Implications of pulsar timing arrays for Gauss-Bonnet Inflation

TL;DR

This paper investigates how pulsar timing arrays constrain inflationary gravitational waves within Gauss-Bonnet (GB) inflation. By deriving the GB-modified background dynamics and scalar/tensor perturbations, the authors show that a blue-tilted tensor spectrum ($n_T>0$) can arise naturally when the inflaton couples to the GB term, yielding a tensor-to-scalar ratio $r$ and scalar tilt compatible with observations. They connect PTA fits to horizon-crossing quantities $V$, $V_{,\phi}$ and $\xi_{,\phi}$, deriving general conditions that a blue tilt requires the inflaton to climb up the potential before descending, and the GB slope to be positive at horizon crossing. Two GB-inflation models are explored: natural inflation with a GB coupling can realize the blue tilt with sub-Planckian decay constants, while a power-law potential cannot realize a blue tilt even with GB coupling. The work highlights that PTAs largely probe the post-horizon-reentry regime and reheating details push high-frequency suppression beyond PTA reach, but combined with future GW bands (LISA, ET) and CMB data, GB inflation offers a testable framework for early-Universe gravity with potential UV completions in string theory.

Abstract

Correlated time-of-arrival measurements by pulsar timing arrays (PTAs) have provided a new means of constraining astrophysical or cosmological models that produce a gravitational wave (GW) background. For this work, we discuss the implications of PTA observations for Gauss-Bonnet (GB) inflationary models through the production and propagation of inflationary GWs. We show that our GB inflationary scenario is consistent with present PTA and cosmological data. A blue-tilted tensor power spectrum supported by PTAs can be naturally accommodated in GB inflation. Using observational constraints, we derive general conditions for the inflaton potential and the GB coupling function, suggesting that in GB inflation, the inflaton must climb up the potential before rolling downhill and reaching the end of inflation. We provide two concrete GB inflationary models to demonstrate the viability of this mechanism.

Figures (4)

• Figure 1: Standard (GR) inflation---Constraints (posteriors) of inflationary parameters $n_T$, $r$, and reheating temperature $T_{\rm rh}$ obtained with the NANOGrav 15 years data (red contours) NANOGrav:2023hvm and the IPTA-DR2 data set (blue contours) Antoniadis:2022pcn. The contours show $68\%$ and $95\%$ confidence levels. The gray and green regions are excluded by CMB and BBN observations, respectively.
• Figure 2: Standard (GR) inflation---[left panel] Best fit curves (bands) of the GW spectrum obtained with the NANOGrav 15 years data (NG15) NANOGrav:2023hde and the IPTA-DR2 data set (IPTA2) Antoniadis:2022pcn; [right panel] best-fit curves to nanohertz data and GW instrument sensitivity curves (aLIGO, ET, LISA, IPTA/SKA) in other bands, created using gwentKaiser:2020tlg. Red violins are free spectra fits by NANOGrav, blue violins by IPTA-DR2.
• Figure 3: Gauss-Bonnet inflation---Constraints (posteriors) of inflationary parameters $n_T$, $r$, reheating temperature $T_{\rm rh}$, and Gauss-Bonnet couplings ($c_1$ and $c_2$) obtained with the NANOGrav 15 years data (NG15, in red) NANOGrav:2023hde and the IPTA-DR2 data set (IPTA2, in blue) Antoniadis:2022pcn. The contours show $68\%$ and $95\%$ confidence intervals. The corresponding marginalized constraints are provided in Table \ref{['tab:1']}. The gray and green regions are excluded by CMB and BBN observations, respectively. The orange dotted line is shown as a reference to standard inflation when the GB terms vanish.
• Figure 4: Gauss-Bonnet inflation---[left panel] Best fit curves (bands) of the GW spectrum obtained with the NANOGrav 15 years data NANOGrav:2023hde and the IPTA-DR2 data set (IPTA2) Antoniadis:2022pcn; [right panel] best-fit curves to nanohertz data and GW instrument sensitivity curves (aLIGO, ET, LISA, IPTA/SKA) in other bands, created using gwentKaiser:2020tlg. Red violins are free spectra fits by NANOGrav, blue violins by IPTA-DR2.