Power Spectrum Of Perturbations Research Articles

Improved model of large-field inflation with primordial black hole production in Starobinsky-like supergravity

Abstract A viable model of large-field (chaotic) inflation with efficient production of primordial black holes is proposed in Starobinsky-like (modified) supergravity leading to the ‘no-scale-type’ Kähler potential and the Wess-Zumino-type (‘renormalizable’) superpotential. The cosmological tilts are in good (within 1σ) agreement with Planck measurements of the cosmic microwave background radiation. In addition, the power spectrum of scalar perturbations has a large peak at smaller scales, which leads to a production of primordial black holes from gravitational collapse of large perturbations with the masses about 1017 g. The masses are beyond the Hawking (black hole) evaporation limit of 1015 g, so that those primordial black holes may be viewed as viable candidates for a significant part or the whole of the current dark matter. The parameters of the superpotential were fine-tuned for those purposes, while the cubic term in the superpotential is essential whereas the quadratic term should vanish. The vacuum after inflation (relevant to reheating) is Minkowskian. The energy density fraction of the gravitational waves induced by the production of primordial black holes and their frequency were also calculated in the second order with respect to perturbations.

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 (MPBH<109g) 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 MPBH and the abundance of PBHs at the time of formation, denoted as ΩPBH,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 τ¯NL, and the primordial curvature perturbation power spectrum PR(k), which reads as τ¯NLPR(k)<4×10−20ΩPBH,f−17/9(MPBH104g)−17/9.

Properties of Central Regions of the Dark Matter Halos in the Model with a Bump in the Power Spectrum of Density Perturbations

A surprisingly large number of galaxies with masses of ~109–1010\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{M}_{ \\odot }}$$\\end{document} at redshifts of \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$z \\geqslant 9$$\\end{document} are discovered with the James Webb Space Telescope. A possible explanation for the increase in the mass function can be the presence of a local maximum (bump) in the power spectrum of density perturbations on the corresponding scale. In this paper, it is shown that simultaneously with the growth of the mass function, galaxies from the bump region must have a higher density (compactness) compared to cosmological models without a bump. These more compact galaxies have been partially included in larger galaxies and have been subjected to tidal gravitational disruption. They have been less destructed than “ordinary” galaxies of the same mass, and some of them could survive to z = 0 and persist on the periphery of some galaxies. The formation and evolution of compact halos in a cube with a volume of (47 Mpc)3 with (1024)3 dark matter particles in the redshift range from 120 to 0 have been numerically simulated and observational implications of the presence of such galaxies in the current Universe have been discussed.

Enhanced curvature perturbation and primordial black hole formation in two-stage inflation with a break

We investigate a model of R2-gravity with a non-minimally coupled scalar field that gives rise to two-stage inflation with a break, that is, with an intermediate stage where inflation momentarily halts. We find that the power spectrum of the primordial curvature perturbation is significantly enhanced at the break scale, which can account for the primordial black hole (PBH) formation, without affecting the CMB constraint on large scales. The behavior of the curvature perturbation is carefully analyzed and we find a few notable new features in the spectrum. In particular, we find that the k3 growth of the spectrum of toward the end of the first stage of inflation. We argue that this is a universal feature common to all two-stage models where the field dominating the second stage is heavy during the first stage. By appropriately tuning the model parameters, we find that our model can realize the scenario of PBHs as the cold dark matter of the Universe. We also find that we can choose the parameters so that the spectrum of the induced gravitational waves from the enhanced curvature perturbation fits the NANOGrav-15yr data of pulsar timing array observation.

Measuring the substructure mass power spectrum of 23 SLACS strong galaxy–galaxy lenses with convolutional neural networks

ABSTRACT Strong gravitational lensing can be used as a tool for constraining the substructure in the mass distribution of galaxies. In this study we investigate the power spectrum of dark matter perturbations in a population of 23 Hubble Space Telescope images of strong galaxy–galaxy lenses selected from The Sloan Lens ACS (SLACS) survey. We model the dark matter substructure as a Gaussian random field perturbation on a smooth lens mass potential, characterized by power-law statistics. We expand upon the previously developed machine learning framework to predict the power-law statistics by using a convolutional neural network (CNN) that accounts for both epistemic and aleatoric uncertainties. For the training sets, we use the smooth lens mass potentials and reconstructed source galaxies that have been previously modelled through traditional fits of analytical and shapelet profiles as a starting point. We train three CNNs with different training set: the first using standard data augmentation on the best-fitting reconstructed sources, the second using different reconstructed sources spaced throughout the posterior distribution, and the third using a combination of the two data sets. We apply the trained CNNs to the SLACS data and find agreement in their predictions. Our results suggest a significant substructure perturbation favouring a high frequency power spectrum across our lens population.

Thermal curvature perturbations in thermal inflation

We compute the power spectrum of super-horizon curvature perturbations generated during a late period of thermal inflation, taking into account fluctuation-dissipation effects resulting from the scalar flaton field's interactions with the ambient radiation bath. We find that, at the onset of thermal inflation, the flaton field may reach an equilibrium with the radiation bath even for relatively small coupling constants, maintaining a spectrum of thermal fluctuations until the critical temperature T c, below which thermal effects stop holding the field at the false potential minimum. This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations. In particular, we find that this inhibits the later formation of primordial black holes, at least on scales that leave the horizon for T > T c. The larger thermal field variance also reduces the duration of a period of fast-roll inflation below T c, as the field rolls to the true potential minimum, which should also affect the generation of (large) curvature perturbations on even smaller scales.

Species Scale and Primordial Gravitational Waves

AbstractThe species scale is a field‐dependent UV cut‐off for any effective field theory weakly coupled to gravity. In this letter, it is shown that in the context of inflationary cosmology, a detection of primordial gravitational waves will set an upper bound on the decay rate of the species scale. Specifically, this is derived in terms of the tensor‐to‐scalar ratio of power spectra of primordial perturbations. Given the targets of current and next generation experiments, it is shown that any successful detection would signify that this upper limit is of the order of unity, which is consistent with recent discussions in the literature.

Simultaneously probing the sound speed and equation of state of the early Universe with pulsar timing arrays

Recently, several major pulsar timing array (PTA) collaborations have assembled strong evidence for the existence of a gravitational-wave background at frequencies around the nanohertz regime. Assuming that the PTA signal is attributed to scalar-induced gravitational waves, we jointly employ the PTA data from the NANOGrav 15-year data set, PPTA DR3, and EPTA DR2 to probe the conditions of the early Universe. Specifically, we explore the equation of state parameter (w), the reheating temperature (T rh), and the sound speed (cs ), finding w = 0.59+0.36 -0.40 (median + 90% credible interval), and T rh ≲ 0.2 GeV at the 95% credible interval for a lognormal power spectrum of the curvature perturbation. Furthermore, we compute Bayes factors to compare different models against the power-law spectrum model, effectively excluding the pressure-less fluid domination model. Our study underscores the significance of scalar-induced gravitational waves as a powerful tool to explore the nature of the early Universe.

One-loop infrared rescattering by enhanced scalar fluctuations during inflation

We show that, whenever the perturbations of some field are excited during inflation by a physical process on sub-horizon scales, they unavoidably generate, even through gravitational interactions alone, a significant resonant IR cascade of power down to scales that are of the order of the horizon at that time (we denote these scales as near IR). We provide general analytic one-loop results for the enhancement of the IR power of the curvature perturbation generated by this effect, highlighting the role played by the resonance. We then study a number of examples in which the excited state is: (i) an isocurvature field, (ii) the curvature perturbation itself, (iii) a mixture of curvature and isocurvature fluctuations driven to an excited state by their coupled dynamics. In the cases shown, the cascade significantly modifies the near IR part of the power spectrum of the curvature perturbation with respect to the linear theory, indicating that this effect can impact the phenomenology associated with a variety of mechanisms considered in the literature, notably concerning primordial black holes and gravitational waves.

Solution for cosmological observables in the Starobinsky model of inflation

This paper focuses on the Starobinsky model of inflation in the Einstein frame. We derive solutions for various cosmological observables, such as the scalar spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}, the tensor-to-scalar ratio r and their runnings, as well as the number of e-folds of inflation, reheating, and radiation, with minimal assumptions. The impact of reheating on inflation is explored by constraining the equation of state parameter ωre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\omega _{re}$$\\end{document} at the end of reheating. An equation linking inflation with reheating is established, which is solved for the spectral index ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}. Using consistency relations of the model, we determine the other observables while the number of e-folds during inflation Nk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_k$$\\end{document}, and the number of e-folds during reheating Nre\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$N_{re}$$\\end{document} are determined by their respective formulas involving ns\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$n_s$$\\end{document}. We find remarkable agreement between the Starobinsky model and current measurements of the power spectrum of primordial curvature perturbations and the present bounds on the spectrum of primordial gravitational waves.

Euclid: The search for primordial features

Primordial features, in particular oscillatory signals, imprinted in the primordial power spectrum of density perturbations represent a clear window of opportunity for detecting new physics at high-energy scales. Future spectroscopic and photometric measurements from the Euclid space mission will provide unique constraints on the primordial power spectrum, thanks to the redshift coverage and high-accuracy measurement of nonlinear scales, thus allowing us to investigate deviations from the standard power-law primordial power spectrum. We consider two models with primordial undamped oscillations superimposed on the matter power spectrum described by 1 + 𝒜X sin (ωXΞX + 2 πϕX), one linearly spaced in k space with Ξlin ≡ k/k* where k* = 0.05 Mpc−1 and the other logarithmically spaced in k space with Ξlog ≡ ln(k/k*). We note that 𝒜X is the amplitude of the primordial feature, ωX is the dimensionless frequency, and ϕX is the normalised phase, where X = {lin, log}. We provide forecasts from spectroscopic and photometric primary Euclid probes on the standard cosmological parameters Ωm, 0, Ωb, 0, h, ns, and σ8, and the primordial feature parameters 𝒜X, ωX, and ϕX. We focus on the uncertainties of the primordial feature amplitude 𝒜X and on the capability of Euclid to detect primordial features at a given frequency. We also study a nonlinear density reconstruction method in order to retrieve the oscillatory signals in the primordial power spectrum, which are damped on small scales in the late-time Universe due to cosmic structure formation. Finally, we also include the expected measurements from Euclid’s galaxy-clustering bispectrum and from observations of the cosmic microwave background (CMB). We forecast uncertainties in estimated values of the cosmological parameters with a Fisher matrix method applied to spectroscopic galaxy clustering (GCsp), weak lensing (WL), photometric galaxy clustering (GCph), the cross correlation (XC) between GCph and WL, the spectroscopic galaxy clustering bispectrum, the CMB temperature and E-mode polarisation, the temperature-polarisation cross correlation, and CMB weak lensing. We consider two sets of specifications for the Euclid probes (pessimistic and optimistic) and three different CMB experiment configurations, that is, Planck, Simons Observatory (SO), and CMB Stage-4 (CMB-S4). We find the following percentage relative errors in the feature amplitude with Euclid primary probes: for the linear (logarithmic) feature model, with a fiducial value of 𝒜X = 0.01, ωX = 10, and ϕX = 0: 21% (22%) in the pessimistic settings and 18% (18%) in the optimistic settings at a 68.3% confidence level (CL) using GCsp+WL+GCph+XC. While the uncertainties on the feature amplitude are strongly dependent on the frequency value when single Euclid probes are considered, we find robust constraints on 𝒜X from the combination of spectroscopic and photometric measurements over the frequency range of (1, 102.1). Due to the inclusion of numerical reconstruction, the GCsp bispectrum, SO-like CMB reduces the uncertainty on the primordial feature amplitude by 32%–48%, 50%–65%, and 15%–50%, respectively. Combining all the sources of information explored expected from Euclid in combination with the future SO-like CMB experiment, we forecast 𝒜lin ≃ 0.010 ± 0.001 at a 68.3% CL and 𝒜log ≃ 0.010 ± 0.001 for GCsp(PS rec + BS)+WL+GCph+XC+SO-like for both the optimistic and pessimistic settings over the frequency range (1, 102.1).

Non-Gaussianity in rapid-turn multi-field inflation

We show that theories of inflation with multiple, rapidly turning fields can generate large amounts of non-Gaussianity. We consider a general theory with two fields, an arbitrary field-space metric, and a potential that supports sustained, rapidly turning field trajectories. Our analysis accounts for non-zero field cross-correlation and does not fix the power spectra of curvature and isocurvature perturbations to be equal at horizon crossing. Using the δN formalism, we derive a novel, analytical formula for bispectrum generated from multi-field mixing on super-horizon scales. Rapid-turn inflation can produce a bispectrum with several potentially large contributions that are not necessarily of the local shape. We exemplify the applicability of our formula with a fully explicit model and show that the new contributions indeed can generate a large amplitude of local non-Gaussianity, f NL loc ∼ 𝒪(1). These results will be important when interpreting the outcomes of future observations.

Primordial black holes dark matter and secondary gravitational waves from warm Higgs-G inflation

We explore the role of dissipative effects during warm inflation leading to the small-scale enhancement of the power spectrum of curvature perturbations. In this paper, we specifically focus on non-canonical warm inflationary scenarios and study a model of warm Higgs-G inflation, in which the Standard Model Higgs boson drives inflation, with a Galileon-like non-linear kinetic term. We show that in the Galileon-dominated regime, the primordial power spectrum is strongly enhanced, leading to the formation of primordial black holes (PBH) with a wide range of the mass spectrum. Interestingly, PBHs in the asteroid mass window ∼ (1017–1023) g are generated in this model, which can explain the total abundance of dark matter in the Universe. In our analysis, we also calculate the secondary gravitational waves (GW) sourced by these small-scale overdense fluctuations and find that the induced GW spectrum can be detected in future GW detectors, such as LISA, BBO, DECIGO, etc. Our scenario thus provides a novel way of generating PBHs as dark matter and a detectable stochastic GW background from warm inflation. We also show that our scenario is consistent with the swampland and the trans-Planckian censorship conjectures and, thus, remains in the viable landscape of UV complete theories.

Primordial black holes in non-canonical scalar field inflation driven by quartic potential in the presence of bump

Here, generation of Primordial Black Holes (PBHs) from quartic potential in the presence of a tiny bump in non-canonical inflationary model has been inquired. It is demonstrated that, a viable inflationary era can be driven through the quartic potential in non-canonical framework with a power-law Lagrangian density. Furthermore, setting a suitable function of inflaton field as a correction term (like a bump) to the quartic potential, causes the inflaton to slow down for a while. In such a short time span, the amplitude of the scalar perturbations power spectrum on small scales grows up sufficiently versus CMB scales. In addition to the bump feature, the enhancing effect of the α parameter of the Lagrangian on the amplitude of the scalar power spectrum has been shown. Fine tuning of three parameter Cases of the model results in generating of three Cases of PBHs. In addition, we investigate the secondary Gravitational Waves (GWs) produced during generation of PBHs and show that their contemporary density parameter spectra (ΩGW0 ) can be tracked down by GWs detectors.

Cancellation of quantum corrections on the soft curvature perturbations

We study the cancellation of quantum corrections on the superhorizon curvature perturbations from subhorizon physics beyond the single-clock inflation from the viewpoint of the cosmological soft theorem. As an example, we focus on the transient ultra-slow-roll inflation scenario and compute the one-loop quantum corrections to the power spectrum of curvature perturbations taking into account nontrivial surface terms in the action. We find that Maldacena’s consistency relation is satisfied and guarantees the cancellation of contributions from the short-scale modes. As a corollary, primordial black hole production in single-field inflation scenarios is not excluded by perturbativity breakdown even for the sharp transition case in contrast to some recent claims in the literature. We also comment on the relation between the tadpole diagram in the in-in formalism and the shift of the elapsed time in the stochastic-δN formalism. We find our argument is not directly generalisable to the tensor perturbations.

Primordial Gravitational Wave- and Curvature Perturbation-Induced Energy Density Perturbations

We study the second-order scalar and density perturbations generated by Gaussian curvature perturbations and primordial gravitational waves in the radiation-dominated era. After presenting all the possible second-order source terms, we obtain the explicit expressions of the kernel functions and the power spectra of the second-order scalar perturbations. We show that the primordial gravitational waves might affect second-order energy density perturbation δ(2)=δρ(2)/ρ(0) significantly. The effects of primordial gravitational waves are studied in terms of different kinds of primordial power spectra.

Model-independent reconstruction of the primordial curvature power spectrum from PTA data

Recently released data from pulsar timing array (PTA) collaborations provide strong evidence for a stochastic signal consistent with a gravitational-wave background, potentially originating from scalar-induced gravitational waves (SIGWs). However, in order to determine whether the SIGWs with a specific power spectrum of curvature perturbations can account for the PTA signal, one needs to estimate the energy density of the SIGWs, which can be computationally expensive.In this paper, we use a model-independent approach to reconstruct the primordial curvature power spectrum using a free spectrum cross over from 101 Mpc-1 to 1020 Mpc-1 with NANOGrav 15-year data set.Our results can simplify the task of assessing whether a given primordial curvature power spectrum can adequately explain the observed PTA signal without calculating the energy density of SIGWs.

Primordial black hole mass function with mass gap

ABSTRACT Primordial black holes (PBHs) are mainly characterized by their mass function, in which there may be some huge suppression for certain mass spans. If this is the case, the absence of these PBHs will form mass gaps. In this paper, we investigate the PBH mass function with the mass gap. First, to obtain a data-supported PBH mass function with the mass gap for subsolar masses PBHs, we fine-tune the coefficients of a model-independent power spectrum of primordial curvature perturbations. Then we take this unique PBH mass function into consideration and calculate the energy-density spectrum of the stochastic gravitational-wave background from PBH mergers. We find the location of its first peak almost has no relationship with the mass gap and is only determined by the probability distribution of frequencies at which PBH binaries merge. Apart from the first peak, there must be an accompanying smaller trough at a higher frequency resulting from the mass gap. Therefore, the detection of this smaller trough will provide more information about inflation and PBH formation.

Perturbations of cosmological redshift drift

In this paper we calculate the linear perturbations of the cosmological redshift drift. We show explicitly that our expressions are gauge-invariant and compute the power spectrum of the redshift drift perturbations and its correlations with galaxy number counts within linear perturbation theory. Our findings show that the perturbations are small, and that the peculiar velocity and acceleration terms are dominating and cannot be neglected when modeling the full perturbative expression for the redshift drift. We also find that the cross-correlations with galaxy number count fluctuations might increase the detectability of the effect and can help to separate the perturbative effects from the background cosmological redshift drift signal.

Constraints on primordial curvature power spectrum with pulsar timing arrays

The stochastic signal detected by NANOGrav, PPTA, EPTA, and CPTA can be explained by the scalar-induced gravitational waves. In order to determine the scalar-induced gravitational waves model that best fits the stochastic signal, we employ both single- and double-peak parameterizations for the power spectrum of the primordial curvature perturbations, where the single-peak scenarios include the δ-function, box, lognormal, and broken power law model, and the double-peak scenario is described by the double lognormal form.Using Bayesian inference, we find that there is no significant evidence for or against the single-peak scenario over the double-peak model, with log (Bayes factors) among these models ln ℬ < 1.Therefore, we cannot distinguish the different shapes of the power spectrum of the primordial curvature perturbation with the current sensitivity of pulsar timing arrays.