[Paper Review] Cosmological effects on $f(\bar{R},\bar{T})$ gravity through a non-standard theory

Arijit Panda, Md. Rabiul Islam+3 more|arXiv (Cornell University)|Jun 28, 2022

Cosmology and Gravitation Theories4 citations

TL;DR

This paper proposes a non-canonical $f(\bar{R},\bar{T})$ gravity model in K-essence geometry using a Dirac-Born-Infeld (DBI) Lagrangian to derive modified Friedmann equations and explore dark energy dynamics. It shows that for specific $f(\bar{R},\bar{T})$ forms—especially $f(\bar{R},\bar{T}) = \bar{R} + \alpha\bar{R}^n + \lambda\bar{T}$—the equation of state parameter $\omega$ evolves from negative values toward $-1$, consistent with SNIa+BAO+H(z) observational data, supporting a kinetically driven early dark energy phase.

ABSTRACT

This study aims to investigate the impact of dark energy in cosmological scenarios by exploiting $f(\bar{R},\bar{T})$ gravity within the framework of a {\it non-standard} theory, called {\it {\bf K-}essence} theory, where $\bar{R}$ represents the Ricci scalar and $\bar{T}$ denotes the trace of the energy-momentum tensor associated with the {\bf K-}essence geometry. The Dirac-Born-Infeld (DBI) non-standard Lagrangian has been employed to generate the emergent gravity metric $(\bar{G}_{μν})$ associated with the {\bf K-}essence. This metric is distinct from the usual gravitational metric $(g_{μν})$. It has been shown that under a flat FLRW background gravitational metric, the modified field equations and the Friedmann equations of the $f(\bar{R},\bar{T})$ gravity are distinct from the usual ones. In order to get the equation of state (EOS) parameter $ω$, we have solved the Friedmann equations by taking into account the function $f(\bar{R},\bar{T})\equiv f(\bar{R})+λ\bar{T}$, where $λ$ represents a parameter within the model. We have found a relationship between $ω$ and time for different kinds of $f(\bar{R})$ by treating the kinetic energy of the {\bf K-}essence scalar field ($\dotϕ^{2}$) as the dark energy density which fluctuates with time. Surprisingly, this result meets the condition of the restriction on $\dotϕ^{2}$. By presenting graphical representations of the EOS parameter with time, we show that our model is consistent with the data of $SNIa$+$BAO$+$H(z)$ within a certain temporal interval.

Motivation & Objective

• To investigate cosmological effects of $f(\bar{R},\bar{T})$ gravity in a non-standard K-essence framework with non-canonical DBI Lagrangian.
• To derive modified field and Friedmann equations under a flat FLRW background with non-conformally equivalent emergent gravity metric $\bar{G}_{\mu\nu}$.
• To examine whether the model can reproduce the observed late-time cosmic acceleration without invoking a cosmological constant.
• To test the consistency of the equation of state parameter $\omega$ with observational data (SNIa+BAO+H(z)) for different $f(\bar{R},\bar{T})$ forms.
• To explore the possibility of dark energy dominance in the early universe via kinetic energy of the K-essence scalar field.

Proposed method

• Formulate a non-canonical $f(\bar{R},\bar{T})$ gravity model using a Dirac-Born-Infeld (DBI) type non-standard Lagrangian for the K-essence scalar field.
• Derive the emergent gravity metric $\bar{G}_{\mu\nu}$ from the DBI action, distinct from the standard gravitational metric $g_{\mu\nu}$, ensuring non-conformal equivalence.
• Construct modified field equations and Friedmann equations in a flat FLRW spacetime background, incorporating $\bar{R}$ (Ricci scalar) and $\bar{T}$ (trace of energy-momentum tensor).
• Assume $f(\bar{R},\bar{T}) = f(\bar{R}) + \lambda\bar{T}$ with $f(\bar{R})$ taking three forms: linear ($\bar{R}$), Starobinsky-type ($\bar{R} + \alpha\bar{R}^2$), and general power-law ($\bar{R} + \alpha\bar{R}^n$).
• Relate the dark energy density to the kinetic energy $\dot{\phi}^2$ of the K-essence scalar field to derive time-evolving $\omega$.
• Plot $\omega(t)$ for various model parameters and compare with observational constraints from SNIa, BAO, and H(z) data.

Experimental results

Research questions

• RQ1 Can a non-canonical $f(\bar{R},\bar{T})$ gravity model in K-essence geometry reproduce the observed late-time cosmic acceleration without a cosmological constant?
• RQ2 How does the equation of state parameter $\omega$ evolve over time in this modified gravity framework, and does it satisfy observational constraints?
• RQ3 Does the model allow for dark energy dominance in the early universe, consistent with K-inflation scenarios?
• RQ4 What role does the kinetic energy of the K-essence scalar field play in driving the equation of state and cosmic expansion?
• RQ5 How do different functional forms of $f(\bar{R},\bar{T})$ affect the consistency of $\omega(t)$ with SNIa+BAO+H(z) data?

Key findings

• The model produces a time-evolving equation of state parameter $\omega$ that satisfies $\omega \leq -1$ for specific choices of model parameters $\lambda$, $\alpha$, and $n$, consistent with late-time cosmic acceleration.
• For the general form $f(\bar{R},\bar{T}) = \bar{R} + \alpha\bar{R}^n + \lambda\bar{T}$, the EoS parameter starts from high negative values and evolves toward $-1$ as $n$ increases, matching the current value of $\omega \approx -1$.
• Graphs of $\omega(t)$ for $n = 3,4,5,6,7$ show that the model is consistent with observational data (SNIa+BAO+H(z)) within a specific time range, validating the model's phenomenological viability.
• The kinetic energy $\dot{\phi}^2$ of the K-essence scalar field is identified as the source of dark energy density, and its time dependence naturally leads to a varying $\omega$, satisfying the required physical constraints.
• The model supports a kinetically driven early dark energy phase, suggesting that dark energy could have played a role in the early universe, consistent with K-inflation scenarios.
• The results are observationally viable and support the idea that $f(\bar{R},\bar{T})$ gravity in K-essence geometry offers a viable alternative to the cosmological constant, without requiring ad-hoc dark energy components.