We study the quantum circuit complexity of cosmological perturbations in different models of the early universe. A natural measure for the complexity of cosmological perturbations is based on the symplectic group, allowing us to identify complexity with geodesics in the hyperbolic plane. We investigate the complexity of both the mode functions and the physical perturbations, arguing that the latter often provides a more insightful description of the physics involved. In all models the total complexity reached is rather large. Inflationary perturbations may be represented by a comparatively simple quantum circuit, while the perturbations during a matter-dominated contracting phase present the most rapid growth in complexity. Ekpyrotic perturbations reside in the middle and are distinguished by the smallest growth of complexity before horizon exit. Our analysis serves to highlight how different cosmological models achieve the same end result for the perturbations via different routes and how all models show a pronounced sensitivity to initial conditions.
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.
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})…
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.
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…
We briefly review the need to perform renormalization of inflationary perturbations to properly work out the physical power spectra. We also summarize the basis of (momentum-space) renormalization in curved spacetime and address several misconceptions found in recent literature on this subject.
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 investigate the relation between the non-Gaussianities of the primordial perturbations and the sound speed of the tensor perturbations, that is, the propagation speed of the gravitational waves. We find that the sound speed of the tensor perturbations is directly related not to the auto-bispectrum of the tensor perturbations but to the cross-bispectrum of the primordial perturbations, especially, the scalar-tensor-tensor bispectrum. This result is in sharp contrast with the case of the scalar (curvature) perturbations, where their reduced sound speed enhances their auto-bispectrum. Our find…
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.
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 …
We study effects on the luminosity distance of a local inhomogeneity seeded by primordial curvature perturbations of the type predicted by the inflationary scenario and constrained by the cosmic microwave background radiation. We find that a local underdensity originated from a one, two or three standard deviations peaks of the primordial curvature perturbations field can induce corrections to the value of a cosmological constant of the order of $0.6%,1%,1.5%$ respectively. These effects cannot be neglected in the precision cosmology era in which we are entering. Our results can be considered …
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 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.
We consider the presence and evolution of primordial density perturbations in a cosmological model based on a simple ansatz which captures -- by providing a set of effective gravitational field equations -- the strength of the enhanced quantum loop effects that can arise during inflation. After deriving the general equations that perturbations obey, we concentrate on scalar perturbations and show that their evolution is quite different than that of conventional inflationary models but still phenomenologically acceptable. The main reason for this novel evolution is the presence of an oscillatin…
We investigate the primordial trispectra of the general multifield DBI inflationary model. In contrast with the single field model, the entropic modes can source the curvature perturbations on the super horizon scales, so we calculate the contributions from the interaction of four entropic modes mediating one adiabatic mode to the trispectra, at the large transfer limit ($T_{RS}\gg1$). We obtained the general form of the 4-point correlation functions, plotted the shape diagrams in two specific momenta configurations, "equilateral configuration" and "specialized configuration". Our figures show…
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 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…
We show that if the inflaton effective potential has multiple discontinuous points in its first derivative, the spectrum of primordial perturbation will be multiple step-like. We give a general analysis by applying a simple model. In principle, as long as the height of step is low enough, the result of spectrum will be consistent with observations.
In this paper we study the generation of primordial perturbation with a modified dispersion relation in various cosmological evolutions. We stress that the formation of the power spectrum is strongly dependent on the background. Working in a bounce model with a matter-like contracting phase, we obtain a red tilt spectrum due to the modified dispersion relation.
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.
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 compute the full bispectra, namely both auto- and cross- bispectra, of primordial curvature and tensor perturbations in the most general single-field inflation model whose scalar and gravitational equations of motion are of second order. The formulae in the limits of k-inflation and potential-driven inflation are also given. These expressions are useful for estimating the full bispectra of temperature and polarization anisotropies of the cosmic microwave background radiation.
We investigate thermal inflation in double-screen entropic cosmology. We find that its realization is general, resulting from the system evolution from non-equilibrium to equilibrium. Furthermore, going beyond the background evolution, we study the primordial curvature perturbations arising from the universe interior, as well as from the thermal fluctuations generated on the holographic screens. We show that the power spectrum is nearly scale-invariant with a red tilt, while the tensor-to-scalar ratio is in agreement with observations. Finally, we examine the non-Gaussianities of primordial cu…
We propose a simple analytic fit for the power spectrum of scalar (curvature) perturbations during inflation, in order to describe slow roll of inflaton and formation of primordial black holes in the early universe, in the framework of single-field models. Our fit is given by a sum of the power spectrum in the slow-roll approximation, needed for a viable description of the cosmic microwave background radiation in agreement with Planck/BICEP/Keck measurements, and the log-normal (Gaussian) fit for the power spectrum enhancement (peak) needed for efficient production of primordial black holes. W…
We propose a mechanism to evade the Lyth bound in models of inflation. We minimally extend the conventional single-field inflation model in general relativity (GR) to a theory with non-vanishing graviton mass in the very early universe. The modification primarily affects the tensor perturbation, while the scalar and vector perturbations are the same as the ones in GR with a single scalar field at least at the level of linear perturbation theory. During the reheating stage, the graviton mass oscillates coherently and leads to resonant amplification of the primordial tensor perturbation. After r…
We propose a new mechanism to generate primordial curvature perturbations, based on the resonant production of particles during inflation. It is known that this phenomenon can trap the inflaton for a fraction of e-fold. This effect is governed by the mass of the produced particles and by their coupling to the inflaton, parameters which can depend on the expectation value of other fields. If one of such additional fields - a 'modulaton' - is light, then its fluctuations, acquired during the earlier stages of inflation, will induce a spatial modulation of the trapping, and thus of the end of inf…
We derive a formula for the halo/galaxy bispectrum on the basis of the integrated Perturbation Theory (iPT). In addition to the gravity-induced non-Gaussianity, we consider the non-Gaussianity of the primordial curvature perturbations, and investigate in detail the effect of such primordial non-Gaussianity on the large-scale halo/galaxy bispectrum. In iPT, the effects of primordial non-Gaussianity are wholly encapsulated in the linear (primordial) polyspectra, and we systematically calculate the contributions to the large-scale behaviors arising from the three types of primordial bispectrum (l…
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…
A contribution $ζ_χ$ to the curvature perturbation will be generated during the waterfall that ends hybrid inflation, that may be significant on small scales. In particular, it may lead to excessive black hole formation. We here consider standard hybrid inflation, where the tachyonic mass of the waterfall field is much bigger than the Hubble parameter. We calculate $ζ_χ$ in the simplest case, and see why earlier calculations of $ζ_χ$ are incorrect.
Non-linear CMB temperature anisotropies up to the third-order on large scales are calculated. On large scales and in the Sachs-Wolfe limit, we give the explicit expression for the observed temperature anisotropy in terms of the primordial curvature perturbation up to the third-order. We derived the final bispectrum and trispectrum of anisotropies and the corresponding non-linear parameters, in which the contributions to the observed non-Gaussianity from primordial perturbations and from the non-linear mapping from primordial curvature perturbation to the temperature anisotropy are transparentl…
We analytically derive a more accurate formula for the power spectrum of the biased objects with the primordial non-Gaussianity parameterized not only by the non-linearity parameter fNL, but also by gNL and tauNL which characterize the trispectrum of the primordial curvature perturbations. We adopt the integrated perturbation theory which was constructed in Matsubara (2011). We discuss an inequality between fNL and tauNL in the context of the scale-dependent bias, by introducing a stochasticity parameter. We also mention higher order loop corrections into the scale-dependency of the bias param…
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.
Based on the effective field theory (EFT) of nonsingular cosmologies, we build a stable model, without the ghost and gradient instabilities, of bounce inflation (inflation is preceded by a cosmological bounce). We perform a full simulation for the evolution of scalar perturbation, and find that the perturbation spectrum has a large-scale suppression (as expected), which is consistent with the power deficit of the cosmic microwave background (CMB) TT-spectrum at low multipoles, but unexpectedly, it also shows itself one marked lower valley, which actually provides a better fit to the dip at mul…
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.
While loop quantum cosmology (LQC) predicts a robust quantum bounce of the background evolution of a Friedmann-Robertson-Walker (FRW) spacetime prior to the standard slow-roll inflation, whereby the big bang singularity is resolved, there are several different quantization procedures to cosmological perturbations, for instance, {\em the deformed algebra, dressed metric, and hybrid quantizations}. This paper devotes to study the quantum bounce effects of primordial perturbations in the hybrid approach. The main discrepancy of this approach is the effective positive mass at the quantum bounce fo…
We study the primordial perturbations generated during a stage of single-field inflation in Einstein-aether theories. Quantum fluctuations of the inflaton and aether fields seed long wavelength adiabatic and isocurvature scalar perturbations, as well as transverse vector perturbations. Geometrically, the isocurvature mode is the potential for the velocity field of the aether with respect to matter. For a certain range of parameters, this mode may lead to a sizable random velocity of the aether within the observable universe. The adiabatic mode corresponds to curvature perturbations of co-movin…
Scalar-tensor gravity is one of the most competitive gravity theory to Einstein's relativity. We reconstruct the exact de Sitter solution in scalar-tensor gravity, in which the non-minimal coupling scalar is rolling along the potential. This solution may have some relation to the early inflation and present acceleration of the universe. We investigated its primordial quantum perturbation around the adiabatic vacuum. We put forward for the first time that exact de Sitter generates non-exactly scale invariant perturbations. In the conformal coupling case, this model predicts that the tensor mode…
In this article, we investigate various physical implications of quantum circuit complexity using squeezed state formalism of Primordial Gravitational Waves (PGW). Recently quantum information theoretic concepts, such as entanglement entropy, and complexity are playing a pivotal role to understand the dynamics of quantum system even in the diverse fields such as, high energy physics and cosmology. This paper is devoted in studying quantum circuit complexity of PGW for various cosmological models, such as de Sitter, inflation, radiation, reheating, matter, bouncing, cyclic and black hole gas mo…
We characterise the primordial perturbations produced due to both inflaton and curvaton fluctuations in models where the curvaton has a quadratic, cosine or hyperbolic potential, and the inflaton potential is characterised by the usual slow-roll parameters. Isocurvature curvaton field perturbations can produce significant non-Gaussianity in the primordial density field, in contrast with adiabatic inflaton field perturbations which produce negligible non-Gaussianity for canonical scalar fields. A non-self-interacting curvaton with quadratic potential produces a local-type non-Gaussianity that i…
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 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 …
One-loop correction to the power spectrum in generic single-field inflation is calculated by using standard perturbation theory. Because of the enhancement inversely proportional to the observed red tilt of the spectral index of curvature perturbation, the correction turns out to be much larger than previously anticipated. As a result, the primordial non-Gaussianity must be much smaller than the current observational bound in order to warrant the validity of cosmological perturbation theory.
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…
Recently, Hořava has proposed a renormalizable theory of gravity with critical exponent z=3 in the UV. This proposal might imply the scale invariant primordial perturbation can be generated in any expansion of early universe with a\sim t^n and n>1/3, which, in this note, will be validated by solving the motion equation of perturbation mode on super sound horizon scale for any background evolution of early universe. However, it is found that it seems that if we require the efolding number of primordial perturbation is suitable for observable universe, n>1 still need to be satisfied, unless the …
In a previous work we have exhibited a clear description of the quantum-to-classical transition of cosmological quantum fluctuations in the inflationary scenario using the de Broglie-Bohm quantum theory. These fluctuations are believed to seed the small inhomogeneities, which are then responsible for the formation of large scale structures. In this work we show that using the de Broglie-Bohm theory it is also possible to describe the quantum-to-classical transition of primordial perturbations which takes place around a bouncing phase, even if the latter is caused by quantum effects due to the …
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 compute the three-point cross-correlation function of the primordial curvature perturbation generated during inflation with two powers of a vector field in a model where conformal invariance is broken by a direct coupling of the vector field with the inflaton. If the vector field is identified with the electromagnetic field, this correlation would be a non-Gaussian signature of primordial magnetic fields generated during inflation. We find that the signal is maximized for the flattened configuration where the wave number of the curvature perturbation is twice that of the vector field and in…
