Reconstruction of f(R, T) gravity describing matter dominated and accelerated phases

Abstract: We investigate the cosmological reconstruction in modified f(R,T) gravity, where R is the Ricci scalar and T the trace of the stress-energy tensor. Special attention is attached to the case in which the function f is given by f (R, T) = f1 (R) + f2 (T). The use of auxiliary scalar field is considered with two known examples for the scale factor corresponding to an expanding universe. In the first example, where ordinary matter is usually neglected for obtaining the unification of matter dominated and accelerated phases with f(R)gravity, it is shown in this paper that this unification can be obtained without neglect ordinary matter. In the second example, as in f(R)gravity, model of f(R, T) gravity with transition of matter dominated phase to the acceleration phase is obtained. In both cases, linear function of the trace is assumed for f2(T) and it is obtained that f1(R) is proportional to a power of R with exponents depending on the input parameters.

• The paper reconstructs f(R, T) gravity models capable of naturally unifying the universe's matter-dominated and accelerated expansion phases.
• The methodology employs auxiliary scalar fields to derive specific forms of the f(R, T) function, finding consistency with observational data like WMAP.
• This framework offers a theoretical avenue for understanding cosmic epoch transitions while potentially addressing non-cosmological gravitational phenomena.

Analysis of "Reconstruction of f(R, T) gravity describing matter dominated and accelerated phases"

The paper presented by M. J. S. Houndjo focuses on the cosmological reconstruction within the framework of modified f(R, T) gravity. This extension of standard general relativity introduces a function that is dependent on both the Ricci scalar R and the trace of the stress-energy tensor T, allowing it to potentially describe both the matter-dominated and accelerated phases of the universe without discarding the ordinary matter contribution. The theoretical nuances of such modifications are explored using the reconstruction program, leveraging auxiliary scalar fields to propose viable cosmological models.

Core Concepts and Methodology

The fundamental aim of this research is to extend the gravitational theory to encompass more general scenarios by considering the variation of both the Ricci scalar and the trace of the energy-momentum tensor in the gravitational Lagrangian. The study assumes the function f(R, T) as a sum of individual arbitrary functions of R and T, specified as f1(R) and f2(T), respectively.

For methodological rigor, the scalar field is employed not as a dynamic field but as an auxiliary construct. The reconstruction methodology pioneered here lays out a systematic way to derive f(R, T) gravity that aligns with existing cosmic expansion histories. The paper discusses two explicit cosmological models where the scale factor is chosen to represent a universe transitioning from a matter-dominated era to an accelerated phase. Importantly, the reconstruction allows for the inclusion of realistic effects in the energy-momentum tensor without necessitating the omission of ordinary matter, contrasting conventional f(R) gravity models.

Findings and Numerical Results

The research concludes that certain forms of f(R, T) gravity can naturally unify matter-dominated and accelerated phases through specific forms of the function f, governed by parameter values. In particular, for scenarios assuming a linear function of the trace, the function f1(R) resolves to power-law forms contingent on input parameters. These theoretical results are corroborated by the consistency with five-year Wilkinson Microwave Anisotropy Probe (WMAP) data, affirming the potential of such models to bridge observations of cosmic acceleration with theoretical predictions.

The paper presents strong numerical insights through derived expressions for effective energy densities and pressures, integrating the effects of modified gravity. For instance, the transition between epoch phases is characterized by changes in the Hubble parameter, following a matter-dominated phase portrayed by different functions of the scale factor.

Implications for Cosmology and Future Work

The theoretical framework proposed provides a promising avenue for understanding the transition in cosmic epochs without abandoning the traits of general relativity principles. Recognizing the intricacies involved in adding the trace component implies potential for addressing non-cosmological phenomena such as gravitational collapse and wave generation within the f(R, T) purview.

Despite these advancements, the study acknowledges possible limitations, particularly a subclass of the theory that may be cosmologically nonviable due to higher-order derivative terms leading to singularities. Future research should address these gaps, with attention on models that emulate ΛCDM cosmology, investigate stability criteria, and examine corrections to Newtonian gravity laws, as is customary in f(R) and f(G) frameworks.

Overall, this paper enriches the modified gravity sector, presenting a robust pathway to analyze universal expansion history through a modified gravitational paradigm that maintains connections with empirical cosmological data while inviting further exploration of its theoretical underpinnings and applications.