arXiv subjects

Zhu Yi

Publications and source records attributed to Zhu Yi.

At least 37 records · Page 2Linked to original sources

arXiv2023

Primordial black holes and scalar-induced gravitational waves from the generalized Brans-Dicke theory

The power spectrum of the scalar-tensor inflation with a quadratic form Ricci scalar coupling function $Ω(ϕ)=1- 2ϕ/ϕ_c+(1+δ^2)(ϕ/ϕ_c)^2$ can be enhanced enough to produce primordial black holes and generate scalar-induced gravitational waves. The masses of primordial black holes and the frequencies of scalar-induced gravitational waves are controlled by the parameter $ϕ_c$, and their amplitudes are determined by the parameter $δ$. Primordial black holes with stellar masses, planetary masses, and masses around $10^{-12} M_\odot$ are produced and their abundances are obtained from the peak theory. The frequencies of the corresponding scalar-induced gravitational waves are around $10^{-9}$ Hz, $10^{-6}$ Hz, and $10^{-3}$ Hz, respectively. The primordial black holes with masses around $10^{-12} M_\odot$ can account for almost all of the dark matter, and the scalar-induced gravitational waves with frequencies around $10^{-9}$ Hz can explain the NANOGrav 12.5yrs signal.

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arXiv2023

Constraints on primordial curvature spectrum from primordial black holes and scalar-induced gravitational waves

The observational data of primordial black holes and scalar-induced gravitational waves can constrain the primordial curvature perturbation at small scales. We parameterize the primordial curvature perturbation by a broken power law form and find that it is consistent with many inflation models that can produce primordial black holes, such as nonminimal derivative coupling inflation, scalar-tensor inflation, Gauss-Bonnet inflation, and K/G inflation. The constraints from primordial black holes on the primordial curvature power spectrum with the broken power law form are obtained, where the fraction of primordial black holes in dark matter is calculated by the peak theory. Both the real-space top-hat and the Gauss window functions are considered. The constraints on the amplitude of primordial curvature perturbation with Gauss window function are around three times larger than those with real-space top-hat window function. The constraints on the primordial curvature perturbation from the NANOGrav 12.5yrs data sets are displayed, where the NANOGrav signals are assumed as the scalar-induced gravitational waves, and only the first five frequency bins are used.

astro-ph.CO↗

arXiv2022

NANOGrav signal and LIGO-Virgo Primordial Black Holes from the Higgs field

We show that the NANOGrav signal can come from the Higgs field with a noncanonical kinetic term in terms of the scalar induced gravitational waves. The scalar induced gravitational waves generated in our model are also detectable by space-based gravitational wave observatories. Primordial black holes with stellar masses that can explain LIGO-Virgo events are also produced. Therefore, the NANOGrav signal and the BHs in LIGO-Virgo events may both originate from the Higgs field.

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arXiv2022

Primordial black holes and secondary gravitational waves from natural inflation

The production of primordial black hole (PBH) dark matter (DM) and the generation of scalar induced secondary gravitational waves by using the enhancement mechanism with a peak function in the non-canonical kinetic term in natural inflation is discussed. We show explicitly that the power spectrum for the primordial curvature perturbation can be enhanced at $10^{12}$ Mpc$^{-1}$, $10^{8}$ Mpc$^{-1}$ and $10^{5}$ Mpc$^{-1}$ by adjusting the model parameters. With the enhanced primordial curvature perturbations, we show the production of PBH DM with peak masses around $10^{-13}\ M_{\odot}$, the Earth's mass and the stellar mass, and the generation of scalar induced gravitational waves (SIGWs) with peak frequencies around mHz, $10^{-6}$ Hz and nHz, respectively. The PBHs with the mass scale $10^{-13}\ M_{\odot}$ can make up almost all the DM and the associated SIGWs is testable by spaced based gravitational wave observatory.

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arXiv2021

Inflationary attractors from a non-canonical kinetic term

We show explicitly how the T-model, E-model, and Hilltop inflations are obtained from the inflation models with a non-canonical kinetic term and an arbitrary potential. By this method, any attractor of observables $n_s$ and $r$ is possible. The presence of attractors poses a challenge to differentiate inflation models.

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arXiv2021

Primordial Non-Gaussianity from G-inflation

Enormous information about interactions is contained in the non-Gaussianities of the primordial curvature perturbations, which are essential to break the degeneracy of inflationary models. We study the primordial bispectra for G-inflation models predicting both sharp and broad peaks in the primordial scalar power spectrum. We calculate the non-Gaussianity parameter $f_{\mathrm{NL}}$ in the equilateral limit and squeezed limit numerically, and confirm that the consistency relation holds in these models. Even though $f_{\mathrm{NL}}$ becomes large at the scales before the power spectrum reaches the peak and the scales where there are wiggles in the power spectrum, it remains to be small at the peak scales. Therefore, the contributions of non-Gaussianity to the scalar induced secondary gravitational waves and primordial black hole abundance are expected to be negligible.

astro-ph.CO↗

arXiv2021

Primordial black holes and secondary gravitational waves from inflationary model with a non-canonical kinetic term

With the enhancement mechanism provided by a noncanonical kinetic term with a peak, the amplitude of primordial curvature perturbations can be enhanced by seven orders of magnitude at small scales while keeping to be consistent with observations at large scales. The peak function and inflationary potential are not restricted in this mechanism. We use the Higgs model and T-model as examples to show how abundant primordial black hole dark matter with different mass and scalar induced secondary gravitational waves with different peak frequency are generated. We also show that the enhanced power spectrum for the primordial curvature perturbations and the energy density of the scalar induced secondary gravitational waves can have either a sharp peak or a broad peak. The primordial black holes with the mass around $10^{-14}-10^{-12} M_{\odot}$ produced with the enhancement mechanism can make up almost all dark matter, and the scalar induced secondary gravitational waves accompanied with the production of primordial black holes can be tested by the pulsar timing arrays and spaced based gravitational wave observatory. Therefore, the mechanism can be tested by primordial black hole dark matter and gravitational wave observations.

astro-ph.CO↗

arXiv2021

Primordial black holes and secondary gravitational waves from the Higgs field

We devise a novel mechanism and for the first time demonstrate that the Higgs model in particle physics can drive the inflation to satisfy the cosmic microwave background observations and simultaneously enhance the curvature perturbations at small scales to explain the abundance of dark matter in our universe in the form of primordial black holes. The production of primordial black holes is accompanied by the secondary gravitational waves induced by the first order Higgs fluctuations which is expected observable by space-based gravitational wave detectors. We propose possible cosmological probes of Higgs field in the future observations for primordial black holes dark matter or stochastic gravitational waves.

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arXiv2020

The Reconstruction of Non-Minimal Derivative Coupling Inflationary Potentials

We derive the reconstruction formulae for the inflation model with the non-minimal derivative coupling term. If reconstructing the potential from the tensor-to-scalar ratio, we could obtain the potential without using the high friction limit. As an example, we reconstruct the potential from the parametrization $r=8α/(N+β)^γ$, which is a general form of the $α$-attractor. The reconstructed potential has the same asymptotic behavior as the T- and E-model if we choose $γ=2$ and $α\ll1$. We also discuss the constraints from the reheating phase preceding the radiation domination by assuming the parameter $w_{re}$ of state equation during reheating is a constant. The scale of big-bang nucleosynthesis could put a up limit on $n_s$ if $w_{re}=2/3$ and a low limit on $n_s$ if $w_{re}=1/6$.

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arXiv2019

Constraints on primordial curvature perturbations from primordial black hole dark matter and secondary gravitational waves

Primordial black holes and secondary gravitational waves can be used to probe the small scale physics at very early time. For secondary gravitational waves produced after the horizon reentry, we derive an analytical formula for the time integral of the source and analytical behavior of the time dependence of the energy density of induced gravitational waves is obtained. By proposing a piecewise power law parametrization for the power spectrum of primordial curvature perturbations, we use the observational constraints on primordial black hole dark matter to obtain an upper bound on the power spectrum, and discuss the test of the model with future space based gravitational wave antenna.

gr-qc↗

arXiv2019

On the constant-roll inflation with large and small $η_H$

We study the seemingly duality between large and small $η_H$ for the constant-roll inflation with the second slow-roll parameter $η_H$ being a constant. In the previous studies, only the constant-roll inflationary models with small $η_H$ are found to be consistent with the observations. The seemingly duality suggests that the constant-roll inflationary models with large $η_H$ may be also consistent with the observations. We find that the duality between the constant-roll inflation with large and small $η_H$ does not exist because both the background and scalar perturbation evolutions are very different. By fitting the constant-roll inflationary models to the observations, we get $-0.016\leη_H\le-0.0078$ at the 95\% C.L if we take $N=60$ for the models with increasing $ε_H$ in which inflation ends when $ε_H=1$, and $3.0135\le η_H\le 3.021$ at the 68\% C.L., and $3.0115\le η_H\le 3.024$ at the 95\% C.L. for the models with decreasing $ε_H$.

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arXiv2018

Gauss-Bonnet inflation and swampland

The two swampland criteria are generically in tension with the single field slow-roll inflation because the first swampland criterion requires small tensor to scalar ratio while the second swampland criterion requires large tensor to scalar ratio. The challenge to the single field slow-roll inflation imposed by the swampland criteria can be avoided by modifying the relationship between the tensor to scalar ratio and the slow-roll parameter. We show that the Gauss-Bonnet inflation with the coupling function inversely proportional to the potential overcomes the challenge by adding a constant factor in the relationship between the tensor to scalar ratio and the slow-roll parameter. For the Gauss-Bonnet inflation, while the swampland criteria are satisfied, the slow-roll conditions are also fulfilled, so the scalar spectral tilt and the tensor to scalar ratio are consistent with the observations. We use the potentials for chaotic inflation and the E-model as examples to show that the models pass all the constraints. The swampland criteria may imply Gauss-Bonnet coupling.

gr-qc↗

arXiv2018

Inflation with Gauss-Bonnet coupling

We consider inflationary models with the inflaton coupled to the Gauss-Bonnet term assuming a special relation $δ_1=2λε_1$ between the two slow-roll parameters $δ_1$ and $ε_1$. For the slow-roll inflation, the assumed relation leads to the reciprocal relation between the Gauss-Bonnet coupling function $ξ(ϕ)$ and the potential $V(ϕ)$, and it leads to the relation $r=16(1-λ)ε_1$ that reduces the tensor-to-scalar ratio $r$ by a factor of $1-λ$. For the constant-roll inflation, we derive the analytical expressions for the scalar and tensor power spectra, the scalar and tensor spectral tilts, and the tensor-to-scalar ratio to the first order of $ε_1$ by using the method of Bessel function approximation. The tensor-to-scalar ratio is reduced by a factor of $1-λ+λ\tilde η$. Comparing the derived $n_s$-$r$ with the observations, we obtain the constraints on the model parameters $\tildeη$ and $λ$.

gr-qc↗

arXiv2018

Constraints on scalar-tensor theory of gravity by the recent observational results on gravitational waves

The speed of gravitational waves provides us a new tool to test alternative theories of gravity. The constraint on the speed of gravitational waves from GW170817 and GRB170817A is used to test some classes of Horndeski theory. In particular, we consider the coupling of a scalar field to Einstein tensor and the coupling of the Gauss-Bonnet term to a scalar field. The coupling strength of the Gauss-Bonnet coupling is constrained to be in the order of $10^{-15}$. In the Horndeski theory we show that in order for this theory to satisfy the stringent constraint on the speed of GWs the mass scale $M$ introduced in the non-minimally derivative coupling is constrained to be in the range $10^{15}\text{GeV}\gg M \gtrsim 2\times 10^{-35}$GeV taking also under consideration the early times upper bound for the mass scale $M$. The large mass ranges require no fine-tuning because the effect of non-minimally derivative coupling is negligible at late times.

gr-qc↗

arXiv2018

On the constant-roll inflation

The primordial power spectra of scalar and tensor perturbations during slow-roll inflation are usually calculated with the method of Bessel function approximation. For constant-roll or ultra slow-roll inflation, the method of Bessel function approximation may be invalid. We compare the numerical results with the analytical results derived from the Bessel function approximation, and we find that they differ significantly on super-horizon scales if the constant slow-roll parameter $η_H$ is not small. More accurate method is needed for calculating the primordial power spectrum for constant-roll inflation.

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arXiv2017

Inflationary attractors from nonminimal coupling

We show explicitly how the E model attractor is obtained from the general scalar-tensor theory of gravity with arbitrary conformal factors in the strong coupling limit. By using conformal transformations, any attractor with the observables $n_s$ and $r$ can be obtained. The existence of attractors imposes a challenge to distinguish different models.

gr-qc↗

arXiv2017

The reconstruction of tachyon inflationary potentials

We derive a lower bound on the field excursion for the tachyon inflation, which is determined by the amplitude of the scalar perturbation and the number of $e$-folds before the end of inflation. Using the relation between the observables like $n_s$ and $r$ with the slow-roll parameters, we reconstruct three classes of tachyon potentials. The model parameters are determined from the observations before the potentials are reconstructed, and the observations prefer the concave potential. We also discuss the constraints from the reheating phase preceding the radiation domination for the three classes of models by assuming the equation of state parameter $w_{re}$ during reheating is a constant. Depending on the model parameters and the value of $w_{re}$, the constraints on $N_{re}$ and $T_{re}$ are different. As $n_s$ increases, the allowed reheating epoch becomes longer for $w_{re}=-1/3$, 0 and $1/6$ while the allowed reheating epoch becomes shorter for $w_{re}=2/3$.

gr-qc↗

arXiv2016

Nonminimal coupling and inflationary attractors

We show explicitly how the T model, E model, and Hilltop inflations are obtained from the general scalar-tensor theory of gravity with arbitrary conformal factors in the strong coupling limit. We argue that $ξ$ attractors can give any observables $n_s$ and $r$ by this method. The existence of attractors imposes a challenge to distinguish different models.

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