We explore the correlations between correlation functions of the primordial curvature perturbation produced during inflation. We find that for general single field inflation, other than the source terms which depend on the model details, higher order correlation functions are characterized by the power spectrum, its spectral index and running. The correlation between the bispectrum and power spectrum is presented as an explicit example of our systematic approach.
Asteroid-mass primordial black holes (PBH) can explain the observed dark matter abundance while being consistent with the current indirect detection constraints. These PBH can produce gamma-ray signals from Hawking radiation that are within the sensitivity of future measurements by the AMEGO and e-ASTROGAM experiments. PBH which give rise to such observable gamma-ray signals have a cosmic origin from large primordial curvature fluctuations. There must then be a companion, stochastic gravitational wave (GW) background produced by the same curvature fluctuations. We demonstrate that the resultin…
Characterizing the physical properties of the stochastic gravitational waves background (SGWB) is a key step towards identifying the nature of its possible origin. We focus our analysis on SGWB anisotropies. The existence of a non-trivial primordial scalar-tensor-tensor (STT) correlation in the squeezed configuration may be inferred from the effect that a long wavelength scalar mode has on the gravitational wave power spectrum: an anisotropic contribution. Crucially, such contribution is correlated with temperature anisotropies in the cosmic microwave background (CMB). We show that, for inflat…
We explore and corroborate, by working out explicit examples, the effectiveness of cross-correlating stochastic gravitational wave background anisotropies with CMB temperature fluctuations as a way to establish the primordial nature of a given gravitational wave signal. We consider the case of gravitational wave anisotropies induced by scalar-tensor-tensor primordial non-Gaussianity. Our analysis spans anisotropies exhibiting different angular behaviours, including a quadrupolar dependence. We calculate the expected uncertainty on the non-linearity parameter $F_{\rm NL}$ obtained as a result o…
Whether or not the primordial gravitational wave (GW) produced during inflation is sufficiently strong to be observable, GWs are necessarily produced from the primordial curvature perturbations in the second order of perturbation. The induced GWs can be enhanced by curvature perturbations enhanced at small scales or by the presence of matter-dominated stages of the cosmological history. We analytically calculate the integral in the expression of the power spectrum of the induced GWs which is a universal part independent of the spectrum of the primordial curvature perturbations. This makes the …
The properties of primordial curvature perturbations on small scales are still unknown while those on large scales have been well probed by the observations of the cosmic microwave background anisotropies and the large scale structure. In this paper, we propose the reconstruction method of primordial curvature perturbations on small scales through the merger rate of binary primordial black holes, which could form from large primordial curvature perturbation on small scales.
We outline a new explanation for the primordial density perturbations in cosmology. Dimension zero fields are a minimal addition to the Standard Model of particle physics: if the Higgs doublet is emergent, they cancel the vacuum energy and both Weyl anomalies without introducing any new particles. Furthermore, the cancellation explains why there are three generations of elementary particles, including RH neutrinos. We show how quantum zero point fluctuations of dimension zero fields seed nearly scale-invariant, Gaussian, adiabatic density perturbations. We calculate the amplitude of the primor…
As a candidate bound for the Binary Black Hole (BBH) merger events detected by LIGO/Virgo, Primordial Black Holes (PBHs) provide a useful tool to investigate the primordial curvature perturbations on small scales. Using the GWTC-1 to GWTC-3 catalogs, under the scenario that PBHs originate from large primordial curvature perturbations on small scales during inflationary epoch, we for the first time reconstruct the power spectrum of primordial curvature perturbations on small scales. It is found that the value of the amplitude of the primordial power spectrum is enhanced to $\mathcal{O}(10^{-2})…
We study the induced primordial gravitational waves (GW) coming from the effect of scalar perturbation on the tensor perturbation at the second order of cosmological perturbation theory. We use the evolution of the standard model degrees of freedom with respect to temperature in the early Universe to compute the induced gravitational waves bakcground. Our result shows that the spectrum of the induced GW is affected differently by the standard model degrees of freedom than the GW coming from first order tensor perturbation. This phenomenon is due to the presence of scalar perturbations as a sou…
Scaler and tensor perturbations couple nonlinearly with each other in the Einstein-Hilbert action. We show that such interaction naturally leads to the quantum decoherence of the primordial perturbations during inflation at horizon crossing. The dominant interaction Hamiltonian contributing to decoherence is identified and the master equation responsible for the decohering process is derived.
If there exist higher-spin particles during inflation which are light compared to the Hubble rate, they may leave distinct statistical anisotropic imprints on the correlators involving scalar and graviton fluctuations. We characterise such signatures using the dS/CFT$_3$ correspondence and the operator product expansion techniques. In particular, we obtain generic results for the case of partially massless higher-spin states.
There is a growing expectation that the gravitational wave detectors will start probing the stochastic gravitational wave backgrounds in the following years. We explore the spectral shapes of gravitational waves induced to second order by scalar perturbations and presumably have been produced in the early universe. We calculate the gravitational wave spectra generated during radiation and kination eras together with the associated primordial black hole counterpart. We employ power spectra for the primordial curvature perturbation generated by $α$-attractors and nonminimal derivative coupling i…
Compared to primordial perturbations on large scales, roughly larger than $1$ megaparsec, those on smaller scales are not severely constrained. We revisit the issue of probing small-scale primordial perturbations using gravitational waves (GWs), based on the fact that, when large-amplitude primordial perturbations on small scales exist, GWs with relatively large amplitudes are induced at second order in scalar perturbations, and these induced GWs can be probed by both existing and planned gravitational-wave projects. We use accurate methods to calculate these induced GWs and take into account …
We compute the spectral index of primordial perturbations in a rainbow universe. We allow the Newton constant $G$ to run at (super-)Planckian energies and we consider both vacuum and thermal perturbations. If the rainbow metric is the one associated to a generalized Horava-Lifshitz dispersion relation, we find that only when $G$ tends asymptotically to zero can one match the observed value of the spectral index and solve the horizon problem, both for vacuum and thermal perturbations. For vacuum fluctuations the observational constraints imply that the primordial universe expansion can be both …
We show that an axionlike field coupled to a new confining gauge group can generate the primordial density perturbation in the post-inflation universe. The axion decay constant and strong coupling scale are uniquely determined by observations of the density perturbation, which further suggest a temporal deconfinement of the gauge group after inflation. The resulting temperature-dependent axion potential, together with its periodic nature, gives rise to the red-tilted density perturbation, with a positive local-type non-Gaussianity of order unity.
We give new constraints on small-scale non-Gaussianity of primordial curvature perturbations by the use of anisotropies in acoustic reheating. Mixing of local thermal or local kinetic equilibrium systems with different temperatures yields a locally averaged temperature rise, which is proportional to the square of temperature perturbations damping in the photon diffusion scale. Such secondary temperature perturbations are indistinguishable from the standard temperature perturbations linearly coming from primordial curvature perturbations and hence should be subdominant compared to the standard …
The next generation of cosmic microwave background, gravitational wave, and large scale structure, experiments will provide an unprecedented opportunity to probe the primordial power spectrum on small scales. An exciting possibility for what lurks on small scales is a sharp rise in the primordial power spectrum: This can lead to the formation of primordial black holes, providing a dark matter candidate or the black holes observed by the LIGO-Virgo collaboration. In this work we develop a mechanism for the amplification of the small-scale primordial power spectrum, in the context of single-fiel…
We analyze primordial non-gaussianities in presence of an ultra-slow phase during the inflationary dynamics, focusing on scenarios relevant for the production of primordial black holes. We compute the three-point correlation function of comoving curvature perturbations finding that non-gaussianities are sizable, and predominantly local. In the context of threshold statistics, we analyze their impact for the abundance of primordial black holes, and their interplay with the non-gaussianities arising from the non-linear relation between density and curvature perturbations. We find that non-gaussi…
We investigate a new mechanism to create large curvature perturbations on small scales due to parameter resonance in a single-field inflationary model with a small periodic structure upon the potential. After reentering the horizon, the amplified curvature perturbations can lead to observable primordial black holes as well as stochastic gravitational waves. The mass of primordial black holes and frequency of the induced gravitational waves depend on the model parameters. The resulted primordial black hole could constitute all dark matter or a fraction of dark matter in the universe, and corres…
Cosmological time crystal (TC) corresponds to a matter state where the periodic motion of field forms a limit cycle in its phase space. We explore what would happen if it existed in inflationary phase. It is found that the limit cycle responsible for TC will inevitably cause the periodic oscillation of the primordial perturbation spectrum. The oscillatory patterns of the spectrum depend on the TC parameters, and so encode the crystalline patterns of TC.
We study primordial perturbations from hyperinflation, proposed recently and based on a hyperbolic field-space. In the previous work, it was shown that the field-space angular momentum supported by the negative curvature modifies the background dynamics and enhances fluctuations of the scalar fields qualitatively, assuming that the inflationary background is almost de Sitter. In this work, we confirm and extend the analysis based on the standard approach of cosmological perturbation in multi-field inflation. At the background level, to quantify the deviation from de Sitter, we introduce the sl…
Probing correlations among short and long-wavelength cosmological fluctuations is known to be decisive for deepening the current understanding of inflation at the microphysical level. Spectral distortions of the CMB can be caused by dissipation of cosmological perturbations when they re-enter Hubble after inflation. Correlating spectral distortions with temperature anisotropies will thus provide the opportunity to greatly enlarge the range of scales over which squeezed limits can be tested, opening up a new window on inflation complementing the ones currently probed with CMB and LSS. In this p…
The large-scale power deficit in the cosmic microwave background fluctuations might be relevant with the physics of pre-inflation, a bounce, or a superinflationary phase preceding slow-roll inflation, which can provide a singular-free realization of inflation. We investigate the primordial perturbations from such pre-inflationary evolutions, which generally may consist of multiple phases with different background dynamics, and give a universal formula for the power spectrum of primordial perturbations in terms of the recursive Bogoliubov coefficients. We also apply our formula to corresponding…
We present a scenario for fast growth of cosmological perturbations; $δ(t) \sim a(t)^s$, $a(t)$ being the scale factor, with $s > 10$ for the numerical examples reported in this article. The basic ingredients of the scenario are an early matter dominated era and the dark fermion which experiences a scalar mediated force during the epoch. Both of these arise in string/supergravity models. The fast growth occurs for sub-horizon density perturbations of the dark fermion. The fast growth has a rich set of phenomenological implications. We outline implications for the formation of primordial black …
We investigate primordial perturbations and non-gaussianities in the Hořava-Lifshitz theory of gravitation. In the UV limit, the scalar perturbation in the Hořava theory is naturally scale-invariant, ignoring the details of the expansion of the Universe. One may thus relax the exponential inflation and the slow-roll conditions for the inflaton field. As a result, it is possible that the primordial non-gaussianities, which are ``slow-roll suppressed'' in the standard scenarios, become large. We calculate the non-gaussianities from the bispectrum of the perturbation and find that the equilateral…
If the very early Universe is dominated by the non-minimally coupled Higgs field and Starobinsky's curvature-squared term together, the potential diagram would mimic the landscape of a valley, serving as a cosmological attractor. The inflationary dynamics along this valley is studied, model parameters are constrained against observational data, and the isocurvature perturbation is evaluated.
The formation of Primordial Black Holes (PBHs) through the collapse of large fluctuations in the early universe is a rare event. This manifests itself, for instance, through the non-Gaussian tail of the formation probability. To compute such probability and the abundance of PBHs, the curvature perturbation is frequently adopted. In this note we emphasize that its use does not provide the correct PBH formation probability. Through a path-integral approach we show that the exact calculation of the PBH abundance demands the knowledge of multivariate joint probabilities of the curvature perturbati…
Primordial perturbations from ultra-slow-roll single-field inflation with quantum loop effects
Institute of Physics, Academia Sinica（中央研究院物理研究所）；Department of Physics, National Dong Hwa University（国立东华大学物理系）；Institute of Astronomy and Astrophysics, Academia Sinica（中央研究院天文及天文物理研究所）
We show that primordial black holes can be produced from the collapse of large isocurvature perturbations of the cold dark matter. We develop a novel procedure to compute the resulting black hole abundance by studying matched perturbations of matter-only universes, and we use our procedure to translate observational constraints on black hole abundances into model-independent constraints on cold dark matter isocurvature perturbations over a wide range of scales. The constraint on the typical amplitude of the primordial perturbations weakens slightly slower than linearly on small scales.
Recently we have proposed a novel method to probe primordial gravitational waves from upper bounds on the abundance of primordial black holes (PBHs). When the amplitude of primordial tensor perturbations generated in the early Universe is fairly large, they induce substantial scalar perturbations due to their second-order effects. If these induced scalar perturbations are too large when they reenter the horizon, then PBHs are overproduced, their abundance exceeding observational upper limits. That is, primordial tensor perturbations on superhorizon scales can be constrained from the absence of…
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 sp…
Primordial black holes could have been formed in the early universe from sufficiently large cosmological perturbations re-entering the horizon when the Universe is still radiation dominated. These originate from the spectrum of curvature perturbations generated during inflation at small-scales. Because of the non-linear relation between the curvature perturbation $ζ$ and the overdensity $δρ$, the formation of the primordial black holes is affected by intrinsic non-Gaussianity even though the curvature perturbation is Gaussian. We investigate the impact of this non-Gaussianity on the critical t…
It has been pointed out that matter bounce cosmology driven by a k-essence field cannot satisfy simultaneously the observational bounds on the tensor-to-scalar ratio and non-Gaussianity of the curvature perturbation. In this paper, we show that this is not the case in more general scalar-tensor theories. To do so, we evaluate the power spectra and the bispectra of scalar and tensor perturbations on a general contracting background in the Horndeski theory. We then discuss how one can discriminate contracting models from inflation based on non-Gaussian signatures of tensor perturbations.
We extend the formalism of time-sliced perturbation theory (TSPT) for cosmological large-scale structure to include non-Gaussian initial conditions. We show that in such a case the TSPT interaction vertices acquire new contributions whose time-dependence factorizes for the Einstein-de Sitter cosmology. The new formulation is free from spurious infrared (IR) enhancements and reveals a clear IR structure of non-Gaussian vertices. We use the new technique to study the evolution of oscillating features in primordial statistics and show that they are damped due to non-linear effects of large bulk f…
