Cosmological Perturbations Research Articles

Primordial Black Holes: Formation, Spin and Type II

Primordial black holes (PBHs) may have formed through the gravitational collapse of cosmological perturbations that were generated and stretched during the inflationary era, later entering the cosmological horizon during the decelerating phase, if their amplitudes were sufficiently large. In this review paper, we will briefly introduce the basic concept of PBHs and review the formation dynamics through this mechanism, the estimation of the initial spins of PBHs and the time evolution of type II fluctuations, with a focus on the radiation-dominated and (early) matter-dominated phases.

The model of the local Universe in the framework of the second-order perturbation theory

Abstract Recently, we constructed the specific solution to the second-order cosmological perturbation theory, around any Friedmann–Lemaître–Robertson–Walker background filled with dust matter and a positive cosmological constant. In this paper, we use the Cosmicflows-4 sample of galaxies from the Extragalactic Distance Database to constrain this metric tensor. We obtain an approximation to the local matter distribution and geometry. We numerically solve for null geodesics for randomly distributed mock sources and compare this model with the Lemaître–Hubble constant inferred from the observations under the assumption of perfect isotropy and homogeneity. We conclude on effects of realistic inhomogeneities on the luminosity distance in the context of the Hubble tension and discuss limitations of our approach.

Spectrum of primordial gravitational waves in the presence of a cosmic string

In this paper we consider an inflating universe with long straight cosmic string along z-axis. We demonstrate that cosmic string's effect can be treated as a perturbation on the background of FRW metric. By performing cosmological perturbations on this inflating cosmic string background, we derived the linearized Einstein field equations. We show that at leading order (neglecting the mixing terms of cosmic string perturbations with gravitational tensor perturbations), the cosmic string appears as an inhomogeneous term on the right hand side of wave equation for tensor perturbations. Finally, by finding analytical solution of the wave equation for slow-roll inflation, we illustrate its impact on the spectrum of primordial gravitational waves.

The open effective field theory of inflation

In our quest to understand the generation of cosmological perturbations, we face two serious obstacles: we do not have direct information about the environment experienced by primordial perturbations during inflation, and our observables are practically limited to correlators of massless fields, heavier fields and derivatives decaying exponentially in the number of e-foldings. The flexible and general framework of open systems has been developed precisely to face similar challenges. Building on previous work, we develop a Schwinger-Keldysh path integral description for an open effective field theory of inflation, describing the possibly dissipative and non-unitary evolution of the Goldstone boson of time translations interacting with an unspecified environment, under the key assumption of locality in space and time. Working in the decoupling limit, we study the linear and interacting theory in de Sitter and derive predictions for the power spectrum and bispectrum that depend on a finite number of effective couplings organised in a derivative expansion. The smoking gun of interactions with the environment is an enhanced but finite bispectrum close to the folded kinematical limit. We demonstrate the generality of our approach by matching our open effective theory to an explicit model. Our construction provides a standard model to simultaneously study phenomenological predictions as well as quantum information aspects of the inflationary dynamics.

Hanbury-Brown and Twiss effect in inflationary cosmological perturbations

Hanbury-Brown and Twiss effect in inflationary cosmological perturbations

Cosmological Bell tests with decoherence effects

The inflationary universe creates particle pairs, which are entangled in their momenta due to momentum conservation. Operators involving the momenta of the fluctuations can be rewritten into pseudo-spin operators, such as the Gour-Khanna-Mann-Revzen (GKMR) pseudo-spin. Making use of these pseudo-spin operators, cosmological Bell inequalities can be formulated. The violation of these Bell inequalities indicates the quantum nature of primordial fluctuations.In this work, we focus on primordial curvature perturbations. Since curvature perturbations arise from gravity, their action includes the Gibbons-Hawking-York boundary term. We clarify the role of the boundary term in selecting suitable initial conditions for linear perturbations.After that, we proceed to the interactions of cosmological perturbations, including the bulk and boundary interaction terms, which introduce decoherence effects. These decoherence effects change the expectation value of the Bell operator, and gradually restore the Bell inequality. We describe this process by a “Bell test curve”, which offers a window around 5 e-folds for testing the quantum origin of cosmological perturbations. We also explore the possibility of extracting the information of the decoherence rate and the structure of primordial interactions from the Bell test curve.

Gravitational wave luminosity distance-weighted anisotropies

Measurements of the luminosity distance of propagating gravitational waves can provide invaluable information on the geometry and content of our Universe. Due to the clustering of cosmic structures, in realistic situations we need to average the luminosity distance of events coming from patches inside a volume. In this work we evaluate, in a gauge-invariant and fully-relativistic treatment, the impact of cosmological perturbations on such averaging process. We find that clustering, lensing and peculiar velocity effects impact estimates for future detectors such as Einstein Telescope, Cosmic Explorer, the Big Bang Observer and DECIGO. The signal-to-noise ratio of the angular power spectrum of the average luminosity distance over all the redshift bins is 17 in the case of binary black holes detected by Einstein Telescope and Cosmic Explorer. We also provide fitting formulas for the corrections to the average luminosity distance due to general relativistic effects.

Induced gravitational waves: the effect of first order tensor perturbations

Scalar induced gravitational waves contribute to the cosmological gravitational wave background. They can be related to the primordial density power spectrum produced towards the end of inflation and therefore are a convenient new tool to constrain models of inflation. These waves are sourced by terms quadratic in perturbations and hence appear at second order in cosmological perturbation theory. While the focus of research so far was on purely scalar source terms we also study the effect of including first order tensor perturbations as an additional source. This gives rise to two additional source terms: a term quadratic in the tensor perturbations and a cross term involving mixed scalar and tensor perturbations. We present full analytical expressions for the spectral density of these new source terms and discuss their general behaviour. To illustrate the generation mechanism we study two toy models containing a peak on small scales. For these models we show that the scalar-tensor contribution becomes non-negligible compared to the scalar-scalar contribution on smaller scales. We also consider implications for future gravitational wave surveys.

Intermediate inflation in a generalized non-minimal derivative coupling model

In this work, we consider intermediate inflation in the context of the generalized non-minimal derivative coupling (GNMDC) model. In the GNMDC model, inflation is driven by a canonical scalar field that is coupled not only to gravity but also to the derivative of the scalar field. The model introduces new dynamics and features during the inflationary epoch. We find inflationary solutions with a power law scalar field for the power law coupling function. Additionally, we determine the inflaton potential that generates intermediate expansion of the scale factor. We also discuss the background equations in the high friction limit and derive constraints on the parameters of our model. Furthermore, we investigate the cosmological perturbations in the slow roll approximation within the GNMDC model, and we calculate the scalar and tensor spectral index and the tensor-to-scalar ratio during intermediate inflation. We compare the results of this model with observational data that can be used to test the model using cosmic microwave background radiation data. Overall, we establish conditions for the inflaton potential that ensure the continuation of accelerated expansion during slow roll inflation. We numerically analyze the power spectrum and spectral index for scalar and tensor modes in intermediate inflation in the high friction limit, and we use Planck 2018 data to obtain constraints on the parameters of the model. We demonstrate that intermediate inflation in the GNMDC model is successful in evaluation and explanation of background and perturbation quantities using observational data.

Peculiar velocities in Friedmann universes with nonzero spatial curvature

We extend the earlier linear studies of cosmological peculiar velocities to Friedmann universes with nonzero spatial curvature. In the process, we also compare our results with those obtained in cosmologies with Euclidean spatial sections. Employing relativistic cosmological perturbation theory, we first provide the differential formulas governing the evolution of peculiar velocities on all Friedmann backgrounds. The technical complexities of the curved models, however, mean that analytic solutions are possible only in special, though characteristic, moments in the lifetime of these universes. Nevertheless, our solutions exhibit persistent patterns that make us confident enough to generalize them. Thus, we confirm earlier claims that, compared to the Newtonian and the quasi-Newtonian studies, the relativistic analysis supports considerably stronger linear growth rates for peculiar-velocity perturbations. This result holds irrespective of the background curvature. Moreover, for positive curvature, the peculiar growth rate is found to be faster than that obtained in a spatially flat Friedman universe. In contrast, linear peculiar velocities appear to grow at a slower pace when their Friedmann host is spatially open. Extrapolating them to the present, our results seem to suggest faster bulk peculiar motions in overdense, rather than in underdense, regions of the Universe. Published by the American Physical Society 2024

Comparing Analytic and Numerical Studies of Tensor Perturbations in Loop Quantum Cosmology

We investigate the implications of different quantization approaches in Loop Quantum Cosmology for the primordial power spectrum of tensor modes. Specifically, we consider the hybrid and dressed metric approaches to derive the effective mass that governs the evolution of the tensor modes. Our study comprehensively examines the two resulting effective masses and how to estimate them in order to obtain approximated analytic solutions to the tensor perturbation equations. Since Loop Quantum Cosmology incorporates preinflationary effects in the dynamics of the perturbations, we do not have at our disposal a standard choice of privileged vacuum, like the Bunch–Davies state in quasi-de Sitter inflation. We then select the vacuum state by a recently proposed criterion which removes unwanted oscillations in the power spectrum and guarantees an asymptotic diagonalization of the Hamiltonian in the ultraviolet. This vacuum is usually called the NO-AHD (from the initials of Non-Oscillating with Asymptotic Hamiltonian Diagonalization) vacuum. Consequently, we compute the power spectrum by using our analytic approximations and by introducing a suitable numerical procedure, adopting in both cases an NO-AHD vacuum. With this information, we compare the different spectra obtained from the hybrid and the dressed metric approaches, as well as from the analytic and numerical procedures. In particular, this proves the remarkable accuracy of our approximations.

Selecting energy–momentum trace dependent gravity theories with LSS

We study scalar cosmological perturbations in f(R,T) modified gravity theories, where T represents the trace of the energy–momentum tensor. We provide detailed equations for the matter energy density contrast. We solve them numerically to facilitate a comparison with available large-scale structure (LSS) formation observational data on fσ8, while also addressing the S8 tension. We identify f(R,T) models that either lead to growth enhancement or suppression. Since recent results in the literature indicate a preference for the latter feature, this type of analysis is quite useful for selecting viable modifications of gravity. The studied class of such f(R,T) models are either ruled out or severely restricted. After selecting the surviving f(R,T) models we show how they deal with the S8 tension.

Scalar cosmological perturbations from quantum gravitational entanglement

Abstract A major challenge at the interface of quantum gravity and cosmology is to explain the emergence of the large-scale structure of the Universe from Planck scale physics. In this letter, we extract the dynamics of scalar isotropic cosmological perturbations from full quantum gravity, as described by the causally complete Barrett-Crane group field theory model. From the perspective of the underlying quantum gravity theory, cosmological perturbations are represented as nearest-neighbor two-body entanglement of group field theory quanta. Their effective dynamics is obtained via mean-field methods and described relationally with respect to a causally coupled physical Lorentz frame. We quantitatively study these effective dynamical equations and show that at low energies they are perfectly consistent with those of General Relativity, while for trans-Planckian scales quantum effects become important. These results therefore not only provide crucial insights into the potentially purely quantum gravitational nature of cosmological perturbations, but also offer rich phenomenological implications for the physics of the early Universe.

Entanglement and Generalized Berry Geometrical Phases in Quantum Gravity

A new formalism is introduced that makes it possible to elucidate the physical and geometric content of quantum space–time. It is based on the Minimum Group Representation Principle (MGRP). Within this framework, new results for entanglement and geometrical/topological phases are found and implemented in cosmological and black hole space–times. Our main results here are as follows: (i) We find the Berry phases for inflation and for the cosmological perturbations and express them in terms of the observables, such as the spectral scalar and tensor indices, nS and nT, and the tensor-to-scalar ratio r. The Berry phase for de Sitter inflation is imaginary with the sign describing the exponential acceleration. (ii) The pure entangled states in the minimum group (metaplectic) Mp(n) representation for quantum de Sitter space–time and black holes are found. (iii) For entanglement, the relation between the Schmidt type representation and the physical states of the Mp(n) group is found: This is a new non-diagonal coherent state representation complementary to the known Sudarshan diagonal one. (iv) Mean value generators of Mp(2) are related to the adiabatic invariant and topological charge of the space–time, (matrix element of the transition −∞<t<∞). (v) The basic even and odd n-sectors of the Hilbert space are intrinsic to the quantum space–time and its discrete levels (in particular, continuum for n→∞), they do not require any extrinsic generation process such as the standard Schrodinger cat states, and are entangled. (vi) The gravity or cosmological on one side and another of the Planck scale are entangled. Examples: The quantum primordial trans-Planckian de Sitter vacuum and the classical late de Sitter vacuum today; the central quantum gravity region and the external classical gravity region of black holes. The classical and quantum dual gravity regions of the space–time are entangled. (vii) The general classical-quantum gravity duality is associated with the Metaplectic Mp(n) group symmetry which provides the complete full covering of the phase space and of the quantum space–time mapped from it.

Analytic and numerical study of scalar perturbations in loop quantum cosmology

Analytic and numerical study of scalar perturbations in loop quantum cosmology

String theory and the first half of the universe

We perform a detailed study of stringy moduli-driven cosmologies between the end of inflation and the commencement of the Hot Big Bang, including both the background and cosmological perturbations: a period that can cover half the lifetime of the universe on a logarithmic scale. Compared to the standard cosmology, stringy cosmologies with vacua that address the hierarchy problem motivate extended kination, tracker and moduli-dominated epochs involving significantly trans-Planckian field excursions.We analyse the cosmology within the framework of the Large Volume Scenario but explain how analogous cosmological features are expected in other string theory models characterized by final vacua located in the asymptotic regions of moduli space.Conventional effective field theory is unable to control Planck-suppressed operators and so such epochs require a stringy completion for a consistent analysis. Perturbation growth in these stringy cosmologies is substantially enhanced compared to conventional cosmological histories. The transPlanckian field evolution results in radical changes to Standard Model couplings during this history and we outline potential applications to baryogenesis, dark matter and gravitational wave production.

Dissipative quintessential cosmic inflation

In this paper we construct a dissipative quintessential cosmic inflation. For this purpose, we add a multiplicative dissipative term in the standard quintessence field Lagrangian. We consider the specific form of dissipation as the time integral including the Hubble parameter and an arbitrary function that describes the dissipative properties of the quintessential scalar field. Inflation parameters and observables are calculated under slow-roll approximations and a detailed calculation of the cosmological perturbations is performed in this setup. We consider different forms of potentials and calculate the scalar spectral index and tensor-to-scalar ratio for a constant as well as variable dissipation function. To check the reliability of this model, a numerical analysis on the model parameters space is done in confrontation with recent observational data. By comparing the results with observational joint datasets at 68% and 95% confidence levels, we obtain some constraints on the model parameters space, specially the dissipation factor with e-folds numbers N=55 and N=60. As some specific results, we show that the power-law potential with a constant dissipation factor and N=60 is mildly consistent with observational data in some restricted domains of the model parameter space with very small and negative dissipation factor and a negligible tensor-to-scalar ratio. But this case with N=55 is consistent with observation considerably. For power-law potential and variable dissipation factor as Q=αϕn, the consistency with observation is also considerable with a reliable tensor-to-scalar ratio. The quadratic and quartic potentials with variable dissipation function as Q=αϕn are consistent with Planck2018 TT, TE, EE+lowE+lensing data at the 68% and 95% levels of confidence for some intervals of the parameter n.

Model for cosmological perturbations in affine gravity

Model for cosmological perturbations in affine gravity

Gravitational waves with generalized holonomy corrections

The cosmological tensor perturbation equation with generalized holonomy corrections is derived in the framework of effective loop quantum gravity. This results in a generalized dispersion relation for gravitational waves, encompassing holonomy corrections. Furthermore, we conduct an examination of the constraint algebra concerning vector modes with generalized holonomy corrections. The requirement of anomaly cancellation for vector modes imposes constraints on the possible functional forms of the generalized holonomy corrections. What’s more, we estimate the theoretical value of the effective graviton mass and discuss the potential detectability of this effective mass in future observations.

Perturbation-theory informed integrators for cosmological simulations

Large-scale cosmological simulations are an indispensable tool for modern cosmology. To enable model-space exploration, fast and accurate predictions are critical. In this paper, we show that the performance of such simulations can be further improved with time-stepping schemes that use input from cosmological perturbation theory. Specifically, we introduce a class of time-stepping schemes derived by matching the particle trajectories in a single leapfrog/Verlet drift-kick-drift step to those predicted by Lagrangian perturbation theory (LPT). As a corollary, these schemes exactly yield the analytic Zel'dovich solution in 1D in the pre-shell-crossing regime (i.e. before particle trajectories cross). One representative of this class is the popular ‘FastPM’ scheme by Feng et al. 2016[1], which we take as our baseline. We then construct more powerful LPT-inspired integrators and show that they outperform FastPM and standard integrators in fast simulations in two and three dimensions with O(1−100) timesteps, requiring fewer steps to accurately reproduce the power spectrum and bispectrum of the density field. Furthermore, we demonstrate analytically and numerically that, for any integrator, convergence is limited in the post-shell-crossing regime (to order 32 for planar-wave collapse), owing to the lacking regularity of the acceleration field, which makes the use of high-order integrators in this regime futile. Also, we study the impact of the timestep spacing and of a decaying mode present in the initial conditions. Importantly, we find that symplecticity of the integrator plays a minor role for fast approximate simulations with a small number of timesteps.