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Register a new userRedshift drift in radially inhomogeneous Lema^itre-Tolman-Bondi spacetimes
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We provide a formula for estimating the redshift and its secular change (redshift drift) in Lema^itre-Tolman-Bondi (LTB) spherically symmetric universes. We compute the scaling of the redshift drift for LTB models that predict Hubble diagrams indistinguishable from those of the standard cosmological model, the flat $Lambda$ Cold Dark Matter ($Lambda$CDM) model. We show that the redshift drift for these degenerate LTB models is typically different from that predicted in the $Lambda$CDM scenario. We also highlight and discuss some unconventional redshift-drift signals that arise in LTB universes and give them distinctive features compared to the standard model. We argue that the redshift drift is a metric observable that allows to reduce the degrees of freedom of spherically symmetric models and to make them more predictive and thus falsifiable.
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In this paper we attempt to answer to the question: can cosmic acceleration of the Universe have a fractal solution? We give an exact solution of a Lema^itre-Tolman-Bondi (LTB) Universe based on the assumption that such a smooth metric is able to describe, on average, a fractal distribution of matter. While the LTB model has a center, we speculate that, when the fractal dimension is not very different from the space dimension, this metric applies to any point of the fractal structure when chosen as center so that, on average, there is not any special point or direction. We examine the observed magnitude-redshift relation of type Ia supernovae (SNe Ia), showing that the apparent acceleration of the cosmic expansion can be explained as a consequence of the fractal distribution of matter when the corresponding space-time metric is modeled as a smooth LTB one and if the fractal dimension on scales of a few hundreds Mpc is $D=2.9 pm 0.02$.
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.
We study the validity of the Newtonian description of cosmological perturbations using the Lemaitre model, an exact spherically symmetric solution of Einsteins equation. This problem has been investigated in the past for the case of a dust fluid. Here, we extend the previous analysis to the more general case of a fluid with non-negligible pressure, and, for the numerical examples, we consider the case of radiation (P=rho/3). We find that, even when the density contrast has a nonlinear amplitude, the Newtonian description of the cosmological perturbations using the gravitational potential psi and the curvature potential phi is valid as long as we consider sub-horizon inhomogeneities. However, the relation psi+phi={cal O}(phi^2), which holds for the case of a dust fluid, is not valid for a relativistic fluid and effective anisotropic stress is generated. This demonstrates the usefulness of the Lemaitre model which allows us to study in an exact nonlinear fashion the onset of anisotropic stress in fluids with non-negligible pressure. We show that this happens when the characteristic scale of the inhomogeneity is smaller than the sound horizon and that the deviation is caused by the nonlinear effect of the fluids fast motion. We also find that psi+phi= max[{cal O}(phi^2),{cal O}(c_s^2phi , delta)] for an inhomogeneity with density contrast delta whose characteristic scale is smaller than the sound horizon, unless w is close to -1, where w and c_s are the equation of state parameter and the sound speed of the fluid, respectively. On the other hand, we expect psi+phi={cal O}(phi^2) to hold for an inhomogeneity whose characteristic scale is larger than the sound horizon, unless the amplitude of the inhomogeneity is large and w is close to -1.
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 $t to +infty$.
Boundary problem for Tolman-Bondi model is formulated. One-to-one correspondence between singularities hypersurfaces and initial conditions of the Tolman-Bondi model is constructed.
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