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Register a new userAnalytic formula for the dynamics around inflation end and implications on primordial gravitational waves
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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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Recent observational constraints indicate that primordial black holes (PBHs) with the mass scale $sim 10^{-12}M_{odot}$ can explain most of dark matter in the Universe. To produce this kind of PBHs, we need an enhance in the primordial scalar curvature perturbations to the order of ${mathcal{O}(10^{-2})}$ at the scale $ k sim 10^{12}~rm Mpc^{-1}$. Here, we investigate the production of PBHs and induced gravitational waves (GWs) in the framework of textbf{$k$-inflation}. We solve numerically the Mukhanov-Sasaki equation to obtain the primordial scalar power spectrum. In addition, we estimate the PBHs abundance $f_{text{PBH}}^{text{peak}}$ as well as the energy density parameter $Omega_{rm GW,0}$ of induced GWs. Interestingly enough is that for a special set of model parameters, we estimate the mass scale and the abundance of PBHs as $sim{cal O}(10^{-13})M_{odot}$ and $f_{text{PBH}}^{text{peak}}=0.96$, respectively. This confirms that the mechanism of PBHs production in our inflationary model can justify most of dark matter. Furthermore, we evaluate the GWs energy density parameter and conclude that it behaves like a power-law function $Omega_{rm GW}sim (f/f_c)^n$ where in the infrared limit $fll f_{c}$, the power index reads $n=3-2/ln(f_c/f)$.
We study the effects of the Gauss-Bonnet term on the energy spectrum of inflationary gravitational waves. The models of inflation are classified into two types based on their predictions for the tensor power spectrum: red-tilted ($n_T<0$) and blue-tilted spectra ($n_T>0$), respectively, and then the energy spectra of the gravitational waves are calculated for each type of model. We find that the gravitational wave spectra are enhanced depending on the model parameter if the predicted inflationary tensor spectra have a blue tilt, whereas they are suppressed for the spectra that have a red tilt. Moreover, we perform the analyses on the reheating parameters involving the temperature, the equation-of-state parameter, and the number of $e$-folds using the gravitational wave spectrum. Our results imply that the Gauss-Bonnet term plays an important role not only during inflation but also during reheating whether the process is instantaneous or lasts for a certain number of $e$-folds until it thermalizes and eventually completes.
The recent observations from CMB have imposed a very stringent upper-limit on the tensor/scalar ratio $r$ of inflation models, $r < 0.064$, which indicates that the primordial gravitational waves (PGW), even though possible to be detected, should have a power spectrum of a tiny amplitude. However, current experiments on PGW is ambitious to detect such a signal by improving the accuracy to an even higher level. Whatever their results are, it will give us much information about the early Universe, not only from the astrophysical side but also from the theoretical side, such as model building for the early Universe. In this paper, we are interested in analyzing what kind of inflation models can be favored by future observations, starting with a kind of general action offered by the effective field theory (EFT) approach. We show a general form of $r$ that can be reduced to various models, and more importantly, we show how the accuracy of future observations can put constraints on model parameters by plotting the contours in their parameter spaces.
The next generation of space-borne gravitational wave detectors may detect gravitational waves from extreme mass-ratio inspirals with primordial black holes. To produce primordial black holes which contribute a non-negligible abundance of dark matter and are consistent with the observations, a large enhancement in the primordial curvature power spectrum is needed. For a single field slow-roll inflation, the enhancement requires a very flat potential for the inflaton, and this will increase the number of $e$-folds. To avoid the problem, an ultra-slow-roll inflation at the near inflection point is required. We elaborate the conditions to successfully produce primordial black hole dark matter from single field inflation and propose a toy model with polynomial potential to realize the big enhancement of the curvature power spectrum at small scales while maintaining the consistency with the observations at large scales. The power spectrum for the second order gravitational waves generated by the large density perturbations at small scales is consistent with the current pulsar timing array observations.
We present a new realization of the resonant production of primordial black holes as well as gravitational waves in a two-stage inflation model consisting of a scalar field phi with an axion-monodromy-like periodic structure in the potential that governs the first stage and another field chi with a hilltop-like potential that dominates the second stage. The parametric resonance seeded by the periodic structure at the first stage amplifies the perturbations of both fields inside the Hubble radius. While the evolution of the background trajectory experiences a turn as the oscillatory barrier height increases, the amplified perturbations of chi remain as they are and contribute to the final curvature perturbation. It turns out that the primordial power spectrum displays a significant resonant peak on small scales, which can lead to an abundant production of primordial black holes. Furthermore, gravitational waves are also generated from the resonantly enhanced field perturbations during inflation, the amplitude of which may be constrained by future gravitational wave interferometers.
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