functional for gravity we consider the spectral action of noncommutative geometry, and we compute its expansion on a space obtained as an Apollonian packing of 3-dimensional spheres inside a 4-dimensional ball. Using information from the zeta function of the Dirac operator of the spectral triple, we compute the leading terms in the asymptotic expansion of the spectral action. They consist of a zeta regularization of a divergent sum which involves the leading terms of the spectral actions of the individual spheres in the packing. This accounts for the contribution of the points 1 and 3 in the dimension spectrum (as in the case of a 3-sphere). There is an additional term coming from the residue at the additional point in the real dimension spectrum that corresponds to the packing constant, as well as a series of fluctuations coming from log-periodic oscillations, created by the points of the dimension spectrum that are off the real line. These terms detect the fractality of the residue set of the sphere packing. We show that the presence of fractality influences the shape of the slow-roll potential for inflation, obtained from the spectral action. We also discuss the effect of truncating the fractal structure at a certain scale related to the energy scale in the spectral action.
We report novel cosmological constraints obtained from cosmic voids in the final BOSS DR12 dataset. They arise from the joint analysis of geometric and dynamic distortions of average void shapes (i.e., the stacked void-galaxy cross-correlation function) in redshift space. Our model uses tomographic deprojection to infer real-space void profiles and self-consistently accounts for the Alcock-Paczynski (AP) effect and redshift-space distortions (RSD) without any prior assumptions on cosmology or structure formation. It is derived from first physical principles and provides an extremely good description of the data at linear perturbation order. We validate this model with the help of mock catalogs and apply it to the final BOSS data to constrain the RSD and AP parameters $f/b$ and $D_AH/c$, where $f$ is the linear growth rate, $b$ the linear galaxy bias, $D_A$ the comoving angular diameter distance, $H$ the Hubble rate, and $c$ the speed of light. In addition, we include two nuisance parameters in our analysis to marginalize over potential systematics. We obtain $f/b=0.540pm0.091$ and $D_AH/c=0.588pm0.004$ from the full void sample at a mean redshift of $z=0.51$. In a flat $Lambda$CDM cosmology, this implies $Omega_mathrm{m}=0.312pm0.020$ for the present-day matter density parameter. When we use additional information from the survey mocks to calibrate our model, these constraints improve to $f/b=0.347pm0.023$, $D_AH/c=0.588pm0.003$, and $Omega_mathrm{m}=0.310pm0.017$. However, we emphasize that the calibration depends on the specific model of cosmology and structure formation assumed in the mocks, so the calibrated results should be considered less robust. Nevertheless, our calibration-independent constraints are among the tightest of their kind to date, demonstrating the immense potential of using cosmic voids for cosmology in current and future data.
Swiss cheese sets are compact subsets of the complex plane obtained by deleting a sequence of open disks from a closed disk. Such sets have provided numerous counterexamples in the theory of uniform algebras. In this paper, we introduce a topological space whose elements are what we call abstract Swiss cheeses. Working within this topological space, we show how to prove the existence of classical Swiss cheese sets (as discussed in a paper of Feinstein and Heath from 2010) with various desired properties. We first give a new proof of the Feinstein-Heath classicalisation theorem. We then consider when it is possible to classicalise a Swiss cheese while leaving disks which lie outside a given region unchanged. We also consider sets obtained by deleting a sequence of open disks from a closed annulus, and we obtain an analogue of the Feinstein-Heath theorem for these sets. We then discuss regularity for certain uniform algebras. We conclude with an application of these techniques to obtain a classical Swiss cheese set which has the same properties as a non-classical example of OFarrell (1979).
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