Observational Constraints on $f(Q,T)$ Gravity in the Presence of DBI-Essence Scalar Field

Abstract: We investigate late-time cosmology in extended symmetric teleparallel gravity coupled to a Dirac-Born-Infeld (DBI) scalar field within $f(Q,T)$ gravity, where $Q$ is the non-metricity scalar and $T$ is the trace of the matter energy-momentum tensor. Working on a spatially flat Friedmann-Lemaître-Robertson-Walker background and treating the cosmic medium as an effective perfect fluid, we derive the background field equations for $f(Q,T)+\mathrm{DBI}$ gravity and obtain analytic solutions for the linear choice $f(Q,T)=αQ+βT$. We then constrain the model parameters with a Markov Chain Monte Carlo analysis using Hubble-rate data, DESI BAO (DR2) measurements, and the Pantheon+SHOES Type~Ia supernova sample. The joint posteriors (Tables II and III) are broadly consistent with current late-time constraints and allow a direct comparison with $Λ$CDM, quantifying the departures driven by the $βT$ coupling and the DBI sector. Although the model does not reproduce every observational feature exactly, it provides a statistically viable alternative avenue to the standard paradigm and a useful framework for exploring potential remedies to existing tensions, including the $H_0$ discrepancy, without claiming a definitive resolution.

• The paper demonstrates that f(Q,T) gravity with DBI-essence effectively models late-time cosmic acceleration using analytic solutions for a linearized case.
• Observational constraints via Hubble-rate, BAO, and Type Ia supernovae data yield parameters that partially alleviate the H0 tension while matching standard cosmic expansion.
• Rigorous model selection using AIC, BIC, and DIC confirms that despite additional parameters, the extended model remains statistically competitive with ΛCDM.

Observational Constraints on $f(Q,T)$ Gravity in the Presence of DBI-Essence Scalar Field

Theoretical Framework: $f(Q,T)$ Gravity and DBI-Essence Coupling

The paper explores a late-time cosmological scenario rooted in the $f(Q,T)$ extension of symmetric teleparallel gravity, where $Q$ denotes the non-metricity scalar and $T$ represents the trace of the energy-momentum tensor. The model is enriched by the inclusion of a Dirac-Born-Infeld (DBI) scalar field, characterized by non-canonical kinetic terms, which are known to generate a variable effective sound speed and diverse cosmological dynamics, including accelerated expansion.

In standard symmetric teleparallel gravity, gravitational dynamics are encoded in the non-metricity scalar $Q$, leading to field equations dynamically equivalent to those of GR. The $f(Q,T)$ extension introduces explicit matter-geometry couplings and non-conservation of the matter energy-momentum tensor, allowing interpretations in terms of effective energy transfer and particle production. Integrating a DBI-essence scalar field (string-motivated, square-root kinetic structure) adds additional dynamical degrees of freedom, enabling models that unify inflation and late-time acceleration with reduced fine-tuning and distinctive perturbative features (e.g., modified sound speeds, non-Gaussianities).

The action constructed is: $$S = \int d^4x \sqrt{-g} \left[ f(Q,T) + \mathcal{L}_\text{DBI}(\phi, X) + \mathcal{L}_m \right]$$ For the linearized case $f(Q,T) = a Q + \beta T$, the non-metricity-matter coupling parameter $\beta$ controls deviations from STEGR ($f(Q,T)$0). The DBI sector is minimally coupled, and the scalar potential and warp factor are chosen as $f(Q,T)$1, $f(Q,T)$2, enabling analytic treatment and phenomenological compatibility with slow-roll dynamics.

Modified Cosmological Dynamics

The cosmological equations are derived in a spatially flat FLRW background. The Friedmann equations are modified by the $f(Q,T)$3 coupling, DBI kinetic structure, and additional geometric terms. The effective energy density and pressure incorporate both matter and DBI contributions, while the deceleration parameter $f(Q,T)$4 and effective equation-of-state parameter $f(Q,T)$5 reflect non-minimal gravitational interaction, energy exchange, and scalar field evolution.

The DBI Lorentz factor $f(Q,T)$6 restricts field motion and is crucial for phenomenological viability (accelerated expansion requires suitable $f(Q,T)$7 ratios), with explicit evolution equations provided. The resulting dynamical system is nonlinear—analytic solutions are available for the linearized $f(Q,T)$8 ansatz and chosen DBI forms, but full parameter evolution is numerically integrated for comparison to observations.

Observational Methodology and Parameter Constraints

Parameter estimation is performed using MCMC sampling (Cobaya), confronting the model with three key datasets:

• Hubble-rate measurements (cosmic chronometers)
• DESI BAO (DR2) data
• Pantheon+SHOES Type Ia supernovae

The parameter vector includes $f(Q,T)$9, $f(Q,T)$0, $f(Q,T)$1, $f(Q,T)$2, $f(Q,T)$3, $f(Q,T)$4 (field velocity), and $f(Q,T)$5 (sound horizon). Bayesian likelihood maximization yields posterior distributions, confidence intervals, and model selection statistics ($f(Q,T)$6, AIC, BIC, DIC).

Numerical results demonstrate:

• $f(Q,T)$7 (consistent with standard late-time cosmology)
• $f(Q,T)$8 (statistically compatible with zero; current data do not require strong matter-geometry coupling)
• DBI parameters ($f(Q,T)$9, $Q$0, $Q$1) moderately constrained, scalar is slow-rolling at late times
• $Q$2 Mpc (consistent with standard BAO ruler values)
• $Q$3 (intermediate between local and CMB measurements; potential partial alleviation of $Q$4 tension)

Comparison with standard models ($Q$5CDM, $Q$6CDM) shows that the $Q$7DBI model fits the expansion history across all redshifts and supernova distances, with reduced $Q$8 nearly unity, demonstrating statistical viability.

Model Selection and Statistical Analysis

Rigorous model comparison is performed using AIC, BIC, and DIC. While $Q$9CDM is preferred due to minimal parameter count and fit quality ($T$0AIC = 8.39, $T$1BIC = 30 for the $T$2DBI model), the DIC penalty is moderate ($T$3DIC = 3.87), implying that the posterior-averaged predictive performance is comparable to that of the standard model. The larger information-criterion penalties for $T$4DBI primarily reflect extended parameter space rather than poor fit.

All models yield reduced $T$5 values close to unity, indicating robust reproduction of observational constraints. Parameter degeneracies are evident but do not preclude competitive fit quality.

Practical and Theoretical Implications

The $T$6DBI framework constitutes a viable extension to late-time cosmology, offering a unified avenue for addressing cosmic acceleration. The model is flexible enough to accommodate subtle deviations from standard expansion history and provides parameter ranges compatible with contemporary datasets.

Key implications include:

• Alternative explanation for cosmic acceleration: Model achieves accelerated expansion without relying solely on a cosmological constant, leveraging non-metricity-matter coupling and nonlinear scalar kinetic effects.
• Potential alleviation of cosmological tensions: The inferred $T$7 value is intermediate, suggesting that modified gravity and scalar-field freedom may help mitigate the $T$8 discrepancy, though not providing a definitive resolution.
• Unified dynamical framework: The approach nests inflationary and late-time acceleration mechanisms within the same theoretical structure, supporting the development of unified models with rich perturbative phenomenology.
• Testability via structure formation and gravitational waves: The non-canonical kinetic sector and matter-geometry coupling introduce distinctive perturbative and thermodynamic signatures relevant for next-generation cosmological probes.
• Observational viability: Despite additional complexity, the model remains statistically competitive and the parameter space is broadly consistent with observational bounds.

Prospects for Future Research

Extensions include:

• Full analysis of perturbations and structure growth (beyond background evolution)
• Inclusion of early-universe CMB constraints and weak lensing data
• Exploration of broader $T$9 and DBI parameterizations
• Examination of implications for modified gravity phenomenology, gravitational wave propagation, and non-Gaussianity signatures

Joint analyses with larger, more diverse datasets will further clarify the relevance of non-metricity-matter coupling and nonlinear kinetic effects in cosmology.

Conclusion

The study presents a comprehensive analysis of late-time cosmological dynamics in $Q$0 gravity coupled to a DBI-essence scalar field, derives analytic solutions for a linearized model, and constrains parameters with robust Bayesian inference against multiple observational datasets. While standard cosmology is statistically favored under information criteria, the $Q$1DBI model remains observationally viable and theoretically well-motivated, offering valuable insights and benchmarks for future modified gravity and dark energy research (2606.21839).