[Paper Review] Broken blue-tilted inflationary gravitational waves: a joint analysis of NANOGrav 15-year and BICEP/Keck 2018 data

Jun-Qian Jiang, Yong Cai+2 more|arXiv (Cornell University)|Jul 28, 2023

Pulsars and Gravitational Waves ResearchPhysics and Astronomy102 references8 citations

TL;DR

This paper performs a joint MCMC analysis of a broken power-law inflationary gravitational wave spectrum using NANOGrav 15-year PTA data and BK18 CMB data, finding a PTA-like blue tilt around PTA scales and a slower, near-constant tilt at CMB scales, with relaxed but present constraints on r.

ABSTRACT

Recently, the pulsar timing array (PTA) collaborations have reported the evidence for a stochastic gravitational wave background (SGWB) at nano-Hertz band. The spectrum of inflationary gravitational wave (IGW) is unknown, which might exhibit different power law at different frequency-bands, thus if the PTA signal is primordial, it will be significant to explore the underlying implications of current PTA and CMB data on IGW. In this paper, we perform a joint Markov Chain Monte Carlo analysis for a broken power-law spectrum of IGW with the NANOGrav 15-year and BICEP/Keck 2018 data. It is found that though the bestfit spectral tilt of IGW at PTA band is $n^ ext{PTA}_ ext{T} =2.42^{+0.32}_{-0.91}$, at CMB band the bestfit is $n^ ext{CMB}_ ext{T} =0.55^{+0.37}_{-0.10}$ while a detectable amplitude of $r$ with $n^ ext{CMB}_ ext{T} \simeq 0$ is still compatible. The implication of our results for inflation is also discussed.

Motivation & Objective

• Motivate testing whether inflationary gravitational waves can have a broken power-law spectrum across PTA and CMB bands.
• Quantify the IGW spectrum via a two-regime model connecting PTA and CMB scales.
• Investigate how CMB and PTA data jointly constrain the tensor-to-scalar ratio r and the tilts n_T at different frequency bands.
• Explore inflationary implications of a blue-tilted IGW and possible NEC-violating or multi-stage inflation scenarios.

Proposed method

• Model the IGW tensor power spectrum as a broken power-law: P_T(k)=r A_s (k/k_pivot)^{n_T^CMB} [1+(k/k_break)]^{-n_T^CMB + n_T^PTA}.
• Connect P_T to the present GW energy spectrum Omega_GW(f) using the standard transfer relation including g_* and g_{*,s} factors.
• Perform a joint MCMC analysis using NANOGrav 15-year PTA data and BK18 CMB likelihoods with CLASS for GW evolution and cobaya for sampling.
• Explore two parameterizations: (i) n_T^CMB free with n_T^CMB ≃ - r/8 fixed in a slow-roll-like scenario, (ii) n_T^CMB = - r/8 fixed, to test slow-roll compatibility.

Experimental results

Research questions

• RQ1 What is the preferred broken-power IGW spectrum given both PTA and CMB data?
• RQ2 How do the best-fit tilts differ between PTA (n_T^PTA) and CMB (n_T^CMB) bands under a broken power-law model?
• RQ3 What constraints on the tensor-to-scalar ratio r arise when allowing a broken spectrum versus slow-roll consistency?
• RQ4 Do the joint data favor models with NEC violation or multi-stage inflation that could produce a blue-tilted IGW at PTA scales?

Key findings

• Best-fit PTA tilt n_T^PTA ≈ 2.42^{+0.32}_{-0.91} (best fit ≈ 2.08).
• Best-fit CMB tilt with n_T^CMB free ≈ 0.55^{+0.37}_{-0.10} (best fit ≈ 0.428).
• Rough 95% upper limit for r at pivot 0.05 Mpc^-1 is < 0.107 (r_0.05) and < 0.0338 (r_0.01) for the broken power-law with free n_T^CMB.
• When imposing slow-roll-like n_T^CMB = - r/8, the best-fit PTA tilt remains ≈ 2, and the 95% upper limit on r is ≈ 0.039 (r_0.05).
• The inferred broken scale k_break ≈ 10^{4.19} ~ between CMB and PTA bands; r can be non-negligible at CMB scales while PTA favors a blue tilt.
• Omega_GW(f) best-fit spectrum spans f ∼ 10^-18 to 10^-8 Hz, suggesting joint PTA-CMB-informed inflationary scenarios and potential detectability by LiteBIRD/SKA/LISA/Taiji in broader bands.