[Paper Review] Why the measured cosmological constant is small

Tahereh Rostami, S. Jalalzadeh|arXiv (Cornell University)|Oct 7, 2015

Cosmology and Gravitation Theories20 references4 citations

TL;DR

This paper proposes that the observed small value of the cosmological constant arises from extrinsic curvature in an 11-dimensional ambient space, where the induced gravitational constant depends on the thickness of the brane—determined by the pion Compton wavelength and strong interaction coupling. The model predicts ΛL²ₚₗ = 2.56×10⁻¹²², matching observations without invoking vacuum energy or fine-tuning.

ABSTRACT

In a quest to explain the small value of the today's cosmological constant, following the approach introduced in [1], we show that the theoretical value of cosmological constant is consistent with its observational value. In more detail, we study the Freidmann-Lama\^ıtre-Robertson-Walker cosmology embedded isometrically in an $11$-dimensional ambient space. The field equations determines $Λ$ in terms of other measurable fundamental constants. Specifically, it predicts that the cosmological constant measured today be $ΛL^2_{ ext{Pl}}=2.56 imes10^{-122}$, as observed.

Motivation & Objective

• To resolve the cosmological constant problem by explaining why Λ is so small, avoiding vacuum energy contributions.
• To show that the cosmological constant arises from gravitational-geometrical effects in a higher-dimensional embedding space.
• To derive a theoretical value of Λ consistent with observational bounds using physical constants from quantum chromodynamics.
• To establish a connection between the brane's thickness and the pion Compton wavelength, linking gravity to strong interaction scale.

Proposed method

• Embed the 4D Friedmann-Lemaître-Robertson-Walker (FLRW) spacetime isometrically in an 11-dimensional Minkowski ambient space using Nash's embedding theorem.
• Model the induced gravitational constant G_N as a time-dependent function of the extrinsic normal curvature, parameterized by the scale factor via a power-law ansatz.
• Use the Gauss-Weingarten equations to derive the field equations, where the extrinsic curvature term acts as a cosmological constant.
• Relate the brane thickness l to the inverse of the pion decay constant f_π ≈ 130.41 MeV, based on hadron size and strong interaction range.
• Incorporate the strong interaction coupling g₀²/4π = 16.8 to compute the energy density of the cosmological constant.
• Derive the theoretical value of ΛL²ₚₗ = 2.56×10⁻¹²² by combining G₀, f_π, and g₀ from known physical constants.

Experimental results

Research questions

• RQ1 Can the small observed value of the cosmological constant be explained without invoking vacuum energy or anthropic fine-tuning?
• RQ2 Does the extrinsic curvature of a brane embedded in higher dimensions naturally generate a small cosmological constant?
• RQ3 Is the brane thickness determined by the Compton wavelength of the lightest hadron, such as the pion?
• RQ4 Can the cosmological constant be derived from low-energy quantum chromodynamics parameters like f_π and g₀²?

Key findings

• The theoretical prediction for the cosmological constant is ΛL²ₚₗ = 2.56×10⁻¹²², matching the observed value within measurement precision.
• The energy density of the cosmological constant is predicted as ρ₀Λ = (4.80×10⁻³ eV)⁴, consistent with Planck data and other astrophysical constraints.
• The model links the cosmological constant to the pion decay constant f_π, with l = 1/f_π setting the brane thickness.
• The result reproduces the scaling law proposed by Zeldovich, suggesting a deep connection between gravity and strong interaction physics.
• The model avoids the vacuum energy problem by attributing Λ to extrinsic geometry, not quantum fluctuations.
• The derived value of ω_Λ ≈ -0.998 is consistent with the cosmological constant's equation of state w = -1.