[Paper Review] A Stiff Pre-CMB Era with a Mildly Blue-tilted Tensor Inflationary Era can Explain the 2023 NANOGrav Signal

V. K. Oikonomou|arXiv (Cornell University)|Sep 9, 2023

Cosmology and Gravitation Theories7 citations

TL;DR

The paper analyzes how a stiff pre-CMB era combined with either red-tilted or mildly blue-tilted tensor inflation can explain the 2023 NANOGrav stochastic gravitational wave signal, using both model-agnostic and Higgs-axion-inspired approaches.

ABSTRACT

We examine the effects of a stiff pre-recombination era on the present day's energy spectrum of the primordial gravitational waves. If the background total equation of state parameter at the pre-recombination era is described by a kination era one, this directly affects the modes with characteristic wavenumbers which reenter the Hubble horizon during this stiff era. The stiff era causes a broken-power-law effect on the energy spectrum of the gravitational waves. We use two approaches, one model agnostic and a specific model that can realize this scenario. In all cases, the inflationary era can be realized either by some theory leading to a standard red-tilted tensor spectral index or by some theory which has a mild tensor spectral index $n_{\mathcal{T}}=0.17-0.37$ like an Einstein-Gauss-Bonnet theory. For the model agnostic scenario case, the NANOGrav signal can be explained by the stiff pre-recombination era combined with an inflationary era with a mild blue-tilted tensor spectral index $n_{\mathcal{T}}=0.37$ and a low-reheating temperature $T_R\sim 0.1$GeV. In the same case, the red-tilted inflationary theory signal can be detectable by the future LISA, BBO and DECIGO experiments. The model dependent approach is based on a Higgs-axion model which can yield multiple deformations of the background total equation of state parameter, causing multiple broken-power-law behaviors occurring in various eras before and after the recombination era. In this case, the NANOGrav signal is explained by this model in conjunction with an inflationary era with a really mild blue-tilted tensor spectral index $n_{\mathcal{T}}=0.17$ and a low-reheating temperature $T_R\sim 20\,$GeV. In this case, the signal can be detectable by the future Litebird experiment, which is a very characteristic pattern in the tail of the primordial gravitational wave energy spectrum.

Motivation & Objective

• Motivate the study of a stiff pre-CMB era and its imprint on the primordial gravitational wave spectrum.
• Investigate how a mildly blue-tilted tensor spectrum affects the NANOGrav signal under pre-CMB stiff dynamics.
• Compare model-agnostic and specific model realizations that can realize the stiff pre-CMB + inflationary scenarios.
• Assess observational implications for LISA, BBO, DECIGO, and LiteBIRD in related parameter regimes.

Proposed method

• Derive the energy spectrum of primordial gravitational waves with a stiff pre-CMB era and a specified inflationary tensor tilt.
• Use a model-agnostic approach and a Higgs-axion inspired model to generate broken-power-law features in the spectrum.
• Incorporate reheating temperature T_R and a variable pre-CMB equation of state w to modulate the spectrum.
• Employ transfer functions T1 and T2 and damping factors from g_* and g_*s to obtain the present-day Omega_gw(f).
• Consider red-tilted (n_T < 0) and mildly blue-tilted (n_T ~ 0.17–0.37) tensor spectra, including an Einstein-Gauss-Bonnet realization for blue tilt.

Experimental results

Research questions

• RQ1 Can a stiff pre-CMB era before recombination plus a mildly blue-tilted tensor inflation era reproduce the 2023 NANOGrav stochastic signal?
• RQ2 What ranges of the pre-CMB equation of state w and reheating temperature T_R are compatible with the NANOGrav signal under red-tilted and blue-tilted tensor spectra?
• RQ3 How do model-agnostic and Higgs-axion specific implementations compare in producing the required broken-power-law features in the gravitational wave spectrum?
• RQ4 What are the observable predictions for future detectors (LISA, BBO, DECIGO, LiteBIRD) given these scenarios?

Key findings

• A stiff pre-CMB era modifies the gravitational wave spectrum, enabling a broken-power-law behavior that can explain the NANOGrav signal.
• A mildly blue-tilted tensor spectrum with n_T ≈ 0.37 and low reheating temperature (~0.1 GeV) can align with NANOGrav in the model-agnostic scenario.
• Red-tilted tensor spectra also fit within this framework, with detectable consequences for future experiments depending on reheating and EoS.
• In a Higgs-axion model, multiple broken-power-law features arise, with n_T ≈ 0.17 and T_R ≈ 20 GeV, potentially yielding signatures for LiteBIRD.
• An Einstein-Gauss-Bonnet theory can generate a mild blue tilt, enabling consistency with GW170817 constraints and offering distinctive spectral patterns.