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Register a new userImplications of the NANOGrav results for inflation
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Sunny Vagnozzi
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The NANOGrav pulsar timing array experiment reported evidence for a stochastic common-spectrum process affecting pulsar timing residuals in its 12.5-year dataset, which might be interpreted as the first detection of a stochastic gravitational wave background (SGWB). I examine whether the NANOGrav signal might be explained by an inflationary SGWB, focusing on the implications for the tensor spectral index $n_T$ and the tensor-to-scalar ratio $r$. Explaining NANOGrav while complying with upper limits on $r$ from BICEP2/Keck Array and Planck requires $r gtrsim {cal O}(10^{-6})$ in conjunction with an extremely blue tensor spectrum, $0.7 lesssim n_T lesssim 1.3$. After discussing models which can realize such a blue spectrum, I show that this region of parameter space can be brought in agreement with Big Bang Nucleosynthesis constraints for a sufficiently low reheating scale, $T_{rm rh} lesssim 100,{rm GeV}-1,{rm TeV}$. With the important caveat of having assumed a power-law parametrization for the primordial tensor spectrum, an inflationary interpretation of the NANOGrav signal is therefore not excluded.
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As suggested by the swampland conjectures, de Sitter (dS) space might be highly unstable if it exists at all. During inflation, the short-lived dS states will decay through a cascade of the first-order phase transition (PT). We find that the gravitational waves (GWs) yielded by such a PT will be reddened by subsequent dS expansion, which may result in a slightly red-tilt stochastic GWs background at low-frequency band, compatible with the NANOGrav 12.5-yr result.
We discuss the possibility of explaining the recent NANOGrav results by inflationary gravitational waves (IGWs) with a blue-tilted primordial spectrum. Although such IGWs can account for the NANOGrav signal without contradicting the upper bound on the tensor-to-scalar ratio at the cosmic microwave background scale, the predicted spectrum is in strong tension with the upper bound on the amplitude of the stochastic gravitational wave background by big-bang nucleosynthesis (BBN) and the second LIGO-Virgo observation run. However, the thermal history of the Universe, such as reheating and late-time entropy production, affects the spectral shape of IGWs at high frequencies and permits evading the upper bounds. We show that, for the standard reheating scenario, when the reheating temperature is relatively low, a blue tensor spectrum can explain the recent NANOGrav signal without contradicting the BBN and the LIGO-Virgo constraints. We further find that, when one considers a late-time entropy production, the NANOGrav signal can be explained even for an instant reheating scenario.
We compare the spectrum of the stochastic gravitational wave background produced in several models of cosmic strings with the common-spectrum process recently reported by NANOGrav. We discuss theoretical uncertainties in computing such a background, and show that despite such uncertainties, cosmic strings remain a good explanation for the potential signal, but the consequences for cosmic string parameters depend on the model. Superstrings could also explain the signal, but only in a restricted parameter space where their network behavior is effectively identical to that of ordinary cosmic strings.
The North American Nanohertz Observatory for Gravitational Waves (NANOGrav) has recently reported strong evidence for a stochastic common-spectrum process affecting the pulsar timing residuals in its 12.5-year data set. We demonstrate that this process admits an interpretation in terms of a stochastic gravitational-wave background emitted by a cosmic-string network in the early Universe. We study stable Nambu-Goto strings in dependence of their tension $Gmu$ and loop size $alpha$ and show that the entire viable parameter space will be probed by an array of future experiments.
We argue that primordial gravitational waves have a spectral break and its information is quite useful for exploring the early universe. Indeed, such a spectral break can be a fingerprint of the end of inflation, and the amplitude and the frequency at the break can tell us the energy scale of inflation and the reheating temperature simultaneously. In order to investigate the spectral break, we give an analytic formula for evolution of the Hubble parameter around the end of inflation where the slow roll approximation breaks down. We also evaluate the spectrum of primordial gravitational waves around the break point semi-analytically using the analytic formula for the inflation dynamics.
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