f(R, T, R_μνT^μν) gravity phenomenology and ΛCDM universe

Abstract: We propose general f(R,T,R_{\mu\nu}T^{\mu\nu}) theory as generalization of covariant Horava-like gravity with dynamical Lorentz symmetry breaking. FRLW cosmological dynamics for several versions of such theory is considered. The reconstruction of the above action is explicitly done, including the numerical reconstruction for the occurrence of \Lambda CDM universe. De Sitter universe solutions in the presence of non-constant fluid are also presented. The problem of matter instability in f(R,T,R_{\mu\nu}T^{\mu\nu}) gravity is discussed.

• The paper introduces an f(R,T,RμνT^μν) gravity model that extends General Relativity by intricately coupling curvature and matter terms.
• It employs FLRW dynamics and numerical methods to demonstrate how specific function forms can replicate ΛCDM features like power-law expansion and de Sitter solutions.
• The study establishes analytical criteria to avert matter instability, offering actionable insights into constructing viable modified gravity configurations.

f(R,T,R_{\mu\nu}T^{\mu\nu}) Gravity Phenomenology and ΛCDM Universe

The paper proposes a comprehensive examination of the $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity theory, presenting it as an extension of the covariant Hořava-like gravity with dynamic Lorentz symmetry breaking. This novel formulation introduces modifications to classical General Relativity (GR) by incorporating additional curvature- and matter-dependent terms. The study explores the cosmological dynamics under several assumptions to assess the viability of these modifications in mimicking realistic cosmological scenarios, including the ΛCDM model.

Theoretical Framework

The authors start by defining the action of the $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity, where the scalar curvature $R$, trace of the energy-momentum tensor $T$, and the Ricci tensor $R_{\mu\nu}$ are intricately coupled. This coupling goes beyond traditional $f(R)$ gravity models, offering additional degrees of freedom potentially useful for modeling cosmological phenomena like dark energy and inflation.

Cosmological Dynamics

The research investigates the FLRW cosmological dynamics under various formulations of the $f(R,T,R_{\mu\nu}T^{\mu\nu})$ theory. It demonstrates how these formulations can reproduce different epochs of cosmological evolution, including the ΛCDM universe, characterized by matter $\Omega_m$ and dark energy $\Omega_\Lambda$ densities. By reconstructing the gravitational action, the study shows how specific choices of the functional form can lead to the desired cosmological dynamics, such as power-law expansion and de Sitter solutions even in the presence of fluctuating fluid components.

Numerical and Analytical Insights

Through numerical reconstruction, the study provides insights into possible function forms $f(P)$ and $g(T)$ associated with desirable cosmological behaviors. Exploring the consequences of different function choices in the context of the ΛCDM model reveals a plethora of possible configurations that replicate the expansion history without the explicit presence of a cosmological constant.

Matter Instability

A critical analysis of the stability of celestial body solutions within these modified gravitational models is conducted. The paper explains how matter instability, often observed in modified gravity theories, can potentially emerge due to the perturbations in the Ricci scalar and Ricci tensor. By presenting analytical criteria for the avoidance of such instabilities, the study sheds light on the viable configurations of $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity that can circumvent the issue.

Implications and Future Work

The implications of this work are multifaceted, opening pathways for further exploration in cosmological modeling. The $f(R,T,R_{\mu\nu}T^{\mu\nu})$ framework provides a versatile setting that could bridge modified gravity theories and Hořava-Lifshitz gravity, offering potential avenues for renormalizable and ghost-free models. Future work could expand on these findings, investigating the quantum gravity aspects and the ultraviolet behaviors of these models to establish broader applicability in theoretical physics and cosmology.

In summary, the paper presents a robust approach to extending GR through $f(R,T,R_{\mu\nu}T^{\mu\nu})$ gravity, with the potential to enhance our understanding of cosmological dynamics and address long-standing questions related to dark energy models and cosmic acceleration. The insights into matter stability and numerical reconstructions lay the groundwork for future studies in this field.