Laxmipriya Pati

In this work, we examine the theoretical framework of modified teleparallel gravity with the inclusion of the boundary term in the action and investigate its cosmological implications by considering the power-law model f(T, B) = -T + α (-B) ^β , with the aim of addressing late-time accelerated expansion and the dark energy. In this context, T denotes the torsion scalar and B represents the boundary term, whose presence allows for departures from standard teleparallel dynamics and provides a unified description that connects torsion and curvature-based formulations, reproducing f(T) and f(R) gravity in appropriate limits. The viability of the model is assessed by confronting its theoretical predictions with observational data while constraining the cosmological and model parameters through a Markov Chain Monte Carlo (MCMC) using cosmic chronometers (CC), the Pantheon plus sample (PPS), and the DESI baryon acoustic oscillation (BAO) Data Release 2 (DR2) datasets, and comparing its performance with the standard ΛCDM model. Our results, for the obtained constraints β from the model parameter, strongly indicate that, within the adopted parameterization and prior ranges, the observational data favor a non-zero correction to the boundary term. The Akaike information criterion (AIC) analysis shows that the combined CC+PPS dataset mildly favors the f(T, B) model, suggesting an improved phenomenological fit to late-time observations over ΛCDM, while in contrast, the Bayesian information criterion (BIC) favors the ΛCDM, as the f(T, B) model is penalized due to an additional free parameter introduced through the initial conditions required to solve the cosmological equations, aiming to constrain from statistical analysis to compare with the observations. Further, our model predicts that the Hubble constant lies between the Planck and SH0ES determinations, which is again consistent with current late-time observations. In addition, the background cosmological quantities suggest that the model exhibits a dynamical phantom-divide crossing while remaining consistent with late-time observations and yields a viable expansion history and characteristic dark energy evolution.

In symmetric teleparallel geometry the curvature and torsion tensors are assumed to vanish identically, while the dynamics of gravity is encoded by nonmetricity. Here the spatially homogeneous and isotropic connections that can accompany flat Friedmann-Lemaitre-Robertson-Walker metric come in three sets. As the trivial set has received much attention, we focus on the two alternative sets which introduce an extra degree of freedom into the equations. Working in the context of symmetric teleparallel scalar-tensor gravity with generic nonminimal coupling and potential, we show that the extra free function in the connection can not play the role of dark matter nor dark energy, but it drastically alters the scalar field behavior. We determine the restrictions on the model functions which permit the standard cosmological scenario of successive radiation, dust matter, and scalar potential domination eras to be stable. However, the alternative connections also introduce a rather general possibility of the system meeting a singularity in finite time.

In symmetric teleparallel geometry the curvature and torsion tensors are assumed to vanish identically, while the dynamics of gravity is encoded by nonmetricity. Here the spatially homogeneous and isotropic connections that can accompany the flat Friedmann-Lemaître-Robertson-Walker metric come in three sets. As the trivial set has received much attention, we focus on the two alternative sets, which introduce an extra degree of freedom into the equations. Working in the context of symmetric teleparallel scalar-tensor gravity with generic nonminimal coupling and potential, we show that the extra free function in the connection cannot play the role of dark matter nor dark energy, but it drastically alters the scalar field behavior. We determine the restrictions on the model functions which permit the standard cosmological scenario of successive radiation, dust matter, and scalar potential domination eras to be stable. However, the alternative connections also introduce a rather general possibility of the system meeting a singularity in finite time.

We present Hamilton’s equations for the teleparallel equivalent of general relativity (TEGR), which is a reformulation of general relativity based on a curvatureless, metric compatible, and torsionful connection. For this, we consider the Hamiltonian for TEGR obtained through the vector, antisymmetric, symmetric and trace-free, and trace irreducible decomposition of the phase space variables. We present the Hamiltonian for TEGR in the covariant formalism for the first time in the literature, by considering a spin connection depending on Lorentz matrices. We introduce the mathematical formalism necessary to compute Hamilton’s equations in both Weitzenböck gauge and covariant formulation, where for the latter we must introduce new fields: Lorentz matrices and their associated momenta. We also derive explicit relations between the conjugate momenta of the tetrad and the conjugate momenta for the metric that are traditionally defined in GR, which are important to compare both formalisms.