[Paper Review] Structure formation and the origin of dark energy

Golam Mortuza Hossain|ArXiv.org|Sep 21, 2007

Cosmology and Gravitation Theories3 citations

TL;DR

This paper proposes that dark energy arises naturally from large-scale structure formation in a spatially-flat Friedmann-Robertson-Walker (FRW) universe, where collapsing matter regions fragment into isolated 'FRW islands' surrounded by vacuum. Using a sharp-boundary approximation and classical general relativity, the model explains late-time cosmic acceleration and the observed 70% dark energy density without requiring a fine-tuned cosmological constant or exotic matter, with the effective dark energy emerging from inhomogeneous dynamics and boundary effects.

ABSTRACT

Cosmological constant a.k.a. dark energy problem is considered to be one major challenge in modern cosmology. Here we present a model where large scale structure formation causes spatially-flat FRW universe to fragment into numerous `FRW islands' surrounded by vacuum. We show that this mechanism can explain the origin of dark energy as well as the late time cosmic acceleration. This explanation of dark energy does not require any exotic matter source nor an extremely fine-tuned cosmological constant. This explanation is given within classical general relativity and relies on the fact that our universe has been undergoing structure formation since its recent past.

Motivation & Objective

• To resolve the cosmological constant problem by explaining dark energy without introducing a fundamental cosmological constant.
• To address the cosmic coincidence problem by showing dark energy emerges dynamically from structure formation.
• To provide a classical GR-based mechanism for late-time acceleration using inhomogeneous spacetime geometry.
• To demonstrate that dark energy can arise from back-reaction effects due to collapsing matter regions and shrinking boundaries.
• To explore whether the observed dark energy density (~70% of critical density) can be reproduced without exotic matter or fine-tuning.

Proposed method

• Model the universe as a spatially-flat FRW spacetime that fragments into discrete, homogeneous 'FRW islands' surrounded by vacuum due to structure formation.
• Use a sharp-boundary approximation to treat matter as confined within spherical, time-evolving regions of coordinate diameter $ l_i(t) $, with vacuum outside.
• Define observer A using the standard FRW metric with global time and scale factor $ a(t) $, while observer B uses a patchwork metric: FRW inside islands and static vacuum outside.
• Derive modified Friedmann and Raychaudhuri equations by averaging over the inhomogeneous structure, introducing two key parameters: $ n $ (related to Hubble rate) and $ r_n $ (related to boundary collapse).
• Compute the effective equation of state $ \omega = (1 - r_n)\omega_i $, showing that pressureless matter ($ \omega_i = 0 $) in islands leads to effective dark energy ($ \omega \approx -1 $) when $ r_n \approx 2.1 $.
• Ensure consistency between observers A and B by equating proper distances measured in the average FRW metric and the inhomogeneous patchwork metric.

Experimental results

Research questions

• RQ1 Can dark energy emerge from structure formation in a spatially-flat FRW universe without introducing a cosmological constant?
• RQ2 How does the inhomogeneous dynamics of collapsing matter regions and shrinking boundaries lead to effective dark energy?
• RQ3 What values of the model parameters $ n $ and $ r_n $ reproduce the observed dark energy density (~70% of critical density)?
• RQ4 Can the cosmic coincidence problem be resolved if dark energy is a consequence of ongoing structure formation rather than a fixed constant?
• RQ5 Is it possible to explain late-time acceleration and dark energy using only classical general relativity and inhomogeneous geometry?

Key findings

• The model reproduces the observed dark energy density of approximately 70% of the critical energy density when the parameter $ r_n = 2.1 $, assuming $ \omega = 0 $ for matter.
• The effective equation of state for the averaged universe becomes $ \omega = -1 $ when $ r_n = 2.1 $, consistent with the observed behavior of dark energy.
• The mechanism explains cosmic acceleration without requiring a cosmological constant or exotic matter, relying instead on inhomogeneous geometry and boundary dynamics.
• The model shows that pressureless matter in collapsing regions ($ \omega_i = 0 $) can produce an effective dark energy component due to the shrinking boundary, as described by $ \omega = (1 - r_n)\omega_i $.
• The parameter $ n = 0.3 $ leads to a dark energy contribution matching observations, indicating a plausible range for structure formation parameters.
• The model avoids the fine-tuning problem of the cosmological constant by deriving dark energy from dynamical structure formation, not from a fundamental constant.