[Paper Review] On astrophysical explanations due to cosmological inhomogeneities for the observational acceleration

Kenji Tomita|ArXiv.org|Jun 7, 2009

Cosmology and Gravitation Theories3 citations

TL;DR

This paper evaluates inhomogeneous cosmological models—particularly local void models and averaged backreaction models—as alternatives to dark energy for explaining the observed acceleration of the universe from Type Ia supernova data. It finds that most such models are ruled out by consistency checks with CMB, BAO, and kinematic Sunyaev-Zeldovich data, leaving only a narrow range of parameters viable, and that significant perturbation amplitudes or gravitational energy densities are required for acceleration without a cosmological constant.

ABSTRACT

We review various cosmological models with a local underdense region (local void) and the averaged models with the backreaction of inhomogeneities, which have been proposed to explain (without assuming a positive cosmological constant) the observed accelerating behaviors appearing in the magnitude-redshift relation of SNIa. To clarify their reality, we consider their consistency with the other observational studies such as CMB temperature anisotropy, baryon acoustic oscillation, kinematic Sunyaev-Zeldovich effect, and so on. It is found as a result that many inhomogeneous models seem to be ruled out and only models with the parametrs in the narrow range remain to be examined, and that, unless we assume very high amplitudes of perturbations or gravitational energies, the averaged models cannot have the accelerated expansion and the fitted effective Lambda has not the value necessary for the observed acceleration.

Motivation & Objective

• To assess whether cosmological inhomogeneities, such as local underdense voids, can explain the observed supernova magnitude-redshift relation without invoking a cosmological constant.
• To test the consistency of local void and averaged backreaction models with multiple independent observations, including CMB anisotropies, baryon acoustic oscillations (BAO), and kinematic Sunyaev-Zeldovich effects.
• To determine whether the effective cosmological constant derived from fitting inhomogeneous models matches the observed value required for acceleration.
• To examine the viability of inhomogeneous models under constraints from current observational data, especially in the absence of a cosmological constant.
• To explore whether gravitational energy or high-amplitude perturbations are necessary to generate apparent acceleration in these models.

Proposed method

• Uses Lemaitre-Tolman-Bondi (LTB) solutions to model spherically symmetric inhomogeneous spacetimes with a central underdense region (local void) and an outer overdense region.
• Applies the Dyer-Roeder equation to compute angular diameter distances in inhomogeneous models, enabling derivation of the theoretical magnitude-redshift relation for SNIa.
• Compares the theoretical magnitude-redshift relation from inhomogeneous models with the observed one to assess fit quality.
• Employs post-Newtonian approximations and nonlinear perturbation models (e.g., swiss-cheese models) to compute effective cosmological constants via fitting to FLRW models with Λ.
• Performs consistency checks against observational data: CMB temperature anisotropies, BAO scale measurements, kinematic Sunyaev-Zeldovich effect, and spectral distortions.
• Analyzes the role of gravitational energy differences across regions (voids, walls, expanding zones) in affecting clock rates and apparent expansion dynamics.

Experimental results

Research questions

• RQ1 Can a local underdense void in a zero-Λ universe reproduce the observed magnitude-redshift relation of Type Ia supernovae without invoking dark energy?
• RQ2 How do averaged backreaction effects from inhomogeneities in a zero-Λ universe compare with the observed cosmic acceleration in terms of effective Λ?
• RQ3 What constraints do CMB, BAO, and kinematic Sunyaev-Zeldovich observations place on local void models and their parameters?
• RQ4 Is it possible to achieve the required effective cosmological constant through fitting inhomogeneous models to ΛCDM models, and what perturbation amplitudes are needed?
• RQ5 What role do gravitational energy differences and high-amplitude perturbations play in generating apparent acceleration in inhomogeneous models?

Key findings

• Many local void models are ruled out by consistency checks with CMB temperature anisotropies, BAO, and kinematic Sunyaev-Zeldovich effects.
• Only models with parameters in a narrow range—particularly those with high-amplitude perturbations or significant gravitational energy contributions—remain viable.
• Averaged backreaction models with sub-horizon perturbations fail to produce sufficient acceleration or the required effective Λ unless perturbation amplitudes exceed CMB normalization levels.
• The effective Λ derived from fitting inhomogeneous models to ΛCDM is only ~0.004 in post-Newtonian approximations, far below the observed value (~0.75), indicating insufficient acceleration from typical perturbations.
• Nonlinear perturbation models with amplitudes much larger than CMB-normalized values can produce an effective Λ comparable to observations, but such high amplitudes are observationally suspect.
• The super-horizon version of the local void model fails to generate acceleration unless the perturbed region size is comparable to the horizon radius of the EdS universe, which is not generally satisfied.