[Paper Review] Are singularities the limits of cosmology?

Mariusz P. Da̧browski|arXiv (Cornell University)|Jul 17, 2014

Cosmology and Gravitation Theories3 citations

TL;DR

This paper investigates whether cosmological singularities—particularly non-Big-Bang types like Big-Rip, sudden, and finite scale factor singularities—are true physical limits or merely artifacts of theory. By modeling the gravitational constant G as a time-varying scalar field, the study shows that certain singularities can be removed or transformed into milder forms, suggesting that some singularities are not absolute barriers to cosmological evolution.

ABSTRACT

We refer to the classic definition of a singularity in Einstein's general relativity (based on geodesic incompletness) as well as to some other criteria to evaluate the nature of singularities in cosmology. We review what different (non-Big-Bang) types of singularities are possible even in the simplest cosmological framework of Friedmann cosmology. We also show that various cosmological singularities may be removed or changed due to the variability of physical constants.

Motivation & Objective

• To assess whether cosmological singularities represent fundamental limits of physical theories or can be avoided through modified gravity.
• To differentiate between various types of non-Big-Bang singularities (e.g., Big-Rip, sudden, finite scale factor) and evaluate their physical strength.
• To investigate the impact of time-varying physical constants—especially the gravitational constant G—on the nature and existence of singularities.
• To determine whether singularities can be removed or transformed into milder forms using a dynamical G field, thus challenging the idea that all singularities are insurmountable barriers.
• To explore the implications of such singularities for multiverse concepts and the observational viability of alternative cosmological models.

Proposed method

• Uses the geodesic incompleteness criterion as the primary definition of spacetime singularities, distinguishing them from mere curvature blow-ups.
• Applies Tipler’s strength criterion to classify singularities based on tidal forces and geodesic deviation, identifying strong vs. weak singularities.
• Introduces a time-dependent gravitational constant G(t) = G₀(1 − t/ts)⁻ᵣ to model varying gravity, treating G as a scalar field.
• Derives modified energy density ρ(t) and pressure p(t) in Friedmann cosmology under the varying-G ansatz, using the full Einstein equations.
• Analyzes the behavior of ρ(t) and p(t) near singularities to determine whether singularities are removed or altered under specific r values.
• Compares conditions for singularity removal (e.g., r > 2−n for SFS, r > 1−n for FSF) and examines transitions between singularity types.

Experimental results

Research questions

• RQ1 Can non-Big-Bang singularities such as sudden or finite scale factor singularities be removed or weakened by allowing the gravitational constant G to vary in time?
• RQ2 What conditions on the time dependence of G (i.e., the exponent r) are required to eliminate specific types of singularities?
• RQ3 How does the strength of a singularity—defined via tidal forces and geodesic deviation—change when G is allowed to evolve?
• RQ4 What are the consequences of varying G for physical fields, particularly in terms of inducing new singularities (e.g., strong coupling singularities in Brans-Dicke theory)?
• RQ5 To what extent can singularities be considered true limits of cosmology if they can be removed or transformed by dynamical constants?

Key findings

• An SFS singularity (1 < n < 2) can be removed if the time dependence of G satisfies r > 2 − n.
• An FSF singularity (0 < n < 1) can be removed when r > 1 − n.
• For r ∈ (−1, 0), a varying G can transform an SFS singularity into a stronger FSF singularity if 0 < r + n < 1.
• A hybrid ansatz G(t) = G₀/t²(1 − t/ts)⁻ᵣ removes the Big-Bang singularity at t = 0 without additional constraints.
• The same hybrid model regularizes SFS and FSF singularities under the conditions r > 2 − n and r > 1 − n, respectively.
• The variation of G introduces a new physical field singularity (e.g., in Brans-Dicke theory) due to Φ ∝ 1/G, but this is consistent with known frameworks like string theory.