Curvature Perturbation Research Articles

Search for scalar induced gravitational waves in the international pulsar timing array data release 2 and NANOgrav 12.5 years datasets

We perform a Bayesian search in the latest Pulsar Timing Array (PTA) datasets for a stochastic gravitational wave (GW) background sourced by curvature perturbations at scales 10^5105 Mpc^{-1}\lesssim−1≲ k\lesssim 10^8≲108 Mpc^{-1}−1. These re-enter the Hubble horizon at temperatures around and below the QCD crossover phase transition in the early Universe. We include a stochastic background of astrophysical origin in our search and properly account for constraints on the curvature power spectrum from the overproduction of primordial black holes (PBHs). We find that the International PTA Data Release 2 significantly favors the astrophysical model for its reported common-spectrum process, over the curvature-induced background. On the other hand, the two interpretations fit the NANOgrav 12.5 years dataset equally well. We then set new upper limits on the amplitude of the curvature power spectrum at small scales. These are independent from, and competitive with, indirect astrophysical bounds from the abundance of PBH dark matter. Upcoming PTA data releases will provide the strongest probe of the curvature power spectrum around the QCD epoch.

Growth of curvature perturbations for PBH formation & detectable GWs in non-minimal curvaton scenario revisited

We revisit the growth of curvature perturbations in non-minimal curvaton scenario with a non-trivial field metric λ(ϕ) where ϕ is an inflaton field, and incorporate the effect from the non-uniform onset of curvaton's oscillation in terms of an axion-like potential. The field metric λ(ϕ) plays a central role in the enhancement of curvaton field perturbation δχ, serving as an effective friction term which can be either positive or negative, depending on the first derivative λ ,ϕ . Our analysis reveals that δχ undergoes the superhorizon growth when the condition η eff ≡ -2 √2ϵ M Pl λ ,ϕ /λ < -3 is satisfied. This is analogous to the mechanism responsible for the amplification of curvature perturbations in the context of ultra-slow-roll inflation, namely the growing modes dominate curvature perturbations. As a case study, we examine the impact of a Gaussian dip in λ(ϕ) and conduct a thorough investigation of both the analytical and numerical aspects of the inflationary dynamics. Our findings indicate that the enhancement of curvaton perturbations during inflation is not solely determined by the depth of the dip in λ(ϕ). Rather, the first derivative λ ,ϕ also plays a significant role, a feature that has not been previously highlighted in the literature. Utilizing the δ𝒩 formalism, we derive analytical expressions for both the final curvature power spectrum and the non-linear parameter f NL in terms of an axion-like curvaton's potential leading to the non-uniform curvaton's oscillation. Additionally, the resulting primordial black hole abundance and scalar-induced gravitational waves are calculated, which provide observational windows for PBHs.

Constraints on compensated isocurvature perturbations from BOSS DR12 galaxy data

We use the BOSS DR12 galaxy power spectrum to constrain compensated isocurvature perturbations (CIP), which are opposite-sign primordial baryon and dark matter perturbations that leave the total matter density unchanged. Long-wavelength CIP σ(x) enter the galaxy density contrast as δg (x) ⊃ bσσ(x), with bσ the linear CIP galaxy bias parameter. We parameterize the CIP spectra as Pσσ = A 2 Pℛℛ and Pσℛ = ξ√PσσPℛℛ , where A is the CIP amplitude and ξ is the correlation with the curvature perturbations ℛ. We find a significance of detection of Ab σ ≠ 0 of 1.8σ for correlated CIP (ξ = 1), consistent with no detection. For uncorrelated CIP (ξ = 0), the constraints are instead more significantly shifted away from zero, although this may be due to large-scale data systematics which have a bigger impact on these type of CIP. The constraints on A depend on the assumed priors for the bσ parameter, which we estimate using separate universe simulations. Assuming bσ values representative of all halos we find σA = 145 for correlated CIP and σ |A| = 475 for uncorrelated CIP. Our strongest uncorrelated CIP constraint is for bσ representative of the 33% most concentrated halos, σ |A| = 197, which is better than the current CMB bounds |A| ≲ 360. We also discuss the impact of the local primordial non-Gaussianity parameter f NL in CIP constraints. Our results demonstrate the power of galaxy data to place tight constraints on CIP, and motivate works to understand better the impact of data systematics, as well as to determine theory priors for bσ .

Scalar Field Evolution at Background and Perturbation Levels for a Broad Class of Potentials

AbstractIn this paper, a non‐interacting scalar field cosmology with an arbitrary potential using the f‐deviser method that relies on the differentiability properties of the potential is investigated. Using this alternative mathematical approach, a unified dynamical system analysis at a scalar field's background and perturbation levels with arbitrary potentials is presented. For illustration, a monomial and double exponential potential is considered. These two classes of potentials comprise the asymptotic behavior of several classes of scalar field potentials, and, therefore, they provide the skeleton for the typical behavior of arbitrary potentials. Moreover, the linear cosmological perturbations in the matterless case by considering three scalar perturbations: the evolution of the Bardeen potentials, the comoving curvature perturbation, the so‐called Sasaki‐Mukhanov variable, or the scalar field perturbation in uniform curvature gauge is analyzed. Finally, an exhaustive dynamical system analysis for each scalar perturbation is presented, including the evolution of Bardeen potentials in the presence of matter.

Scale invariant curvature perturbations from a spontaneously decaying scalar field

The evolution of superhorizon curvature perturbations in a two-component interacting Universe is considered. It is found that adiabatic modes conserve the total curvature perturbation , unless there are stages in which the rate of dissipation of one component into another is not constant. Moreover, our result shows that when the rate is varying it is possible for ‘isocurvature’ perturbations generated during reheating to alter the amplitude of an adiabatic curvature mode even when the mode is outside the horizon. Specifically, if an indefinitely large rate Γ for massive particles decaying into photons develops rapidly amid vanishingly small initial values (before decay) of the total curvature and Newtonian potential , such that the product and become a pair of finite and universal constants for all superhorizon scales afterwards, Harrison–Zel’dovich scale-invariant power spectrum could be synthesized from a homogeneous state without inflation at all.

Logarithmic Duality of the Curvature Perturbation.

We study the comoving curvature perturbation 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 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 R(δφ,δπ) reduces to a single logarithm, which yields either the renowned "exponential tail" of the probability distribution function of R or a Gumbel-distribution-like tail.

Viable vector coherent oscillation dark matter

We construct a viable model of the vector coherent oscillation dark matter. The vector boson is coupled to the inflaton through the kinetic function so that the effective Hubble mass term is cancelled out. In order to avoid strong constraints from isocurvature perturbation and statistically anisotropic curvature perturbation, the inflaton is arranged so that it does not contribute to the observed large scale curvature perturbation and we introduce a curvaton. We found viable vector coherent oscillation dark matter scenario for the wide vector mass range from 10-21 eV to 1 eV.

Structure formation and quasispherical collapse from initial curvature perturbations with numerical relativity simulations

Structure formation and quasispherical collapse from initial curvature perturbations with numerical relativity simulations

On the decoherence of primordial gravitons

It is well-known that the primordial scalar curvature and tensor perturbations, ζ and γij, are conserved on super-horizon scales in minimal inflation models. However, their wave functional has a rapidly oscillating phase which is slow-roll unsuppressed, as can be seen either from boundary (total-derivative) terms of cosmological perturbations, or the WKB approximation of the Wheeler-DeWitt equation. Such an oscillatory phase involves gravitational non-linearity between scalar and tensor perturbations. By tracing out unobserved modes, the oscillatory phase causes faster decoherence of primordial gravitons compared to those by bulk interactions. Our results put a stronger lower bound of decoherence effect to the recent proposals probing squeezed primordial gravitons.

Production of Primordial Black Holes in Improved E-Models of Inflation

E-type α-attractor models of single-field inflation were generalized further in order to accommodate production of primordial black holes (PBHs) via adding a near-inflection point to the inflaton scalar potential at smaller scales, in good agreement with measurements of cosmic microwave background (CMB) radiation. A minimal number of new parameters were used but their fine-tuning was maximized in order to increase the possible masses of PBHs formed during an ultra-slow-roll phase, leading to a large enhancement in the power spectrum of scalar (curvature) perturbations by 6 or 7 orders of magnitude against the power spectrum of perturbations observed in CMB. It was found that extreme fine-tuning of the parameters in our models can lead to the formation of moon-sized PBHs, with masses of up to 1026 g, still in agreement with CMB observations. Quantum corrections are known to lead to the perturbative upper bound on the amplitude of large scalar perturbations responsible for PBH production. The quantum (one-loop) corrections in our models were found to be suppressed by one order of magnitude for PBHs with masses of approximately 1019 g, which may form the whole dark matter in the Universe.

Primordial black holes generated by the non-minimal spectator field

We improve and generalize the non-minimal curvaton model originally proposed in arXiv: 2112.12680 to a model in which a spectator field non-minimally couples to an inflaton field and the power spectrum of the perturbation of spectator field at small scales is dramatically enhanced by the sharp feature in the form of non-minimal coupling. At or after the end of inflation, the perturbation of the spectator field is converted into curvature perturbation and leads to the formation of primordial black holes (PBHs). Furthermore, for example, we consider three phenomenological models for generating PBHs with mass function peaked at ~ 10−12Mʘ and representing all the cold dark matter in our universe and find that the scalar induced gravitational waves generated by the curvature perturbation can be detected by the future space-borne gravitational-wave detectors such as Taiji, TianQin, and LISA.

From inflation to reheating and their dynamical stability analysis in Gauss–Bonnet gravity

We investigate the inflation and reheating phenomenology in scalar-Einstein-Gauss–Bonnet theory of gravity where a scalar field non-minimally couples with the Gauss-Bonnet (GB) curvature term. Regarding the inflationary phenomenology, we find – (1) the inflation starts with a quasi de-Sitter phase and has an exit at a finite e-fold, which is indeed consistent with the resolution of horizon and flatness problems, (2) the scalar and tensor perturbations prove to be ghost free and do not suffer from gradient instability, (3) the curvature perturbation amplitude as well as its tilt and the tensor-to-scalar ratio turn out to be simultaneously compatible with the recent Planck data for suitable values of the parameters which also results to the inflationary energy scale ∼1012GeV. After the inflation ends, the scalar field starts to decay to radiation with a constant decay width. For our considered scalar potential and the GB coupling function, the model results to an analytic power law solution of the Hubble parameter and a logarithmic solution of the scalar field during the reheating era, where the exponent of the Hubble parameter determines the effective EoS parameter (weff) during the same. The stability of such reheating dynamics is examined by dynamical analysis which ensures that weff can go beyond unity and reach up-to the maximum value of max(weff)=1.56. The scenario with weff>1 proves to be purely due to the presence of the GB coupling function, which in turn may have important consequences on enhancing the primordial gravitational waves’ amplitude observed today. The inflationary e-fold number (Nf) gets further constrained by the input of the reheating stage, and we critically examine the constraint of Nf coming from both the inflation and reheating phenomenology. We finally construct the complete forms of scalar potential (V(ϕ)) and the GB coupling function (ξ(ϕ)) that smoothly transits from inflation to reheating, and numerically solve the Hubble parameter and the scalar field for such complete forms of V(ϕ) and ξ(ϕ). Such numerical solutions match with analytic ones in the respective regime. After the reheating ends, the GB term gets decouple from the theory and the radiation energy density dominates the energy budget of the universe, which in turn produces the standard radiation era of the universe.

An update on adiabatic modes in cosmology and δN formalism

In this paper, we generalize the Weinberg's procedure to determine the comoving curvature perturbation ℛ to non-attractor inflationary regimes. We show that both modes of ℛ are related to a symmetry of the perturbative equations in the Newtonian gauge. As a byproduct, we clarify that adiabaticity does not generally imply constancy of ℛ, not even in the k ⟶ 0 limit. We then show that there exist non-equivalent definitions of δN that would reproduce ℛ or the uniform density curvature perturbation ζ at linear order. We have then shown that the perturbative δN definition in terms of difference between the number of e-foldings of different gauges, can be extended non-perturbatively at leading order in gradient expansion. Nevertheless, the computer friendly definition in terms of the difference of e-foldings obtained from the evolution of a local FRW Universe, respectively with perturbed and un-perturbed initial conditions, might only give information about the linear order curvature perturbations, contrary to what is stated in the literature.

Gauge invariance on the light-cone: curvature perturbations and radiative degrees of freedom

We derive the expressions on the observed light-cone for some relevant cosmological gauge invariant variables, such as the Mukhanov-Sasaki variable and E- and B- modes of the tensor perturbations. Since the structure of the light-cone does not reflect in a direct way the FLRW symmetries, we develop a formalism which is coordinate independent and classifies the perturbations according to their helicities. Even though we work with linear perturbations, our formalism can be readily extended to non-linear theory and put the basis to study the evolution of cosmological perturbations, since the early- until the late-time Universe, directly along the observed light-cone.

Primordial black hole formation in Starobinsky's linear potential model

We study the power spectrum of the comoving curvature perturbation 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 ∼ 2.61 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.

Pinning down the primordial black hole formation mechanism with gamma-rays and gravitational waves

Primordial black holes (PBHs) are predicted in many models via different formation mechanisms. Identifying the origin of PBHs is of the same importance as probing their existence. We propose to probe the asteroid-mass PBHs [\U0001d4aa(1017) g ≲ M ≲ \U0001d4aa (1022) g] with gamma-rays from Hawking radiation and the stochastic gravitational waves (GWs) from the early Universe. We consider four concrete formation mechanisms, including collapse from primordial curvature perturbations, first-order phase transitions, or cosmic strings, and derive the extended PBH mass functions of each mechanism for phenomenological study. The results demonstrate that by combining gamma-rays and GW signals we can probe PBHs up to \U0001d4aa(1019) g and identify their physical origins.

Revealing the amplitude of primordial curvature perturbations on small scales from Primordial black hole binaries for gravitational wave detection

Revealing the amplitude of primordial curvature perturbations on small scales from Primordial black hole binaries for gravitational wave detection

Primordial black holes and induced gravitational waves from double-pole inflation

The primordial black hole (PBH) productions from the inflationary potential with an inflection point usually rely heavily on the fine-tuning of the model parameters. We propose in this work a new kind of the α-attractor inflation with asymmetric double poles that naturally and easily lead to a period of non-attractor inflation, during which the PBH productions are guaranteed with less fine-tuning the model parameters. This double-pole inflation can be tested against the observational data in the future with rich phenomenological signatures: (1) the enhanced curvature perturbations at small scales admit a distinctive feature of ultraviolet oscillations in the power spectrum; (2) the quasi-monochromatic mass function of the produced PBHs can be made compatible to the asteroid-mass PBHs as the dominant dark matter component, the planet-mass PBHs as the OGLE ultrashort-timescale microlensing events, and the solar-mass PBHs as the LIGO-Virgo events; (3) the induced gravitational waves can be detected by the gravitational-wave detectors in space and Pulsar Timing Array/Square Kilometer Array.

Implications for Primordial Black Holes from Cosmological Constraints on Scalar-induced Gravitational Waves

Sufficiently large scalar perturbations in the early universe can create overdense regions that collapse into primordial black holes (PBHs). This process is accompanied by the emission of scalar-induced gravitational waves that behave like an extra radiation component, thus contributing to the relativistic degrees of freedom (N eff). We show that the cosmological constraints on N eff can be used to pose stringent limits on PBHs created from this particular scenario as well as the relevant small-scale curvature perturbation (). We show that the combination of cosmic microwave background (CMB), baryon acoustic oscillation, and Big Bang nucleosynthesis data sets can exclude supermassive PBHs with peak mass M • ∈ [5 × 105, 5 × 1010] M ⊙ as the major component of dark matter, while the detailed constraints depend on the shape of the PBHs’ mass distribution. A future CMB mission such as CMB-S4 can greatly broaden this constraint window to M • ∈ [8 × 10−5, 5 × 1010] M ⊙, covering substellar masses. These limits on PBHs correspond to a tightened constraint on on scales of k ∈ [10, 1022] Mpc−1, much smaller than those probed by direct CMB and large-scale structure power spectra.

Unitary paradox of cosmological perturbations

If we interpret the Bekenstein–Hawking entropy of the Hubble horizon as thermodynamic entropy, then the entanglement entropy of the superhorizon modes of curvature perturbation entangled with the subhorizon modes will exceed the Bekenstein–Hawking bound at some point; we call this the unitary paradox of cosmological perturbations by analogy with black hole. In order to avoid a fine-tuned problem, the paradox must occur during the inflationary era at the critical time [Formula: see text] (in Planck units), where [Formula: see text] is the first Hubble slow-roll parameter and [Formula: see text] is the Hubble rate during inflation. If we instead accept the fine-tuned problem, then the paradox will occur during the dark energy era at the critical time [Formula: see text], where [Formula: see text] is the Hubble rate dominated by dark energy, [Formula: see text] is the total number of e-folds of inflation and [Formula: see text] is a purification factor that takes the range [Formula: see text].