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Shi Pi

Publications and source records attributed to Shi Pi.

At least 37 records · Page 2Linked to original sources
arXiv2024

Revisiting the Ultraviolet Tail of the Primordial Gravitational Wave

High-frequency primordial gravitational waves (PGWs) with wave numbers larger than the Hubble parameter at the end of inflation are originated from the ultraviolet (UV) modes, which are never stretched out of the horizon. Such a UV tail of the PGW energy spectrum has a spurious logarithmic divergence. We study the origin of such a divergence, and find that it comes from the instantaneous inflation-to-post-inflation transition, which can be removed by considering a finite duration. For the first time, we obtain a semi-analytical expression for the PGW energy spectrum. We find that the UV tail decays exponentially, while the decay rate depends solely on the transition rate. When there is a stiff post-inflationary stage, the enhanced PGW displays a characteristic spectral shape of power-law increasing and exponential decaying. We propose a fitting formula which can be used for signal searching.

astro-ph.CO↗
arXiv2024

Induced Gravitational Wave interpretation of PTA data: a complete study for general equation of state

We thoroughly study the induced gravitational wave interpretation of the possible gravitational wave background reported by PTA collaborations, considering the unknown equation of state $w$ of the early universe. We perform a Bayesian analysis of the NANOGrav data using the publicly available \textsc{PTArcade} code together with \textsc{SIGWfast} for the numerical integration of the induced gravitational wave spectrum. We focus on two cases: a monochromatic and a log-normal primordial spectrum of fluctuations. For the log-normal spectrum, we show that, while the results are not very sensitive to $w$ when the GW peak is close to the PTA window, radiation domination is out of the $2σ$ contours when only the infra-red power-law tail contributes. For the monochromatic spectrum, the $2σ$ bounds yield $0.1\lesssim w\lesssim0.9$ so that radiation domination is close to the central value. We also investigate the primordial black hole (PBH) counterpart using the peak formalism. We show that, in general terms, a larger width and stiffer equation of state alleviates the overproduction of PBHs. No PBH overproduction requires $w\gtrsim0.42$ up to 2-$σ$ level for the monochromatic spectrum. Furthermore, including bounds from the cosmic microwave background, we find in general that the mass range of the PBH counterpart is bounded by $10^{-5} M_\odot\lesssim M_{\rm PBH}\lesssim10^{-1} M_\odot$. Lastly, we find that the PTA signal can explain the microlensing events reported by OGLE for $0.42\lesssim w\lesssim 0.50$. Our work showcases a complete treatment of induced gravitational waves and primordial black holes for general $w$ for future data analysis.

astro-ph.CO↗
arXiv2023

Primordial Black Hole Formation in Non-Minimal Curvaton Scenario

In the curvaton scenario, the curvature perturbation is generated after inflation at the curvaton decay, which may have a prominent non-Gaussian effect. For a model with a non-trivial kinetic term, an enhanced curvature perturbation on a small scale can be realized, which can lead to copious production of primordial black holes (PBHs) and induce secondary gravitational waves (GWs). Using the probability distribution function (PDF) which takes full nonlinear effects into account, we calculate the PBH formation. We find that under the assumption that thus formed PBHs would not overclose the universe, the non-Gaussianity of the curvature perturbation can be well approximated by the local quadratic form, which can be used to calculate the induced GWs. In this model the limit of large non-Gaussianity can be reached when the curvaton energy fraction $r$ is small at the moment of curvaton decay. We also show that in the $r\to1$ limit the PDF is similar to that of ultraslow-roll inflation.

astro-ph.CO↗
arXiv2023

NANOGrav Hints on Planet-Mass Primordial Black Holes

Recently, the North American Nanohertz Observatory for Gravitational Waves (NANOGrav) claimed the detection of a stochastic common-spectrum process of the pulsar timing array (PTA) time residuals from their 12.5 year data, which might be the first detection of the stochastic background of gravitational waves (GWs). We show that the amplitude and the power index of such waves imply that they could be the secondary GWs induced by the peaked curvature perturbation with a dust-like post inflationary era with $-0.091\lesssim w\lesssim0.048$. Such stochastic background of GWs naturally predicts substantial existence of planet-mass primordial black holes (PBHs), which can be the lensing objects for the ultrashort-timescale microlensing events observed by the Optical Gravitational Lensing Experiment (OGLE).

astro-ph.CO↗
arXiv2023

Logarithmic Duality of the Curvature Perturbation

We study the comoving curvature perturbation $\mathcal{R}$ in the single-field inflation models whose potential can be approximated by a piecewise quadratic potential $V(φ)$ by using the $δN$ formalism. We find a general formula for $\mathcal{R}(δφ, δπ)$, consisting of a sum of logarithmic functions of the field perturbation $δφ$ and the velocity perturbation $δπ$ at the point of interest, as well as of $δπ_*$ at the boundaries of each quadratic piece, which are functions of ($δφ, δπ$) through the equation of motion. Each logarithmic expression has an equivalent dual expression, due to the second-order nature of the equation of motion for $φ$. We also clarify the condition under which $\mathcal{R}(δφ, δπ)$ reduces to a single logarithm, which yields either the renowned ``exponential tail'' of the probability distribution function of $\mathcal{R}$ or a Gumbel-distribution-like tail.

astro-ph.CO↗
arXiv2023

Primordial Black Hole Formation in Starobinsky's Linear Potential Model

We study the power spectrum of the comoving curvature perturbation $\cal R$ in the model that glues two linear potentials of different slopes, originally proposed by Starobinsky. We find that the enhanced power spectrum reaches its maximum at the wavenumber which is $π$ times the junction scale. The peak is $\sim2.61$ times larger than the ultraviolet plateau. We also show that its near-peak behavior can be well approximated by a constant-roll model, once we define the effective ultra-slow-roll $e$-folding number appropriately by considering the contribution from non-single-clock phase only. Such an abrupt transition to non-attractor phase can leave some interesting characteristic features in the energy spectrum of the scalar-induced gravitational waves, which are detectable in the space-borne interferometers if the primordial black holes generated at such a high peak are all the dark matter.

astro-ph.CO↗
arXiv2021

The Gravitational-Wave Physics II: Progress

It has been a half-decade since the first direct detection of gravitational waves, which signifies the coming of the era of the gravitational-wave astronomy and gravitational-wave cosmology. The increasing number of the detected gravitational-wave events has revealed the promising capability of constraining various aspects of cosmology, astronomy, and gravity. Due to the limited space in this review article, we will briefly summarize the recent progress over the past five years, but with a special focus on some of our own work for the Key Project ``Physics associated with the gravitational waves'' supported by the National Natural Science Foundation of China. In particular, (1) we have presented the mechanism of the gravitational-wave production during some physical processes of the early Universe, such as inflation, preheating and phase transition, and the cosmological implications of gravitational-wave measurements; (2) we have put constraints on the neutron star maximum mass according to GW170817 observations; (3) we have developed a numerical relativity algorithm based on the finite element method and a waveform model for the binary black hole coalescence along an eccentric orbit.

gr-qc↗
arXiv2021

Measuring the gravitomagnetic distortion from rotating halos I: methods

Source galaxy images are distorted not only by a static gravitational potential, but also by frame-dragging induced by massive rotating objects like clusters of galaxies. Such effect is well understood theoretically, it is therefore of great interest to estimate its detectability for future surveys. In this work, we analyze the lensing convergence $κ$ around rotating dark matter halos. The rotation of the massive objects generates a gravitomagnetic potential giving rise to an anisotropic contribution to the lensing potential. We construct an estimator $δκ$ to describe the difference between the symmetric enhancement and reduction of $κ$ around the halo rotation axis, finding that it is well approximated by a function proportional to the halo velocity dispersion squared times a dimensionless angular momentum parameter. Using simulation mocks with realistic noise level for a survey like LSST, we test our estimator, and show that the signal from frame-dragging of stacked rotating lenses is consistent with zero within $1σ$. However, we find that the most massive cluster in SDSS DR7 spectroscopic selected group catalog has a line-of-sight rotation velocity of 195.0km/s and velocity dispersion of 667.8km/s, which is at $1.2\times 10^{-8}$ odds according to the angular momentum probability distribution inferred from N-body simulations. By studying SDSS DR7 spectroscopic selected group catalog, we show how rotating clusters can be identified, and, finding that fast rotating clusters might be more abundant than in estimates based on simulations, a detection of gravitomagnetic distortion may be at reach in future surveys

astro-ph.CO↗
arXiv2020

Primordial black holes and gravitational waves from resonant amplification during inflation

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 ϕwith an axion-monodromy-like periodic structure in the potential that governs the first stage and another field χwith 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 χremain 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.

astro-ph.CO↗
arXiv2020

Universal infrared scaling of gravitational wave background spectra

We study the general infrared behavior of the power spectrum of a stochastic gravitational wave background produced by stress tensor in the form bilinear in certain dynamical degrees of freedom. We find $Ω_{\text{GW}}\propto k^3$ for a very wide class of the sources which satisfy a set of reasonable conditions. Namely, the $k^3$ scaling is universally valid when the source term is bounded in both frequency and time, is effective in a radiation-dominated stage, and for $k$ smaller than all the physical scales associated with the source, like the peak frequency, peak width, and time duration, etc. We also discuss possible violations of these conditions and their physical implications.

astro-ph.CO↗
arXiv2020

Gravitational Waves Induced by Scalar Perturbations with a Lognormal Peak

We study the stochastic gravitational wave (GW) background induced by the primordial scalar perturbation with the spectrum having a lognormal peak of width $Δ$ at $k=k_*$. We derive an analytical formula for the GW spectrum $Ω_\text{GW}$ for both narrow ($Δ\ll1$) and broad ($Δ\gtrsim1$) peaks. In the narrow-peak case, the spectrum has a double peak feature with the sharper peak at $k= 2k_*/\sqrt{3}$. On the infrared (IR) side of the spectrum, we find power-law behavior with a break at $k=k_b$ in the power-law index where it chages from $k^3$ on the far IR side to $k^2$ on the near IR side. We find the ratio of the break frequency to the peak frequency is determined by $Δ$ as $f_b/f_p\approx\sqrt{3}Δ$, where $f_b$ and $f_p$ are the break and peak frequencies, respectively. In the broad-peak case, we find the GW spectrum also has a lognormal peak at $k=k_*$ but with a smaller width of $Δ/\sqrt2$. Using these derived analytic formulae, we also present expressions for the maximum values of $Ω_\text{GW}$ for both narrow and broad cases. Our results will provide a useful tool in searching for the induced GW signals in the coming decades.

gr-qc↗
arXiv2020

Induced gravitational waves as a probe of thermal history of the universe

The scalar perturbation induced gravitational waves are a probe of the primordial density perturbation spectrum on small scales. In this paper, we show that they can also probe the thermal history of the universe. We assume the universe underwent a stage with a constant equation of state parameter $w$, followed by the radiation-dominated stage of the conventional big bang universe. We find that the infrared slope of the power spectrum of the induced stochastic gravitational wave background for decelerating cosmologies is related to the equation of state of the universe. Furthermore, the induced gravitational wave spectrum has in general a broken power-law shape around the scale of reheating. Interestingly, below the threshold $w=0$ of the equation of state parameter, the broken power-law presents a peak for a Dirac delta peak in the scalar spectrum. For a finite width peak, the threshold changes to $w=-1/15$ depending on the value of the width. In some cases, such a broken power-law gravitational wave spectrum may degenerate to the spectrum from other sources like phase transitions or global cosmic strings.

gr-qc↗
arXiv2020

Universal Upper Bound on the Inflationary Energy Scale from the Trans-Planckian Censorship Conjecture

We study the constraint on the inflationary energy scale from the recently proposed Trans-Planckian Censorship Conjecture (TCC). We find a universal upper bound on the inflationary Hubble expansion rate $H_\text{inf}$ which is solely determined by the reheating temperature $T_\text{rh}$: $H_\text{inf}/M_\text{Pl}\lesssim T_0/T_\text{rh}$, where $T_0$ is the photon temperature today. The upper limit can be saturated by a post-inflationary oscillatory stage with the critical equation-of-state parameter $w\approx-1/3$, or by an inflation model with multiple stages. In the lowest reheating temperature required for big bang nucleosynthesis, the upper bound on the tensor-to-scalar ratio $r$ at the CMB scales is $r\lesssim10^{-8}$, which can be realized in many string-inspired inflation models.

astro-ph.CO↗
arXiv2019

Hyperbolic field space and swampland conjecture for DBI scalar

We study a model of two scalar fields with a hyperbolic field space and show that it reduces to a single-field Dirac-Born-Infeld (DBI) model in the limit where the field space becomes infinitely curved. We apply the de Sitter swampland conjecture to the two-field model and take the same limit. It is shown that in the limit, all quantities appearing in the swampland conjecture remain well-defined within the single-field DBI model. Based on a consistency argument, we then speculate that the condition derived in this way can be considered as the de Sitter swampland conjecture for a DBI scalar field by its own. The condition differs from those proposed in the literature and only the one in the present paper passes the consistency argument. As a byproduct, we also point out that one of the inequalities in the swampland conjecture for a multi-field model with linear kinetic terms should involve the lowest mass squared for scalar perturbations and that this quantity can be significantly different from the lowest eigenvalue of the Hessian of the potential in the local orthonormal frame if the field space is highly curved. Finally, we propose an extension of the de Sitter swampland conjecture to a more general scalar field with the Lagrangian of the form $P(X,φ)$, where $X=-(\partialφ)^2/2$.

hep-th↗
arXiv2019

Pulsar Timing Array Constraints on the Induced Gravitational Waves

If the black holes detected by LIGO/VIRGO are primordial black holes (PBHs) sourcing from a large primordial curvature perturbation on small scales, the corresponding induced gravitational waves (GWs) would peak at nanohertz that is detectable by the current and future observations of pulsar timing array (PTA). In this paper we show that with the mass function estimated from the merger rate of LIGO O1 and O2 events, the induced GWs from such a curvature perturbation with a Gaussian narrow peak at some small scale would be in a seemingly mild tension with current constraints from PTA. However, if the curvature perturbation is of local-type non-Gaussianity with a non-linear parameter $f_\text{NL}\gtrsim\mathcal{O}(10)$, the tension could be relieved. Nevertheless, such an induced GWs must be detectable by the Square Kilometer Array in a decade or less.

astro-ph.CO↗
arXiv2019

Primordial Tensor Perturbation in Double Inflationary Scenario with a Break

We study the primordial tensor perturbation produced from the double inflationary scenario with an intermediate break stage. Because of the transitions, the power spectrum deviates from the vacuum one and there will appear oscillatory behavior. In the case of a scalar-type curvature perturbation, it is known that the amplitude of these oscillations may be enhanced to result in the power spectrum larger than the one for the vacuum case. One might expect the similar enhancement for the tensor perturbation as well. Unfortunately, it is found that when the equation of state (EOS) parameter $w=p/ρ$ of the break stage is a constant with $w>-1/3$, the amplitude of oscillations is never large enough to enhance the power spectrum. On the contrary, the power spectrum is found to be suppressed even on those scales that leave the horizon at the first inflationary stage and remain superhorizon throughout the entire stage. We identify the cause of this suppression with the correction terms in additional to the leading order constant solution on superhorizon scales. We argue that our result is general in the sense that any intermediate break stage during inflation cannot yield an enhancement of the tensor spectrum as long as the Hubble expansion rate is non-increasing in time.

gr-qc↗
arXiv2019

Gravitational Waves Induced by non-Gaussian Scalar Perturbations

We study gravitational waves (GWs) induced by non-Gaussian curvature perturbations. We calculate the density parameter per logarithmic frequency interval, $Ω_\text{GW}(k)$, given that the power spectrum of the curvature perturbation $\mathcal{P}_\mathcal{R}(k)$ has a narrow peak at some small scale $k_*$, with a local-type non-Gaussianity, and constrain the nonlinear parameter $f_\text{NL}$ with the future LISA sensitivity curve as well as with constraints from the abundance of the primordial black holes (PBHs). We find that the non-Gaussian contribution to $Ω_\text{GW}$ increases as $k^3$, peaks at $k/k_*=4/\sqrt{3}$, and has a sharp cutoff at $k=4k_*$. The non-Gaussian part can exceed the Gaussian part if $\mathcal{P}_\mathcal{R}(k)f_\text{NL}^2\gtrsim1$. If both a slope $Ω_\text{GW}(k)\propto k^β$ with $β\sim3$ and the multiple-peak structure around a cutoff are observed, it can be recognized as a smoking gun of the primordial non-Gaussianity. We also find that if PBHs with masses of $10^{20}\text{g}$ to $10^{22}\text{g}$ are identified as cold dark matter of the Universe, the corresponding GWs must be detectable by LISA-like detectors, irrespective of the value of $\mathcal{P}_\mathcal{R}$ or $f_\text{NL}$.

astro-ph.CO↗
arXiv2019

Resonant multiple peaks in the induced gravitational waves

We identify analytically a multiple-peak structure in the energy-density spectrum of induced gravitational waves (GWs) generated at second-order from a primordial scalar perturbations also with multiple($n$) peaks at small scales $k_{*i}$. The energy-density spectrum of induced GWs exhibits at most $C_{n+1}^2$ and at least $n$ peaks at wave-vectors $k_{ij}\equiv(k_{*i}+k_{*j})/\sqrt{3}$ due to resonant amplification, and, under the narrow-width approximation, it contains an universal factor that can be interpreted as a result of momentum conservation. We also extend these discussions to the case of non-Gaussian perturbations.

astro-ph.CO↗