Inflationary models in $f(R,T)$ gravity: Constraints from $Planck$, BICEP/$Keck$, and Atacama

TL;DR

This work investigates inflationary dynamics in the simple $f(R,T)$ gravity model $f(R,T)=R+16\pi G\lambda T$ for three motivated potentials: Mutated hilltop inflation, D-brane (KKLT-type) inflation, and Woods-Saxon inflation. By deriving the modified slow-roll framework and computing $n_s$, $r$, and $n_{sk}$ at $N=60$ e-folds, the authors confront predictions with Planck 2018, BK18, ACT DR6, and DESI DR2, and also assess compatibility with the projected sensitivities of LiteBIRD and CMB-S4. The results show that Mutated hilltop inflation can yield $r$ as small as $\sim10^{-4}$ for suitable $\lambda$, while KKLT-type D-brane models produce $r$ in the $10^{-2}$ to $10^{-3}$ range with $n_s$ around $0.965$–$0.969$ and $n_{sk}\sim-10^{-4}$; Woods-Saxon inflation gives $r\sim10^{-4}$ and $n_s\approx0.965$–$0.966$, but may be disfavored by ACT/ Atacama constraints. Overall, two of the three models remain viable under current data, highlighting f(R,T)$ gravity as a flexible framework to accommodate inflationary scenarios within evolving observational bounds.

Abstract

The advent of high-precision cosmological observations has challenged many traditional inflationary models. Data from $Planck$ 2018 along with the BICEP/$Keck$ 2018 result have already ruled out most of the established models by placing tight constraints on the tensor-to-scalar ratio $r$. Upcoming missions like LiteBIRD & CMB-S4 are expected to impose an even more stringent bound on $r$ , potentially excluding further models from the viable landscape. In this evolving observational context, modified gravity theories offer a promising way to reconcile inflationary models with data. In this work, we explore several inflationary models, namely mutated hilltop inflation, D-brane inflation, and Woods-Saxon inflation, within the framework of $f(R, T)$ gravity. The cosmological observable parameters, viz. scalar spectral tilt $n_s$, tensor-to-scalar ratio $r$, and running of scalar spectral index $n_{sk}$ are estimated for the three models, and their trajectories are plotted in the $n_s-r$ plane. The model results are evaluated in light of the $Planck$, BICEP/$Keck$, DESI DR2, and ACT DR6 data. We observe that for a certain model parameter space, these potentials are viable within the current observational bounds.

Figures (4)

• Figure 1: The $n_s-r$ plot predicted by the mutated hilltop potential. The marginalized joint 68% and 95% C.L. regions for $n_s$ and $r$ at $k=0.002 Mpc^{-1}$ from $Planck$ 2018 data are shown in blue and pink colour where as for $Planck$+BK18 are shown in orange and green respectively.
• Figure 2: The $n_s-r$ trajectory predicted by the KKLT potential at 60 $e$-folding. The marginalized joint 68% and 95% C.L. regions for $n_s$ and $r$ at $k=0.002 Mpc^{-1}$ from $Planck$ 2018 data are shown in blue and pink colour where as for $Planck$+BK18 are shown in orange and green respectively.
• Figure 3: The $n_s-r$ trajectory predicted by the Woods-Saxon potential at 60 $e$-folding. The marginalized joint 68% and 95% C.L. regions for $n_s$ and $r$ at $k=0.002 Mpc^{-1}$ from $Planck$ 2018 data are shown in blue and pink colour where as for $Planck$+BK18 are shown in orange and green respectively.
• Figure 4: The $n_s-r$ trajectory predicted by the mutated hilltop potential, KKLT $(n=2, m=0.5)$, KKLT $(n=4, m=0.5)$, Woods-Saxon potential $(b=0.001, c=-5)$ at 60 $e$-folding are shown in red, black, blue, and green colour respectively. The marginalized joint 68% and 95% C.L. regions for $n_s$ and $r$ at $k=0.002 Mpc^{-1}$ from the combined P-ACT-LB-BK18 data are shown in purple and orange colour.