Qing Gao

Recent analyses combining Atacama Cosmology Telescope (ACT) data with other cosmological datasets report a higher scalar spectral index $$n_s$$ n s , creating tension with a wide range of inflationary models. Since a Gauss–Bonnet term with a coupling function $$\xi (\phi ) = 3\lambda /[4V(\phi )]$$ ξ ( ϕ ) = 3 λ / [ 4 V ( ϕ ) ] leaves $$n_s$$ n s nearly unchanged (up to a field rescaling) while reducing the tensor-to-scalar ratio r by a factor $$(1-\lambda )$$ ( 1 - λ ) , so choosing $$(1-\lambda )$$ ( 1 - λ ) sufficiently small effectively removes r as a limiting observable, making it easier for inflationary models to satisfy the latest observational constraints and alleviating this tension. Applying this mechanism to chaotic inflation, E-models, T-models, and hilltop inflation, we find that broad regions of parameter space become consistent with the latest ACT-based cosmic microwave background (CMB) constraints. These results demonstrate that Gauss–Bonnet couplings can help bring a broad class of inflationary models into agreement with current CMB measurements.

The latest ACT data release disfavors the attractor $n_s=1-2/N$. In inflationary models with nonminimal coupling, such attractors typically arise in the strong coupling limit. To align with observational constraints, we focus on nonminimal coupling models with small coupling constants. For the model with the coupling function $Ω(φ) = 1 + ξf(φ)$ and the potential $V(φ) = λ^2 f^2(φ)$, we find that observational data constrain the parameters as $0.1 \lesssim ξ\lesssim 35$ and $0 \lesssim k \lesssim 1.5$ for $f(φ) = φ^k$ at the $1σ$ confidence level. With the help of the nonmiminal coupling $Ω(φ) = 1 + ξφ^2$, the hilltop inflation and power-law inflation models with power indices $2/3$ and $1/3$ can be consistent with observational data within the $1σ$ range. We also give the viable parameter regions for $ξ$ for these three models.

To elucidate the robustness of the baryon acoustic oscillation (BAO) data measured by the dark energy spectroscopic instrument (DESI) in capturing the dynamical behavior of dark energy, we assess the model dependence of the evidence for dynamical dark energy inferred from the DESI BAO data. While the DESI BAO data slightly tightens the constraints on model parameters and increases the tension between the Chevallier–Polarski–Linder (CPL) model and the $\Lambda$CDM model, we find that the influence of DESI BAO data on the constraint of $w_0$ is small in the SSLCPL model. In comparison to the CPL model, the tension with the $\Lambda$CDM model is reduced for the SSLCPL model, suggesting that the evidence for dynamical dark energy from DESI BAO data is dependent on cosmological models. The inclusion of spatial curvature has little impact on the results in the SSLCPL model.

To elucidate the robustness of the baryon acoustic oscillation (BAO) data measured by the Dark Energy Spectroscopic Instrument (DESI) in capturing the dynamical behavior of dark energy, we assess the model dependence of the evidence for dynamical dark energy inferred from the DESI BAO data. While the DESI BAO data slightly tightens the constraints on model parameters and increases the tension between the Chevallier-Polarski-Linder (CPL) model and the $Λ$CDM model, we find that the influence of DESI BAO data on the constraint of $w_0$ is small in the SSLCPL model. In comparison to the CPL model, the tension with the $Λ$CDM model is reduced for the SSLCPL model, suggesting that the evidence for dynamical dark energy from DESI BAO data is dependent on cosmological models. The inclusion of spatial curvature has little impact on the results in the SSLCPL model.

There is a duality in the observables $n_s$, $r$ and the inflaton potential between large and small $η_H$ for the constant-roll inflation if the slow-roll parameter $ε_H$ is negligible. In general, the duality between $η_H$ and $\barη_H$ does not hold for the background evolution of the inflation. For some particular solutions for the constant-roll inflation with $η_H$ being a constant, we find that in the small field approximation, the potential takes the quadratic form and it remains the same when the parameter $η_H$ changes to $\barη_H=3-η_H$. If the scalar field is small and the contribution of $ε_H$ is negligible, we find that there exists the logarithmic duality and the duality between large and small $η_H$ for the primordial curvature perturbation in inflationary models with the quadratic potential.

Strong evidence of the existence of the stochastic gravitational wave background (SGWB) has been reported recently by the North American Nanohertz Observatory for Gravitational Waves, the Parkes Pulsar Timing Array, the European Pulsar Timing Array, and the Chinese Pulsar Timing Array Collaborations. The Bayesian posteriors of the SGWB amplitude and spectrum are compatible with astrophysical predictions for the SGWB from a population of supermassive black hole binaries (SMBHBs). We discuss the modifications arising from the extra scalar or vector radiation to the characteristic dimensionless strain of gravitational waves from SMBHBs and explore the possibility of detecting charges carried by supermassive black holes in modified gravity. The Bayesian posteriors on the tensor amplitude and the spectral exponent of SGWB are ${\log }_{10}{A}_T=-14.64_{-0.27}^{+0.19}$ and $\alpha =-0.35_{-0.25}^{+0.23}$, and a rough upper limit ${\log }_{10}{A}_{V,S}\le -15.2$ is obtained for the SGWB scalar or vector amplitude. The Bayesian factor between the models with and without charge is only 0.6, so the current PTA data do not favor charged SMBHBs over neutral SMBHBs.