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Revisiting the energy-momentum squared gravity

Mihai Marciu

TL;DR

This work extends energy-momentum-squared gravity by incorporating the second derivative of the matter Lagrangian with respect to the metric, motivated by thermodynamics, and casts the theory into a scalar-tensor form with two auxiliary fields. Using this formulation, it performs a dynamical-systems analysis for two common matter Lagrangians, $L_m = p$ and $L_m = -\rho$, identifying critical structures that yield matter-dominated epochs and late-time acceleration close to de-Sitter behavior, though stability can depend on the chosen matter Lagrangian. The study also provides non-exhaustive numerical explorations via a phenomenological $H(z)$ fit showing quintessence-like late-time behavior and energy exchange between matter and geometry, highlighting how the modified coupling reshapes cosmic evolution relative to $\Lambda$CDM. The results support the viability of EMT-squared gravity with the second-derivative correction in certain thermodynamically motivated setups and point to data-driven constraints and astrophysical tests as promising future directions.

Abstract

In this paper we have revisited the energy-momentum squared gravity theory, by taking into account the second derivative of the matter Lagrangian with respect to the metric, encapsulating relations originated from thermodynamical grounds. After obtaining the scalar tensor representation of the energy-momentum squared gravity with the new corrections, we have analyzed the physical implications by relying on the linear stability theory. The results show that the current cosmological system is compatible with the expansion of the Universe for some specific matter Lagrangians, explaining the emergence of matter domination era, approaching the late time accelerated expansion era close to the de-Sitter phenomenology.

Revisiting the energy-momentum squared gravity

TL;DR

This work extends energy-momentum-squared gravity by incorporating the second derivative of the matter Lagrangian with respect to the metric, motivated by thermodynamics, and casts the theory into a scalar-tensor form with two auxiliary fields. Using this formulation, it performs a dynamical-systems analysis for two common matter Lagrangians, and , identifying critical structures that yield matter-dominated epochs and late-time acceleration close to de-Sitter behavior, though stability can depend on the chosen matter Lagrangian. The study also provides non-exhaustive numerical explorations via a phenomenological fit showing quintessence-like late-time behavior and energy exchange between matter and geometry, highlighting how the modified coupling reshapes cosmic evolution relative to CDM. The results support the viability of EMT-squared gravity with the second-derivative correction in certain thermodynamically motivated setups and point to data-driven constraints and astrophysical tests as promising future directions.

Abstract

In this paper we have revisited the energy-momentum squared gravity theory, by taking into account the second derivative of the matter Lagrangian with respect to the metric, encapsulating relations originated from thermodynamical grounds. After obtaining the scalar tensor representation of the energy-momentum squared gravity with the new corrections, we have analyzed the physical implications by relying on the linear stability theory. The results show that the current cosmological system is compatible with the expansion of the Universe for some specific matter Lagrangians, explaining the emergence of matter domination era, approaching the late time accelerated expansion era close to the de-Sitter phenomenology.
Paper Structure (7 sections, 90 equations, 11 figures)

This paper contains 7 sections, 90 equations, 11 figures.

Table of Contents

  1. Introduction
  2. Fundamental relations for the energy-momentum-squared gravity
  3. The model and the gravitational field equations
  4. The dynamical analysis for $L_m=p$
  5. The dynamical analysis for $L_m=-\rho$
  6. Non-exhaustive numerical analysis
  7. Conclusions

Figures (11)

  • Figure 1: The effective equation of state for the $P_2$ solution.
  • Figure 2: The phase space directions near the $P_1$ solution in the $(z, \Omega_m)$ plane.
  • Figure 3: The phase space directions near the $P_3$ solution in the $(z, y)$ plane.
  • Figure 4: The phase space directions near the $Q_1$ solution in the $(z,\Omega_m)$ plane.
  • Figure 5: The phase space directions near the $Q_1$ solution in the $(z,y)$ plane.
  • ...and 6 more figures