Constraints of relic gravitational waves by Pulsar Timing Array: Forecasts for the FAST and SKA projects

Abstract: Measurement of the pulsar timing residuals provides a direct way to detect relic gravitational waves at the frequency $f\sim 1/{\rm yr}$. In this paper, we investigate the constraints on the inflationary parameters, the tensor-to-scalar ratio $r$ and the tensor spectral index $n_t$, by the current and future Pulsar Timing Arrays (PTAs). We find that Five-hundred-meter Aperture Spherical radio Telescope (FAST) in China and the planned Square Kilometer Array (SKA) projects have the fairly strong abilities to test the phantom-like inflationary models. If $r=0.1$, FAST could give the constraint on the spectral index $n_t<0.56$, and SKA gives $n_t<0.32$. While an observation with the total time T=20 yr, the pulsar noise level $\sigma_w=30$ns and the monitored pulsar number $n=200$, could even constrain $n_t<0.07$. These are much tighter than those inferred from the current results of Parkers Pulsar Timing Array (PPTA), European Pulsar Timing Array (EPTA) and North American Nanohertz Observatory for Gravitational waves (NANOGrav). Especially, by studying the effects of various observational factors on the sensitivities of PTAs, we found that compared with $\sigma_w$ and $n$, the total observation time $T$ has the most significant effect.

Overview of Constraints of Relic Gravitational Waves by Pulsar Timing Array

The paper "Constraints of Relic Gravitational Waves by Pulsar Timing Array: Forecasts for the FAST and SKA Projects" addresses the detection of relic (or primordial) gravitational waves (RGWs) using Pulsar Timing Arrays (PTAs). The authors have investigated the constraints on inflationary parameters, specifically the tensor-to-scalar ratio (r) and the tensor spectral index (n_t), by current and future PTA endeavors, including the Five-hundred-meter Aperture Spherical radio Telescope (FAST) and the Square Kilometer Array (SKA).

Key Findings

• Sensitivity of Current PTAs: Pulsar Timing Arrays such as the Parkers Pulsar Timing Array (PPTA), European Pulsar Timing Array (EPTA), and North American Nanohertz Observatory for Gravitational waves (NANOGrav) have provided baseline constraints on RGWs. These constraints, while relatively broad, still offer valuable insights into inflationary models with particularly blue spectra (i.e., (n_t > 0)).

• Projection for FAST and SKA: The paper predicts that both FAST and SKA have significantly enhanced capabilities to constrain the parameters (r) and (n_t). If (r=0.1), FAST could constrain (n_t) to be less than 0.56, and SKA could improve this to 0.32. Moreover, under optimal conditions—20 years of observation, 30 ns pulsar noise level, and monitoring 200 pulsars—(n_t) could be limited to below 0.07, offering a substantially stricter test for phantom-like inflationary models.

• Factors Affecting Sensitivity: The authors emphasize that the observation preparation in PTAs significantly impacts the detecting potential for RGWs. They found that the overall observation time (T) has the greatest impact on enhancing sensitivity compared to the number of monitored pulsars (n) and the pulsar noise level (\sigma_w).

Practical Implications

The constraints delineated by this paper furnish astrophysicists with critical parameters to test early Universe models. Specifically, they could exclude or validate phantom inflationary models, characterized by a blue RGW spectral index. The collaborative potential of future PTA projects like FAST and SKA lies in their scale and technological sophistication, which could offer unparalleled insights into cosmic inflation processes.

Theoretical Impact

The enhanced sensitivity of the FAST and SKA projects is expected to push the boundaries of experimental cosmology, providing more precise data against which theoretical models of inflation can be assessed. Furthermore, understanding the constraints on RGWs also offers a robust testbed for the intersection of general relativity and quantum mechanics at high energy scales.

Future Prospects

The successful detection and analysis of RGWs will illuminate the early Universe's physics, offering hints about the energy scales and dynamics at play. The paper recommends longer observation periods to improve detection capability and advises on prioritizing pulsar noise reduction when feasible.

Continued advancements and increased cooperation between international projects will be crucial in approaching the foreseen sensitivity thresholds that could reveal new astronomical phenomena. Overall, this paper serves as a critical roadmap for the forthcoming endeavors in the field of gravitational wave astronomy and the study of cosmological inflation.