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The cosmological principle postulates that our universe is homogeneous and isotropic. Based on such assumptions, the LCDM model is proposed with its underlying FLRW metric. The structure formation in the late time universe breaks the assumption of homogeneity. From the perspective of general relativity, inhomogeneous matter distribution should also be coupled with an inhomogeneous background metric, while most of the current N-body simulations tend to solve the evolution of the background metric under the assumption of homogeneity. In the standard Newtonian N-body simulations, the cold dark matter particles’ motion is calculated with the Poisson equation coupled with the homogeneous background scale factor. A caveat of such approaches is that it ignores the backreaction from inhomogeneous metric. The inhomogeneous metric induced by the inhomogeneous matter field may again backreacts on the motion of dark matter particles.
Using the Buchert’s averaging scheme, one could calculate the backreaction effects of inhomogeneity by taking the average of scalar fields in space-time foliation. The backreaction effects essentially come down to two extra terms in the effective Friedmann equation: averaged curvature $\langle R \rangle$ and kinetic backreaction $Q$, with an additional conservation equation coupling terms $\langle R \rangle$ and $Q$. The effective Friedmann equation in this case is not closed. One still has the freedom to define the scaling relation for either of the terms above.
This work estimates the evolution of the magnitude of the averaged curvature induced by halos, based on N-body simulation code Gadget-2 and Uchuu’s simulations. Assuming Navarro-Frenk-White density profile for each halo, an underlying Lemaître–Tolman–Bondi metric is fitted, ensuring it converges to the FLRW metric at the edge of the halo. With the inhomogeneous underlying metric, the averaged curvature term could be estimated by setting the radial peculiar velocity of the halo to zero with a variance given by its radial circular velocity. Both the EdS universe and LCDM universe are examined, yielding an averaged curvature of $\Omega_R=9.98\times10^{-4}\pm 6.69\times10^{-5}$ and $\Omega_R=9.46\times10^{-5}$ respectively at $z=0$.
| Research Area | Cosmology: late universe |
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