[Paper Review] The Role of Anisotropy in the Void Models without Dark Energy

Masayuki Tanimoto, Yasusada Nambu+1 more|ArXiv.org|Jun 26, 2009

Cosmology and Gravitation Theories5 references3 citations

TL;DR

This paper investigates anisotropic void models as an alternative to dark energy by deriving an effective distance equation through angular averaging of the optical scalar equation in inhomogeneous, anisotropic spacetimes. The resulting equation resembles a Dyer-Roeder-like extension of the Lemaütre-Tolman-Bondi model, and numerical analysis shows that anisotropy allows smaller voids and higher matter density parameters ($\Omega_m$) to better fit Type Ia supernova data.

ABSTRACT

Void models provide a possible explanation of the "accelerated expansion" of the Universe without dark energy. To make the conventional void models more realistic, we allow the void, an underdense region around us, to be anisotropic and consider an average of the distance-redshift relations over the solid angle subtended at the observer. We first show that after taking the average of a form of the optical scalar equation (distance equation), the effective distance equation we obtain coincides with the one for the Lemaitre-Tolman-Bondi universe with a Dyer-Roeder-like extension. We then numerically solve the equation to compare with observational data of Type Ia supernovae. We find that anisotropy allows smaller size of void and larger Omega_m.

Motivation & Objective

• To address the limitation of isotropic void models by incorporating cosmological anisotropy in the matter distribution.
• To derive a physically motivated effective distance equation that accounts for inhomogeneity and anisotropy in light propagation.
• To test whether anisotropic void models can reproduce Type Ia supernova distance-redshift data without invoking dark energy.
• To determine how anisotropy affects the required size of the void and the matter density parameter $\Omega_m$.
• To provide a framework that generalizes the Dyer-Roeder approach by deriving the effective inhomogeneity factor from first principles rather than introducing it phenomenologically.

Proposed method

• Derives the optical scalar equation for inhomogeneous and anisotropic spacetimes, assuming negligible lensing effects.
• Applies spherical averaging over the past light cone to the distance equation, yielding an effective form suitable for observational comparison.
• Shows that the averaged equation reduces to the LTB model with a modified matter density $\alpha(z)\rho_{\text{LTB}}$, where $\alpha(z)$ emerges naturally from averaging.
• Treats $\alpha(z)$ as a function that encodes the combined effects of spatial inhomogeneity and anisotropy in expansion rate and density.
• Numerically solves the effective distance equation for a specific void model and compares the luminosity distance to observed Type Ia supernova data.
• Performs parameter space exploration to find optimal values of void size and $\Omega_m$ that best fit the supernova data under the anisotropic model.

Experimental results

Research questions

• RQ1 How does angular anisotropy in the matter distribution affect the distance-redshift relation in void models?
• RQ2 Can anisotropy in the void structure allow a better fit to Type Ia supernova data without requiring dark energy?
• RQ3 What is the impact of anisotropy on the required size of the void and the value of the matter density parameter $\Omega_m$?
• RQ4 How does the derived effective distance equation compare to the standard Dyer-Roeder and LTB models?
• RQ5 Can the effective inhomogeneity factor $\alpha(z)$ be derived from first principles in anisotropic spacetimes, rather than being introduced phenomenologically?

Key findings

• The averaged distance equation derived from the optical scalar equation in anisotropic spacetimes reduces to a form equivalent to the LTB model with a Dyer-Roeder-like modification.
• Anisotropy allows for smaller void sizes compared to isotropic models while still fitting Type Ia supernova data.
• The matter density parameter $\Omega_m$ can be larger in anisotropic void models than in isotropic ones, with the model favoring higher $\Omega_m$ values.
• The effective inhomogeneity factor $\alpha(z)$ arises naturally from the averaging procedure, avoiding the need for ad hoc phenomenological functions like $\beta_M(z)$.
• The model shows that anisotropy enhances the effective expansion rate along light paths, mimicking dark energy effects without requiring it.
• Future work should extend the model to include CMB and baryon acoustic oscillation data, which may require a redshift-dependent $\alpha(z)$ function.