arXiv subjects

Xiao-Han Ma

Publications and source records attributed to Xiao-Han Ma.

13 recordsLinked to original sources

arXiv2026

ASI-Bench: At the Dawn of Artificial Superintelligence

Artificial superintelligence (ASI) requires AI to move beyond mastering existing knowledge toward exploring the unknown, creating new knowledge, and turning new ideas into verifiable results. However, the capabilities of today's AI systems are still largely built on learning, compressing, and applying existing human knowledge. Accordingly, existing benchmarks primarily test whether AI can produce correct answers based on learned knowledge, or whether it can complete tasks under extensive human guidance. We therefore introduce ASI-Bench, the first benchmark to jointly evaluate AI systems' capabilities of innovative exploration and autonomous scientific execution across general research domains, and the first to progressively withdraw human methodological guidance within the same research project to test how far AI can proceed on its own. Built by over 40 experts with the cost of 31,000+ human hours, ASI-Bench contains 60 project-level research tasks across 11 scientific domains and progressively reduces methodological guidance to test whether AI can independently select methods, conduct research, and produce verifiable results. All tasks undergo expert review, AI-assisted auditing, sandbox execution, and scorer validation. Across 18 state-of-the-art agent--model configurations, the average score drops from 50.91 with full methodological guidance to 29.10 with only the method specified and 26.62 when agents must determine the method themselves. This sharp decline shows that current systems remain heavily dependent on human guidance and are still far from autonomously conducting end-to-end, project-level scientific research. ASI-Bench is open to the world. We invite researchers and builders everywhere to contribute new tasks, challenge the limits of today's AI, and help accelerate humanity's collective path toward artificial superintelligence at https://asibench.apexin.ai/submit.

cs.AI↗

arXiv2026

Universal Suppression of Gravitational Waves from Black Hole Evaporation Dynamics

Evaporating black holes can leave distinct imprints on gravitational wave (GW) backgrounds. We show that black hole populations with finite width mass distributions exhibit a universal late time evolution governed by the evaporation dynamics rather than the details of the initial mass distribution, leading to a characteristic power law suppression of the induced GWs. We demonstrate this for a broad class of mass functions in primordial black hole (PBH) scenarios featuring an early Universe matter-dominated era, and identify the suppression of PBH-induced GWs found for critical collapse distributions as a manifestation of this general phenomenon. Our results establish a direct connection between the asymptotic GW spectrum and the underlying law of black hole evaporation.

astro-ph.CO↗

arXiv2025

Primordial Black Hole Formation from the Upward Step Model: Avoiding Overproduction

We investigate the formation of primordial black holes (PBHs) in an upward step inflationary model, where nonlinearities between curvature perturbations and field fluctuations introduce a cutoff, deviating from the Gaussian case. This necessitates a reevaluation of PBH formation, as $\mathcal{R}$ is not the optimal variable for estimating abundance. Using the extended Press-Schechter formalism, we show that non-Gaussianity modifies both the curvature perturbation profile $\mathcal{R}(r)$ and the integration path in probability space, significantly impacting PBH abundance. Our results reveal that the abundance initially increases with the parameter $h$, which characterizes the relaxation stage after the step. However, beyond a critical value ($h \simeq 5.9$), it sharply declines before rising again. Furthermore, we demonstrate that non-Gaussianity introduces uncertainties in indirect PBH observations via gravitational waves. Notably, we present an example where a positive $f_{\rm NL}$ does not necessarily enhance PBH production, contrary to conventional expectations. Finally, by accounting for non-perturbative effects, we resolve the overproduction of PBHs suggested by pulsar timing array (PTA) data, underscoring the critical importance of incorporating non-Gaussianity in future studies.

astro-ph.CO↗

arXiv2025

Ultra-light dark matter with non-canonical kinetics reopening the mass window

Fuzzy dark matter (FDM) with mass around $10^{-22}$ eV is viewed as a promising paradigm in understanding the structure formation of the local universe at small scales. Recent observations, however, begin to challenge FDM in return. We focus on the arguments between the solution to CDM small-scale curiosities and recent observations on matter power spectrum, and find its implication on an earlier formation of small-scale structure. In this article, we propose a scheme of k-ULDM scalar field with a differently-evolving sound speed, thanks to the non-canonical kinetics. With the help of the Dirac-Born-Infeld (DBI) theory, we illustrate to change the behavior of the quantum pressure term countering collapse, therefore change the history of structure growth. We find that it can truly reopen the ULDM mass window closed by the Lyman-$α$ problem. We will discuss such examples in this paper, while more possibilities remain to be explored.

astro-ph.CO↗

arXiv2024

A complete analysis of inflation with piecewise quadratic potential

We conduct a thorough study of the comoving curvature perturbation $\mathcal{R}$ in single-field inflation with two stages, represented by a piecewise quadratic potential, where both the first and second derivatives are allowed to be discontinuous at the transition point. We calculate the evolution of $\mathcal{R}$ by combining the perturbative and non-perturbative methods consistently, and obtain the power spectrum and the non-Gaussian features in the probability distribution function. We find that both the spectrum and the statistics of $\mathcal{R}$ depend significantly on the second derivatives of the potential at both the first and second stages. Furthermore, we find a new parameter constructed from the potential parameters, which we call $α$, plays a decisive role in determining various features in the spectrum such as the amplitude, the slope, and the existence of a dip. In particular, we recover the typical $k^4$ growth of the spectrum in most cases, but the maximum growth rate of $k^5(\log k)^2$ can be obtained by fine-tuning the parameters. Then, using the $δN$ formalism valid on superhorizon scales, we give fully nonlinear formulas for $\cal{R}$ in terms of the scalar field perturbation $δϕ$ and its time derivative. In passing, we point out the importance of the nonlinear evolution of $δϕ$ on superhorizon scales. Finally, using the Press-Schechter formalism for simplicity, we discuss the effect of the non-Gaussian tails of the probability distribution function on the primordial black hole formation.

astro-ph.CO↗

arXiv2024

Gravitational waves from primordial black hole isocurvature: the effect of non-Gaussianities

Ultra-light primordial black holes (PBHs) with masses $M_{\rm PBH}<5\times 10^8\mathrm{g}$ can dominate transiently the energy budget of the Universe and reheat the Universe through their evaporation taking place before Big Bang Nucleosynthesis. The isocurvature energy density fluctuations associated to the inhomogeneous distribution of a population of such PBHs can induce an abundant production of GWs due to second-order gravitational effects. In this work, we discuss the effect of primordial non-Gaussianity on the clustering properties of PBHs and study the effect of a clustered PBH population on the spectral shape of the aforementioned induced GW signal. In particular, focusing on local-type non-Gaussianity we find a double-peaked GW signal with the amplitude of the low-frequency peak being proportional to the square of the non-Gaussian parameter $τ_\mathrm{NL}$. Remarkably, depending on the PBH mass $M_{\rm PBH}$ and the initial abundance of PBHs at formation time, i.e. $Ω_\mathrm{PBH,f}$, this double-peaked GW signal can lie well within the frequency bands of forthcoming GW detectors, namely LISA, ET, SKA and BBO, hence rendering this signal falsifiable by GW experiments and promoting it as a novel portal probing the primordial non-Gaussianity.

astro-ph.CO↗

arXiv2024

New probe of non-Gaussianities with primordial black hole induced gravitational waves

We propose a new probe of primordial non-Gaussianities (NGs) through the observation of gravitational waves (GWs) induced by ultra-light ($M_{\text{PBH}}< 10^{9}\rm{g}$) primordial black holes (PBHs). Interestingly enough, the existence of primordial NG can leave imprints on the clustering properties of PBHs and the spectral shape of induced GW signals. Focusing on a scale-dependent local-type NG, we identify a distinct double-peaked GW energy spectrum that, contingent upon $M_{\text{PBH}}$ and the abundance of PBHs at the time of formation, denoted as $Ω_\mathrm{PBH,f}$, may fall into the frequency bands of upcoming GW observatories, including LISA, ET, SKA, and BBO. Thus, such a signal can serve as a novel portal for probing primordial NGs. Intriguingly, combining BBN bounds on the GW amplitude, we find for the first time the joint limit on the product of the effective non-linearity parameter for the primordial tri-spectrum, denoted by $\barτ_\mathrm{NL}$, and the primordial curvature perturbation power spectrum $\mathcal{P}_{\cal R}(k)$, which reads as $\barτ_\mathrm{NL} \mathcal{P}_{\cal R}(k) < 4\times 10^{-20} Ω^{-17/9}_\mathrm{PBH,f} \left( \frac{M_{\rm PBH}}{10^4\mathrm{g}} \right)^{-17/9}$.

astro-ph.CO↗

arXiv2024

A Compaction Function Analysis of CMB $μ$ distortion Constraints on Primordial Black Holes

Primordial black holes (PBHs) are considered viable candidates for dark matter and the seeds of supermassive black holes (SMBHs), with their fruitful physical influences providing significant insights into the conditions of the early Universe. Cosmic microwave background (CMB) $μ$ distortion tightly constrain the abundance of PBHs in the mass range of $10^4 \sim 10^{11} M_{\odot}$ recently, limiting their potential to serve as seeds for the SMBHs observed. Given that $μ$ distortion directly constrain the primordial power spectrum, it is crucial to employ more precise methods in computing PBH abundance to strengthen the reliability of these constraints. By a Press-Schechter (PS) type method utilizing the compaction function, we find that the abundance of PBHs could be higher than previously estimated constraints from $μ$ distortion observations. Furthermore, our analysis shows that variations in the shape of the power spectrum have a negligible impact on our conclusions within the mass ranges under consideration. This conclusion provides us a perspective for further research on the constrain of PBH by $μ$ distortion.

astro-ph.CO↗

arXiv2024

Primordial black hole mass functions as a probe of cosmic origin

We discuss a novel window to probe the origin of our universe via the mass functions of primordial black holes (PBHs). The mass functions of PBHs are simply estimated using the conventional Press-Schechter formalism for two paradigms of cosmic origin, including inflationary $Λ$CDM and bounce cosmology. The standard inflationary $Λ$CDM model cannot generate an appreciable number of massive PBHs; however, non-trivial inflation models with blue-tilted power spectra at small scales and matter bounce cosmology provide formation mechanisms for heavy PBHs, which in turn, may seed the observed supermassive black holes (SMBHs). By fitting the SMBH mass functions at high redshift ($z \sim 6$) derived from Sloan Digital Sky Survey (SDSS) and Canada-France High-z Quasar Survey (CFHQS) quasars, for two paradigms of cosmic origin, we derive constraints on the PBH density fraction $f_{\mathrm{PBH}}$ at $z \sim 6$ and the characteristic mass $M_{\star}$, with the prior assumption that all SMBHs stem from PBHs. We demonstrate that this newly proposed procedure, relying on astronomical measurements that utilize deep-field surveys of SMBHs at high redshift, can be used to constrain models of cosmic origin. Additionally, although not the main focus of this paper, we evolve the mass function from $z\sim6$ to $z\sim0$ through an assumption of $3\times 10^8$-year Eddington's accretion, and give a rough estimation of $f_{\mathrm{PBH}}$ at $z \sim 0$.

astro-ph.CO↗

arXiv2023

Limits on scalar-induced gravitational waves from the stochastic background by pulsar timing array observations

Recently, the NANOGrav, PPTA, EPTA, and CPTA collaborations independently reported their evidence of the Stochastic Gravitational Waves Background (SGWB). While the inferred gravitational-wave background amplitude and spectrum are consistent with astrophysical expectations for a signal from the population of supermassive black-hole binaries (SMBHBs), the search for new physics remains plausible in this observational window. In this work, we explore the possibility of explaining such a signal by the scalar-induced gravitational waves (IGWs) in the very early universe. We use a parameterized broken power-law function as a general description of the energy spectrum of the SGWB and fit it to the new results of NANOGrav, PPTA and EPTA. We find that this approach can put constraints on the parameters of IGW energy spectrum and further yield restrictions on various inflation models that may produce primordial black holes (PBHs) in the early universe, which is also expected to be examined by the forthcoming space-based GW experiments.

gr-qc↗

arXiv2022

Highly non-Gaussian tails and primordial black holes from single-field inflation

For primordial perturbations, deviations from Gaussian statistics on the tail of the probability distribution can be associated with non-perturbative effects of inflation. In this paper, we present some particular examples in which the tail of the distribution becomes highly non-Gaussian although the statistics remains almost Gaussian in the perturbative regime. We begin with an extension of the ultra-slow-roll inflation that incorporates a transition process, where the inflaton climbs up a tiny potential step at the end of the non-attractor stage before it converges to the slow-roll attractor. Through this example, we identify the key role of the off-attractor behaviour for the upward-step transition, and then extend the analysis to another type of the transition with two slow-roll stages connected by a tiny step. We perform both the perturbative and non-perturbative analyses of primordial fluctuations generated around the step in detail, and show that the tiny but nontrivial transition may affect large perturbations in the tail of the distribution, while the perturbative non-Gaussianity remains small. Our result indicates that the non-Gaussian tails can have rich phenomenology which has been overlooked in conventional analyses. We also study the implications of this non-Gaussian tail for the formation of primordial black holes, and find that their mass fraction can be parametrically amplified by several orders of magnitudes in comparison with the case of the Gaussian distribution. Additionally, we also discuss a mechanism of primordial black holes formation for this upward step inflation model by trapping the inflaton in the bottom of the step.

astro-ph.CO↗

arXiv2022

One Small Step for an Inflaton, One Giant Leap for Inflation: a novel non-Gaussian tail and primordial black holes

We report a novel prediction from single-field inflation that even a tiny step in the inflaton potential can change our perception of primordial non-Gaussianities of the curvature perturbation. Our analysis focuses on the tail of probability distribution generated by an upward step transition between two stages of slow-roll evolution. The nontrivial background dynamics with off-attractor behavior is identified. By using a non-perturbative $δN$ analysis, we explicitly show that a highly non-Gaussian tail can be generated by a tiny upward step, even when the conventional nonlinearity parameters $f_{NL}$, $g_{NL}$, etc. remain small. With this example, we demonstrate for the first time the sensitive dependence of non-perturbative effects on the tail of probability distribution. Our scenario has an inconceivable application to primordial black holes by either significantly boosting their abundance or completely forbidding their appearance.

astro-ph.CO↗

arXiv2020

Dirac-Born-Infeld realization of sound speed resonance mechanism for primordial black holes

We present a concrete realization of the sound speed resonance (SSR) mechanism for primordial black hole (PBH) formation within a specific model of Dirac-Born-Infeld (DBI) inflation. We perform a perturbative approach to phenomenologically construct such a viable DBI inflation model that involves the nonoscillating stage and the oscillating stage, with a type of specific forms of the warp factor and the potential. We show that the continuous but nonsmooth conjunction of sound speed between two stages does not yield manifest effects on the phenomenology of SSR, and thus, our model gives rise to the same PBH mass spectrum as the original predictions of SSR. Additionally, we also demonstrate that the violation of adiabaticity of the Mukhanov-Sasaki equation does not affect the comoving curvature perturbation after Hubble crossing in the nonresonant region. Making use of observational data, we derive various cosmological constraints on the parameter space. Our analyses show that the predicted tensor-to-scalar ratio is typically small, while the amplitude of primordial non-Gaussianity can meet with cosmic microwave background bounds, and additionally, the consistency relation for single-field slow-roll inflation is softly violated in our case due to the small sound speed variations.

astro-ph.CO↗