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Register a new userCosmological model dependence of the galaxy luminosity function: far-infrared results in the Lemaitre-Tolman-Bondi model
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This is the first paper of a series aiming at investigating galaxy formation and evolution in the giant-void class of the Lemaitre-Tolman-Bondi (LTB) models that best fits current cosmological observations. Here we investigate the Luminosity Function (LF) methodology, and how its estimates would be affected by a change on the cosmological model assumed in its computation. Are the current observational constraints on the allowed Cosmology enough to yield robust LF results? We use the far-infrared source catalogues built on the observations performed with the Herschel/PACS instrument, and selected as part of the PACS evolutionary probe (PEP) survey. Schechter profiles are obtained in redshift bins up to z approximately 4, assuming comoving volumes in both the standard model, that is, Friedmann-Lemaitre-Robertson-Walker metric with a perfect fluid energy-momentum tensor, and non-homogeneous LTB dust models, parametrized to fit the current combination of results stemming from the observations of supernovae Ia, the cosmic microwave background, and baryonic acoustic oscillations. We find that the luminosity functions computed assuming both the standard model and LTB void models show in general good agreement. However, the faint-end slope in the void models shows a significant departure from the standard model up to redshift 0.4. We demonstrate that this result is not artificially caused by the used LF estimator which turns out to be robust under the differences in matter-energy density profiles of the models. The differences found in the LF slopes at the faint end are due to variation in the luminosities of the sources, which depend on the geometrical part of the model. It follows that either the standard model is over-estimating the number density of faint sources or the void models are under-estimating it.
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This work provides a general discussion of the spatially inhomogeneous Lema^itre-Tolman-Bondi (LTB) cosmology, as well as its basic properties and many useful relevant quantities, such as the cosmological distances. We apply the concept of the single null geodesic to produce some simple analytical solutions for observational quantities such as the redshift. As an application of the single null geodesic technique, we carry out a fractal approach to the parabolic LTB model, comparing it to the spatially homogeneous Einstein-de Sitter cosmology. The results obtained indicate that the standard model, in this case represented by the Einstein-de Sitter cosmology, can be equivalently described by a fractal distribution of matter, as we found that different single fractal dimensions describe different scale ranges of the parabolic LTB matter distribution. It is shown that at large ranges the parabolic LTB model with fractal dimension equal to 0.5 approximates the matter distribution of the Einstein-de Sitter universe.
The cosmic far-infrared background (CFIRB) is expected to be generated by faint, dusty star-forming galaxies during the peak epoch of galaxy formation. The anisotropy power spectrum of the CFIRB captures the spatial distribution of these galaxies in dark matter halos and the spatial distribution of dark matter halos in the large-scale structure. Existing halo models of CFIRB anisotropy power spectrum are either incomplete or lead to halo model parameters that are inconsistent with the galaxy distribution selected at other wavelengths. Here we present a conditional luminosity function approach to describe the far-IR bright galaxies. We model the 250 um luminosity function and its evolution with redshift and model-fit the CFIRB power spectrum at 250 um measured by the Herschel Space Observatory. We introduce a redshift dependent duty-cycle parameter so that we are able to estimate the typical duration of the dusty star formation process in the dark matter halos as a function of redshifts. We find the duty cycle of galaxies contributing to the far-IR background is 0.3 to 0.5 with a dusty star-formation phase lasting for sim0.3-1.6 Gyrs. This result confirms the general expectation that the far-IR background is dominated by star-forming galaxies in an extended phases, not bright starbursts that are driven by galaxy mergers and last sim10-100 Myrs. The halo occupation number for satellite galaxies has a power-law slope that is close to unity over 0<z<4. We find that the minimum halo mass for dusty, star-forming galaxies with L_250>10^{10} L_Sun is 2times10^{11}M_Sun and 3times 10^{10}M_Sun at z=1 and 2, respectively. Integrating over the galaxy population with L_250>10^{9} L_Sun, we find that the cosmic density of dust residing in the dusty, star-forming galaxies responsible for the background anisotropies Omega_{dust}sim3times10^{-6} to 2times10^{-5}.
We extended the modified Lemaitre-Tolman model taking into account the effect of angular momentum and dynamical friction. The inclusion of these quantities in the equation of motion modifies the evolution of a perturbation, initially moving with the Hubble flow. Solving the equation of motions we got the relationships between mass, $M$, and the turn-around radius, $R_0$. Knowing $R_0$, the quoted relation allows the determination of the mass of the object studied. The relationships for the case in which also the angular momentum is taken into account gives a mass $simeq 90$ % larger than the standard Lemaitre-Tolman model, and two times the value of the standard Lemaitre-Tolman model, in the case also dynamical friction is taken into account. As a second step, we found relationships between the velocity, $v$, and radius, $R$, and fitted them to data of the Local Group, M81, NGC 253, IC342, CenA/M83, and to the Virgo clusters obtained by Ref.[New Astronomy 11(4):325, A&A 488(3):845]. This allowed us to find optimized values of the mass and Hubble constant of the objects studied. The fit gives values of the masses smaller with respect to the $M-R_0$ relationship method, but in any case 30-40% larger than the $v-R$ relationship obtained from the standard Lemaitre-Tolman model. Differently from mass, the Hubble parameter becomes smaller with respect to the standard Lemaitre-Tolman model, when angular momentum, and dynamical friction are introduced. This is in agreement with Ref.[New Astronomy 11(4):325, A&A 488(3):845], who improved the standard Lemaitre-Tolman model taking into account the cosmological constant. Finally, we used the mass, $M$, and $R_0$ of the studied objects to put constraints to the dark energy equation of state parameter, $w$. Comparison with previous studies show different constraints on $w$.
The Maxwell electromagnetic theory embedded in an inhomogeneous Lema^{i}tre-Tolman-Bondi (LTB) spacetime background was described a few years back in the literature. However, terms concerning the mass or high-derivatives were no explored. In this work we studied the inhomogeneous spacetime effects on high-derivatives and massive electromagnetic models. We used the LTB metric and calculated the physical quantities of interest, namely the scale factor, density of the electromagnetic field and Hubble constant, for the Proca and higher-derivative Podolsky models. We found a new singularity in both models, and that the magnetic field must be zero in the Proca model.
The Bondi formula for calculation of the invariant mass in the Tolman- Bondi (TB) model is interprated as a transformation rule on the set of co-moving coordinates. The general procedure by which the three arbitrary functions of the TB model are determined explicitly is presented. The properties of the TB model, produced by the transformation rule are studied. Two applications are studied: for the falling TB flat model the equation of motion of two singularities hypersurfaces are obtained; for the expanding TB flat model the dependence of size of area with friedmann-like solution on initial conditions is studied in the limit $t to +infty$.
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