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Can an Extra Degree of Freedom in Scalar-Tensor Non-Metricity Gravity Account for the Evolution of the Universe?

Ghulam Murtaza, Avik De, Andronikos Paliathanasis, Tee-How Loo

TL;DR

The paper investigates whether an extra scalar degree of freedom in scalar-tensor non-m metricity gravity, arising from the second connection class, can reproduce and enrich the cosmic expansion history. Using a Hubble-normalized dynamical-systems approach on a spatially flat FLRW background, it analyzes four representative coupling-potential scenarios and derives a closed autonomous system to identify fixed points and their cosmological interpretations. The results reveal a hierarchy of critical points—including matter-dominated, stiff-fluid, and de Sitter solutions—along with asymptotic Big-Crunch and Big-Rip trajectories, with a ΛCDM-like sequence recoverable under suitable parameters, and additional late-time/high-curvature regimes exclusive to the non-metricity sector. A comparison with scalar-torsion and metric-scalar theories exposes distinctive stability properties and potential observational discriminants, suggesting that the extra dynamical degree of freedom can be tested by upcoming surveys.

Abstract

We investigate whether the extra scalar degree of freedom that arises in the second connection class of scalar-tensor non-metricity gravity can accurately replicate and potentially enrich the cosmic expansion history. Focusing on a spatially flat FLRW background, we introduce Hubble-normalized variables and recast the field equations into an autonomous dynamical system. Four representative scenarios are analyzed comprehensively. Phase-space research reveals a rich hierarchy of critical points: matter-dominated, stiff-fluid, and de Sitter solutions, together with asymptotic trajectories leading to Big-Crunch/Rip singularities and transient, unstable matter epochs. With suitable parameter choices, the standard $Λ$CDM sequence is reinstated; however, novel late-time and high-curvature regimes arise exclusively from the non-metricity sector. A systematic comparison of metric scalar-tensor and teleparallel scalar-torsion theories reveals unique stability characteristics and potential observational discriminants. Our findings indicate that the additional time-dependent function inherent to scalar-tensor non-metricity gravity can effectively explain the Universe's evolution while providing new phenomenology that can be tested by upcoming surveys.

Can an Extra Degree of Freedom in Scalar-Tensor Non-Metricity Gravity Account for the Evolution of the Universe?

TL;DR

The paper investigates whether an extra scalar degree of freedom in scalar-tensor non-m metricity gravity, arising from the second connection class, can reproduce and enrich the cosmic expansion history. Using a Hubble-normalized dynamical-systems approach on a spatially flat FLRW background, it analyzes four representative coupling-potential scenarios and derives a closed autonomous system to identify fixed points and their cosmological interpretations. The results reveal a hierarchy of critical points—including matter-dominated, stiff-fluid, and de Sitter solutions—along with asymptotic Big-Crunch and Big-Rip trajectories, with a ΛCDM-like sequence recoverable under suitable parameters, and additional late-time/high-curvature regimes exclusive to the non-metricity sector. A comparison with scalar-torsion and metric-scalar theories exposes distinctive stability properties and potential observational discriminants, suggesting that the extra dynamical degree of freedom can be tested by upcoming surveys.

Abstract

We investigate whether the extra scalar degree of freedom that arises in the second connection class of scalar-tensor non-metricity gravity can accurately replicate and potentially enrich the cosmic expansion history. Focusing on a spatially flat FLRW background, we introduce Hubble-normalized variables and recast the field equations into an autonomous dynamical system. Four representative scenarios are analyzed comprehensively. Phase-space research reveals a rich hierarchy of critical points: matter-dominated, stiff-fluid, and de Sitter solutions, together with asymptotic trajectories leading to Big-Crunch/Rip singularities and transient, unstable matter epochs. With suitable parameter choices, the standard CDM sequence is reinstated; however, novel late-time and high-curvature regimes arise exclusively from the non-metricity sector. A systematic comparison of metric scalar-tensor and teleparallel scalar-torsion theories reveals unique stability characteristics and potential observational discriminants. Our findings indicate that the additional time-dependent function inherent to scalar-tensor non-metricity gravity can effectively explain the Universe's evolution while providing new phenomenology that can be tested by upcoming surveys.

Paper Structure

This paper contains 15 sections, 72 equations, 4 figures, 5 tables.

Table of Contents

  1. Introduction
  2. Non-metricity version of scalar-tensor gravity theory
  3. Energy conservation - a note
  4. Cosmological application
  5. Cosmological dynamical system
  6. $\lambda=\lambda_0$, $\zeta=\zeta_0$
  7. $\lambda=\lambda_0$ and $\zeta$ is variable
  8. Finite fixed point analysis
  9. Analysis at infinity
  10. $\zeta=\zeta_0$ and $\lambda$ is variable
  11. Finite fixed point analysis
  12. Analysis at infinity
  13. Discussion when $\lambda$ and $\zeta$ both are variable
  14. A brief comparison with scalar-torsion and scalar-tensor frameworks
  15. Concluding remarks

Figures (4)

  • Figure 1: 3D phase portrait for the dynamical system given in Eqs. (\ref{['eq1_case1_infinite']})-(\ref{['eq2_case1_infinite']}) for $\lambda_0=2,~h=0.5$ (Case \ref{['case II']}).
  • Figure 2: Qualitative evolution of the equation of state parameter of the dynamical system (\ref{['eq1_case1_infinite']})-(\ref{['eq2_case1_infinite']}) for different values of $\lambda$, with initial conditions ($X[0]=0.5,~Y[0]=0.4 ,~Z[0]=0.3,~\zeta[0]=0.7$). The left plot corresponds to $h=-1$ and the right to $h=1$. (Case \ref{['case II']}).
  • Figure 3: 3D phase portrait for the dynamical system given in Eqs. (\ref{['case2_infinite']})-(\ref{['eq2_case2_infinite']}) for $\zeta_0=2,~h=0.5$ (Case \ref{['case III']}).
  • Figure 4: Qualitative evolution of the equation of state parameter of the dynamical system (\ref{['case2_infinite']})-(\ref{['eq2_case2_infinite']}) for different values of $\zeta$, with initial conditions ($X[0]=0.1,~Y[0]=0.3 ,~Z[0]=0.3,~\lambda[0]=0.7$). The left plot corresponds to $h=1$ and the right to $h=-1$. (Case \ref{['case III']}).