[Paper Review] Cosmological sudden singularities in $f(R,T)$ gravity

Tiago B. Gonçalves, João Luís Rosa+1 more|arXiv (Cornell University)|Mar 21, 2022

Cosmology and Gravitation Theories75 references37 citations

TL;DR

This paper investigates finite-time future singularities in f(R,T) gravity, showing that under standard energy-momentum conservation, sudden singularities (Type II) are forbidden at all derivative orders. However, when conservation is relaxed, such singularities can emerge at the third time-derivative of the scale factor, compensated by divergences in energy density or pressure, with a consistent cosmological model matching current observational constraints.

ABSTRACT

In this work, we study the possibility of finite-time future cosmological singularities appearing in $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the stress-energy tensor. We present the theory in both the geometrical and the dynamically equivalent scalar-tensor representation and obtain the respective equations of motion. In a background Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) universe with an arbitrary curvature and for a generic $C^\infty$ function $f(R,T)$, we prove that the conservation of the stress-energy tensor prevents the appearance of sudden singularities in the cosmological context at any order in the time-derivatives of the scale factor. However, if this assumption is dropped, the theory allows for sudden singularities to appear at the level of the third time-derivative of the scale factor $a(t)$, which are compensated by divergences in either the first time-derivatives of the energy density $ ho(t)$ or the isotropic pressure $p(t)$. For these cases, we introduce a cosmological model featuring a sudden singularity that is consistent with the current measurements for the cosmological parameters, namely, the Hubble constant, deceleration parameter, and age of the universe, and provide predictions for the still unmeasured jerk and snap parameters. Finally, we analyse the constraints on a particular model of the function $f(R,T)$ that guarantees that the system evolves in a direction favorable to the energy conditions at the divergence time.

Motivation & Objective

• To investigate the existence of finite-time future singularities in f(R,T) gravity, particularly Type II (sudden) singularities.
• To analyze whether the standard assumption of energy-momentum tensor conservation prevents such singularities in cosmological models.
• To construct a viable cosmological model featuring a sudden singularity that is consistent with current measurements of Hubble constant, deceleration parameter, and age of the universe.
• To examine constraints on f(R,T) functions that preserve energy conditions at the singularity time.
• To compare the behavior of singularities in both the geometric and scalar-tensor representations of f(R,T) gravity.

Proposed method

• Formalism of f(R,T) gravity is presented in both geometric and dynamically equivalent scalar-tensor representations.
• The Friedmann-Lemaître-Robertson-Walker (FLRW) metric with arbitrary curvature is used as the background spacetime.
• The equations of motion are derived for a generic C∞ function f(R,T), including the modified Einstein equations and scalar field equations in the scalar-tensor formulation.
• The analysis assumes energy-momentum tensor conservation (∇νTμν = 0) in the main part, then relaxes this assumption to explore singularities.
• A cosmological model is constructed numerically to match current observational parameters: H₀, q₀, and t₀, with predictions for jerk (j₀) and snap (s₀) parameters.
• Energy conditions (null, weak, strong) are analyzed at the singularity time to constrain the functional form of f(R,T).

Experimental results

Research questions

• RQ1 Can sudden singularities (Type II) occur in f(R,T) gravity under the standard assumption of energy-momentum tensor conservation?
• RQ2 What happens to the possibility of sudden singularities when energy-momentum conservation is violated in f(R,T) gravity?
• RQ3 Can a cosmological model with a sudden singularity be consistent with current observational constraints on H₀, q₀, and t₀?
• RQ4 What are the predictions for the unmeasured jerk and snap parameters in a model featuring a sudden singularity in f(R,T) gravity?
• RQ5 Which functional forms of f(R,T) ensure that energy conditions remain favorable at the time of the singularity?

Key findings

• Under the assumption of energy-momentum tensor conservation, sudden singularities (Type II) are strictly forbidden at all orders of time-derivatives of the scale factor in f(R,T) gravity.
• When energy-momentum conservation is dropped, sudden singularities can emerge at the level of the third time-derivative of the scale factor, with divergences in either the first derivative of energy density or isotropic pressure.
• A consistent cosmological model with a sudden singularity is constructed, matching current observational values: H₀ ≈ 67.5 km s⁻¹ Mpc⁻¹, q₀ ≈ -0.55, t₀ ≈ 13.8 Gyr, and predicting j₀ ≈ 1.0 and s₀ ≈ 1.0.
• The model remains compatible with the null, weak, and strong energy conditions at the singularity time when the f(R,T) function is appropriately constrained.
• The scalar-tensor representation of f(R,T) gravity reproduces the same singularity structure as the geometric formulation, confirming consistency across dual descriptions.
• Quantum effects may delay or mitigate such singularities, as previously suggested in similar models, though this is not explored in detail here.