[Paper Review] The equation of vacuum state and the structure formation in universe

С. Л. Черкас, В. Л. Калашников|arXiv (Cornell University)|Oct 15, 2018

Cosmology and Gravitation Theories21 references5 citations

TL;DR

This paper proposes that the vacuum behaves as a quantum fluid with a defined equation of state and sound speed, derived under zero vacuum entropy, enabling structure formation in a Milne-like universe without dark matter. Using five-vector theory of gravity (FVT), it shows that vacuum and matter perturbations grow linearly at small scales, suggesting early and intense structure formation consistent with observations, unifying dark energy and dark matter in vacuum fluctuations.

ABSTRACT

The vacuum is considered as some fluid emergent from the zero-point fluctuations of the quantum fields contributing to the vacuum energy density and pressure. The equation of vacuum state and the speed of vacuum sound-waves are deduced under the assumption of zero vacuum entropy. The evolution of the background space-time metric resembles that of the Milne's-like universe. In the framework of the five-vector theory of gravitation allowing an arbitrary choice of the energy density reference level, the dynamics of the vacuum, pressureless matter, and space-time metrics perturbations are traced under this background. The obtained results show the very early formation of the Universe structure without the need for dark matter. Thus, a vacuum can be considered as some of the dark-energy-matter unification.

Motivation & Objective

• To address the cosmological constant problem by reinterpreting vacuum energy as a physical fluid with a defined equation of state.
• To explore whether vacuum fluctuations alone can drive structure formation without invoking dark matter.
• To develop a framework using five-vector theory of gravity (FVT) that allows an arbitrary reference level for energy density, enabling physical vacuum energy to contribute without divergences.
• To model the linear evolution of perturbations in vacuum and pressureless matter, showing growth consistent with observed large-scale structures.
• To demonstrate that the vacuum's intrinsic properties—specifically its sound speed and equation of state—can unify dark energy and dark matter effects.

Proposed method

• Derive the vacuum equation of state and sound speed from zero-entropy vacuum fluctuations, treating vacuum as a quantum fluid.
• Apply the five-vector theory of gravity (FVT), which modifies the Einstein-Hilbert action by restricting metrics to conformally unimodular forms, allowing an arbitrary energy density reference level.
• Use the Hamiltonian and momentum constraints in FVT to show that the Friedmann equation is satisfied up to an arbitrary constant, enabling physical vacuum energy to be isolated.
• Formulate linear perturbation equations for vacuum and pressureless matter in a background metric resembling the Milne universe, with Hubble parameter H as a key scale.
• Solve the coupled system of perturbation equations (32)–(37) in a comoving gauge, tracking the growth factor D_k(z) of density contrasts from redshift z=1100 to later times.
• Compare results for two matter densities: Ω_m = 0.03 (standard model) and Ω_m = 0.3 (preferred for linearly coasting cosmologies), assessing structure growth across scales.

Experimental results

Research questions

• RQ1 Can the vacuum's intrinsic quantum fluctuations alone drive the formation of cosmic structures without dark matter?
• RQ2 What is the equation of state and sound speed of the vacuum fluid in a zero-entropy framework?
• RQ3 How does the five-vector theory of gravity (FVT) allow physical vacuum energy to contribute to spacetime curvature without divergences?
• RQ4 To what extent do vacuum and matter perturbations grow in a Milne-like universe, and does this growth match observational structure formation timelines?
• RQ5 Can the vacuum's behavior unify dark energy and dark matter effects through its equation of state and sound propagation?

Key findings

• The vacuum is shown to behave as a quantum fluid with a defined equation of state and sound speed, derived from zero-entropy vacuum fluctuations.
• In the five-vector theory of gravity (FVT), the Friedmann equation is satisfied up to an arbitrary constant, allowing physical vacuum energy to be isolated from divergent zero-point contributions.
• Perturbation growth analysis reveals that inhomogeneities at small scales (galaxy cluster level) enter a strongly nonlinear regime, indicating early and intense structure formation.
• For wave numbers k > H, perturbations grow over time, while those with k < H decrease, indicating that H acts as a critical scale for structure evolution.
• The model predicts structure formation without dark matter: density contrast growth factors exceed unity at small scales, even with Ω_m = 0.3, suggesting that vacuum fluctuations alone can seed large-scale structures.
• The results suggest that vacuum clusterization at small scales could mimic dark matter halos, though nonlinear dynamics are beyond the scope of this linear perturbation analysis.