[Paper Review] Large Scale Cosmological Inhomogeneities, Inflation and Acceleration Without Dark Matter

J. W. Moffat|arXiv (Cornell University)|Mar 31, 2005

Cosmology and Gravitation Theories1 references3 citations

TL;DR

This paper proposes that cosmic acceleration can emerge from long-wavelength super-horizon inflationary perturbations in an inhomogeneous, spherically symmetric universe model without requiring dark energy or a cosmological constant. Using exact inhomogeneous Friedmann equations, it derives a non-perturbative deceleration parameter $ q $ that can become negative due to vorticity and shear, suggesting intrinsic cosmic variance and a potential explanation for observed acceleration via inhomogeneity effects alone.

ABSTRACT

We describe the universe as a local, inhomogeneous spherical bubble embedded in a flat matter dominated FLRW universe. Generalized exact Friedmann equations describe the expansion of the universe and an early universe inflationary de Sitter solution is obtained. A non-perturbative expression for the deceleration parameter q is derived that can possibly describe the acceleration of the universe without dark energy, due to the effects associated with very long wave length super-horizon inflationary perturbations. The suggestion by Kolbe et al. [9] that long wave length super-horizon inflationary modes can affect a local observable through inhomogeneities is considered in the light of our exact inhomogeneous model.

Motivation & Objective

• To investigate whether large-scale inhomogeneities from super-horizon inflationary modes can explain cosmic acceleration without dark energy.
• To develop an exact inhomogeneous cosmological model that embeds a local expanding bubble in a flat FLRW background.
• To derive a non-perturbative expression for the deceleration parameter $ q $ that accounts for vorticity and shear effects.
• To challenge the standard interpretation of Type Ia supernova and CMB data as evidence for dark energy.
• To explore the implications of observer-dependent luminosity distances and redshifts due to spatial inhomogeneities.

Proposed method

• Formulates a spherically symmetric inhomogeneous metric with time- and space-dependent scale factors $ X(r,t) $ and $ R(r,t) $.
• Derives generalized Friedmann equations from an action principle including a scalar field $ \phi $, potential $ V(\phi) $, and cosmological constant $ \Lambda $.
• Applies the barytropic fluid assumption $ p = p(\rho) $ and uses the energy-momentum tensor $ T^\mu_\nu $ with non-zero vorticity $ \omega \neq 0 $.
• Introduces a non-perturbative expression for the deceleration parameter $ q $ that includes contributions from shear $ \sigma $, vorticity $ \omega $, and spatial gradients.
• Considers the backreaction of long-wavelength super-horizon modes on the local expansion, avoiding the limitations of second-order perturbation theory.
• Analyzes the conditions under which $ q $ can become negative without violating the strong energy condition, particularly when $ \omega \neq 0 $.

Experimental results

Research questions

• RQ1 Can cosmic acceleration be explained without dark energy by considering non-perturbative effects of super-horizon inflationary modes?
• RQ2 How do inhomogeneities in a spherically symmetric expanding bubble affect local observables like luminosity distance and redshift?
• RQ3 Under what conditions can the deceleration parameter $ q $ become negative in an inhomogeneous universe with non-zero vorticity?
• RQ4 To what extent do observer-dependent quantities such as $ d_L $ and $ z $ introduce intrinsic cosmic variance in cosmological measurements?
• RQ5 Can a non-perturbative treatment of inhomogeneities reconcile the observed acceleration with a matter-dominated universe without $ \Lambda $ or dark energy?

Key findings

• A non-perturbative expression for the deceleration parameter $ q $ is derived that includes contributions from shear, vorticity, and spatial gradients, allowing $ q < 0 $ even when $ \rho + 3p \geq 0 $.
• The model shows that vorticity $ \omega \neq 0 $ in the exact inhomogeneous solution invalidates the perturbative conclusion that $ q_1 \geq 0 $ under the strong energy condition.
• Super-horizon, long-wavelength inflationary modes can induce a non-zero variance in $ q $, leading to intrinsic cosmic variance in local expansion parameters.
• The luminosity distance $ d_L $ and redshift $ z $ are observer-dependent due to spatial inhomogeneities, challenging the standard FLRW interpretation of cosmological data.
• The model predicts that the alignment of large-scale CMB anisotropy multipoles (dipole, quadrupole, octopole) with the axis toward the center of the inhomogeneous bubble can emerge naturally.
• The results suggest that the observed acceleration may not require dark energy, but instead arise from non-perturbative inhomogeneity effects, particularly from long-wavelength super-horizon modes.