super-Hubble Scales Research Articles

Production of ultralight dark matter from inflationary spectator fields

We investigate inflationary particle production associated with a spectator ultralight scalar field, which has recently been proposed as a plausible dark matter candidate. In this framework, we select the Starobinsky potential to drive the inflationary epoch, also discussing the case of a nonminimally coupled inflaton field fueled by a quartic symmetry-breaking potential. We focus on particle production arising from spacetime perturbations, which are induced by inflaton fluctuations during the quasi–de Sitter stage of inflation. In particular, we construct the first-order Lagrangian describing interaction between inhomogeneities and the spectator field, quantifying superhorizon particle production during slow-roll. We then compare this mechanism with gravitational particle production associated with an instantaneous transition from inflation to the radiation dominated era. We show that the number of particles obtained from perturbations is typically non-negligible, and it is significantly enhanced on super-Hubble scales by the nonadiabatic inflationary expansion. Possible implications for primordial entanglement generation are also debated. Published by the American Physical Society 2024

The separate-universe approach and sudden transitions during inflation

The separate-universe approach gives an intuitive way to understand the evolution of cosmological perturbations in the long-wavelength limit. It uses solutions of the spatially-homogeneous equations of motion to model the evolution of the inhomogeneous universe on large scales. We show that the separate-universe approach fails on a finite range of super-Hubble scales at a sudden transition from slow roll to ultra-slow roll during inflation in the very early universe. Such transitions are a feature of inflation models giving a large enhancement in the primordial power spectrum on small scales, necessary to produce primordial black holes after inflation. We show that the separate-universe approach still works in a piece-wise fashion, before and after the transition, but spatial gradients on finite scales require a discontinuity in the homogeneous solution at the transition. We discuss the implications for the δN formalism and stochastic inflation, which employ the separate-universe approximation.

Holographic realization of constant roll inflation and dark energy: An unified scenario

In the formalism of generalized holographic dark energy, the infrared cut-off LIR is generalized to the form, LIR=LIR(Lp,L˙p,L¨p,⋯,Lf,L˙f,L¨f,⋯,a,H,H˙,H¨,⋯), where Lp and Lf are the particle horizon and the future horizon, respectively (moreover, a is the scale factor and H is the Hubble parameter of the universe). Based on such formalism, we establish a holographic realization of constant roll inflation during the early universe, where the corresponding cut-off depends on the Hubble parameter and its derivatives (up to the second order). The viability of this holographic constant roll inflation with respect to the Planck data in turn puts a certain bound on the infrared cut-off at the time of horizon crossing. Such holographic correspondence of constant roll inflation is extended to the scenario where the infrared cut-off is corrected by the ultraviolet one, which may originate due to quantum effects. Besides the mere inflation, we further propose the holographic realization of an unified cosmic scenario from constant roll inflation (at the early time) to the dark energy era (at the late time) with an intermediate radiation dominated era followed by a Kamionkowski like reheating stage. In such a unified holographic scenario, the inflationary quantities (like the scalar spectral index and the tensor-to-scalar ratio) and the dark energy quantities (like the dark energy EoS parameter and the present Hubble rate) prove to be simultaneously compatible with observable constraints for suitable ranges of the infrared cut-off and the other model parameters. Moreover the curvature perturbations at super-Hubble scale prove to be a constant (with time) during the entire cosmic era, which in turn ensures the stability of the model under consideration.

Scale-invariant enhancement of gravitational waves during inflation

The inflationary 1-loop tensor power spectrum from a spectator scalar field with a sharp peak is calculated. Recent studies on primordial black holes suggest that the inflationary curvature perturbation may be huge on small scales. An enhanced curvature perturbation may arise from a drastic enhancement of spectator scalar field fluctuations. In this paper, using the in-in formalism, we calculate 1-loop quantum corrections to primordial gravitational waves by such a spectator field with a sharp peak in momentum space. We find scale-invariant loop corrections in this full quantum setup, in contrast to the sharply peaked corrections in the previously calculated scalar-induced tensor modes. Especially on super Hubble scales, the primordial gravitational waves are also amplified, which can be understood as a Bogoliubov transformation of the vacuum due to the enhanced scalar field. This mechanism allows us to probe the scalar field properties on extremely short-distance scales with the current and future cosmic microwave background and gravitational wave experiments, opening a novel window for inflationary cosmology.

Suppression of scalar power on large scales and associated bispectra

A sharp cutoff in the primordial scalar power spectrum on large scales has been known to improve the fit to the cosmic microwave background (CMB) data when compared to the more standard, nearly scale invariant power spectra that arise in slow roll inflation. Over the last couple of years, there has been resurgent interest in arriving at such power spectra in models with kinetically dominated initial conditions for the background scalar field which leads to inflation of specific duration. In an earlier work, we had numerically investigated the characteristics of the scalar bispectrum generated in such models. In this work, we compare the scenario with two other competing scenarios (viz., punctuated inflation and a model proposed by Starobinsky) which also suppress the scalar power in a roughly similar fashion on large scales. We further consider two other scenarios involving inflation of a finite duration, one wherein the scalar field begins on the inflationary attractor and another wherein the field starts with a smaller velocity and evolves toward the attractor. These scenarios too exhibit a sharp drop in power on large scales if the initial conditions on the perturbations for a range of modes are imposed on super-Hubble scales as in the kinetically dominated model. We compare the performance of all the models against the Planck CMB data at the level of scalar power spectra. The model wherein the background field always remains on the inflationary attractor is interesting for the reason that it permits analytical calculations of the scalar power and bi-spectra. We also compare the amplitudes and shapes of the scalar non-Gaussianity parameter ${f}_{\mathrm{NL}}$ in all these cases which lead to scalar power spectra of similar form. Interestingly, we find that, in the models wherein the initial conditions on the perturbations are imposed on super-Hubble scales, the consistency relation governing the scalar bispectrum is violated for the large-scale modes, whereas the relation is satisfied for all the modes in the other scenarios. These differences in the behavior of the scalar bispectra can conceivably help us observationally discriminate between the various models which lead to scalar power spectra of roughly similar shape.

A void in the Hubble tension? The end of the line for the Hubble bubble

The Universe may feature large-scale inhomogeneities beyond the standard paradigm, implying that statistical homogeneity and isotropy may be reached only on much larger scales than the usually assumed ∼100 Mpc. This means that we are not necessarily typical observers and that the Copernican principle could be recovered only on super-Hubble scales. Here, we do not assume the validity of the Copernican principle and let cosmic microwave background, baryon acoustic oscillations, type Ia supernovae, local H 0, cosmic chronometers, Compton y-distortion and kinetic Sunyaev–Zeldovich observations constrain the geometrical degrees of freedom of the local structure, which we parametrize via the ΛLTB model—basically a non-linear radial perturbation of a FLRW metric. In order to quantify if a non-Copernican structure could explain away the Hubble tension, we pay careful attention to computing the Hubble constant in an inhomogeneous Universe, and we adopt model selection via both the Bayes factor and the Akaike information criterion. Our results show that, while the ΛLTB model can successfully explain away the H 0 tension, it is favored with respect to the ΛCDM model only if one solely considers supernovae in the redshift range that is used to fit the Hubble constant, that is, 0.023 < z < 0.15. If one considers all the supernova sample, then the H 0 tension is not solved and the support for the ΛLTB model vanishes. Combined with other data sets, this solution to the Hubble tension barely helps. Finally, we have reconstructed our local spacetime. We have found that data are best fit by a shallow void with δ L ≈ −0.04 and Mpc, which, interestingly, lies on the border of the 95% credible region relative to the standard model expectation.

Interacting dark sector from the trace-free Einstein equations: Cosmological perturbations with no instability

In trace-free Einstein gravity, the stress-energy tensor of matter is not necessarily conserved and so the theory offers a natural framework for interacting dark energy models where dark energy has a constant equation of state $w=-1$. We derive the equations of motion for linear cosmological perturbations in interacting dark energy models of this class, focusing on the scalar sector. Then, we consider a specific model where the energy-momentum transfer potential is proportional to the energy density of cold dark matter; this transfer potential has the effect of inducing an effective equation of state $w_{\rm eff}\neq0$ for cold dark matter. We analyze in detail the evolution of perturbations during radiation domination on super-Hubble scales, finding that the well-known large-scale instability that affects a large class of interacting dark energy models is absent in this model. To avoid a gradient instability, energy must flow from dark matter to dark energy. Finally, we show that interacting dark energy models with $w=-1$ are equivalent to a class of generalized dark matter models.

Primordial black hole formation from massless scalar isocurvature

We numerically study the primordial black hole (PBH) formation by an isocurvature perturbation of a massless scalar field on super Hubble scales in the radiation-dominated Universe. As a first step we perform simulations of spherically symmetric configurations. For the initial condition, we employ the spatial gradient expansion and provide the general form of the growing mode solutions valid up through the second order in this expansion. The initial scalar field profile is assumed to be Gaussian with a characteristic comoving wave number $k$; $\ensuremath{\sim}\mathrm{exp}(\ensuremath{-}{k}^{2}{R}^{2})$, where $R$ is the radial coordinate. We find that a PBH is formed for a sufficiently large amplitude of the scalar field profile. Nevertheless, we find that the late time behavior of the gravitational collapse is dominated by the dynamics of the fluid but not by the scalar field, which is analogous to the PBH formation from an adiabatic perturbation in the radiation-dominated Universe.

Inflationary model in minimally modified gravity theories

We have investigated inflationary model constructed from minimally modified gravity (MMG) theories. The MMG theory in the form of $f({\bf H}) \propto {\bf H}^{1+p}$ gravity where, ${\bf H}$ is the Hamiltonian constraint in the Einstein gravity and $p$ is constant, has been studied. An inflation is difficult to be achieved in this theory of gravity unless an additional scalar field playing a role of inflaton is introduced in the model. We have found that the inflaton with exponential potential can drive inflation with graceful exist different from the case of Einstein gravity. The slow-roll parameter for both the exponential and the power-law potentials is inversely proportional to number of e-folding similar to the case of the Einstein gravity. We also have found for the scalar perturbation that the curvature perturbation in the comoving gauge on super Hubble radius scales grows rapidly during inflation unless $p =0$. For the tensor modes, the amplitude of the perturbations is constant on large scales, and sound speed of the perturbations can diviate from unity and can vary with time depending on the form of $f({\bf H})$.

Perturbations in tachyon dark energy and their effect on matter clustering

A non-canonical scalar tachyon field is a viable candidate for dark energy and has been found to be in good agreement with observational data. Background data alone cannot completely rule out degeneracy between this model and others. To further constrain the parameters, apart from the distance measurements, we study perturbations in tachyon scalar field and how they affect matter clustering. We consider two tachyon potentials for this study, an inverse square potential and an exponential potential. We study the evolution of the gravitational potential, matter density contrast and dark energy density contrast, and compare them with the evolution in the ΛCDM model. Although perturbations in dark energy at sub-Hubble scales are negligible in comparison with matter perturbations, they cannot be ignored at Hubble and super-Hubble scales (λp > 1000 Mpc). We also study the evolution of growth function and growth rate of matter, and find that the growth rate is significantly suppressed in dark energy dominated era with respect to the growth rate for Λ CDM model. A comparison of these models with Redshift Space Distortion growth rate data is presented by way of calculating fσ8(z). There is a tension of 2.9σ (2.26σ) between growth rate data and Planck-2015 (Planck-2018) Cosmic Microwave Background Radiation data for Λ CDM model. We present constraints on free parameters of these models and show that perturbations in tachyon scalar field reduce this tension between different data sets.

Can a nonminimal coupling restore the consistency condition in bouncing universes?

An important property of the three-point functions generated in the early universe is the so-called consistency condition. According to the condition, in the squeezed limit wherein the wavenumber of one of the three modes (constituting the triangular configuration of wavevectors) is much smaller than the other two, the three-point functions can be completely expressed in terms of the two-point functions. It is found that, while the consistency condition is mostly satisfied by the primordial perturbations generated in the inflationary scenario, it is often violated in the bouncing models. The validity of the consistency condition in the context of inflation can be attributed to the fact that the amplitude of the scalar and tensor perturbations freeze on super-Hubble scales. Whereas, in the bouncing scenarios, the amplitude of the scalar and tensor perturbations often grow rapidly as one approaches the bounce, leading to a violation of the condition. In this work, with the help of a specific example involving the tensor perturbations, we explicitly show that suitable non-minimal couplings can restore the consistency condition even in the bouncing models. We briefly discuss the implications of the result.

Clustering of primordial black holes with non-Gaussian initial fluctuations

Abstract We formulate the two-point correlation function of primordial black holes (PBHs) at their formation time, based on the functional integration approach which has often been used in the context of halo clustering. We find that PBH clustering on super-Hubble scales could never be induced in the case where the initial primordial fluctuations are Gaussian, while it can be enhanced by the so-called local-type trispectrum (four-point correlation function) of the primordial curvature perturbations.

Inflationary perturbations with Lifshitz scaling

Instead of Lorentz invariance, gravitational degrees of freedom may obey Lifshitz scaling at high energies, as it happens in Hořava's proposal for quantum gravity. We study consequences of this proposal for the spectra of primordial perturbations generated at inflation. Breaking of 4D diffeomorphism (Diff) invariance down to the foliation-preserving Diff in Hořava-Lifshitz (HL) gravity leads to appearance of a scalar degree of freedom in the gravity sector, khronon, which describes dynamics of the time foliation. One can naively expect that mixing between inflaton and khronon will jeopardize conservation of adiabatic perturbations at super Hubble scales. This indeed happens in the projectable version of the theory. By contrast, we find that in the non-projectable version of HL gravity, khronon acquires an effective mass which is much larger than the Hubble scale well before the Hubble crossing time and decouples from the adiabatic curvature perturbation ζ sourced by the inflaton fluctuations. As a result, at super Hubble scales the adiabatic perturbation ζ behaves as in an effectively single field system and its spectrum is conserved in time. Lifshitz scaling is imprinted in the power spectrum of ζ through the modified dispersion relation of the inflaton. We point out violation of the consistency relation between the tensor-to-scalar ratio and the spectral tilt of primordial gravitational waves and suggest that it can provide a signal of Lorentz violation in inflationary era.

Open quantum cosmological system

We derive the evolution equation for the density matrix of a UV- and IR- limited band of comoving momentum modes of the canonically normalized scalar degree of freedom in two examples of nearly de Sitter universes. Including the effects of a cubic interaction term from the gravitational action and tracing out a set of longer wavelength modes, we find that the evolution of the system is non-Hamiltonian and non-Markovian. We find linear dissipation terms for a few modes with wavelength near the boundary between system and bath and nonlinear dissipation terms for all modes. The non-Hamiltonian terms persist to late times when the scalar field dynamics is such that the curvature perturbation continues to evolve on super-Hubble scales.

Constraints on long-lived, higher-spin particles from the galaxy bispectrum

The presence of massive particles with spin during inflation induces distinct signatures on correlation functions of primordial curvature fluctuations. In particular, the bispectrum of primordial perturbations obtains an angular dependence determined by the spin of the particle, which can be used to set constraints on the presence of such particles. If these particles are long-lived on super-Hubble scales, as is the case, e.g., for partially massless particles, their imprint on correlation functions of curvature perturbations would be unsuppressed. In this paper, we make a forecast for how well such angular dependence can be constrained by the upcoming EUCLID spectroscopic survey via the measurement of the galaxy bispectrum.

Detecting higher spin fields through statistical anisotropy in the CMB bispectrum

Inflation may provide a suitable collider to probe physics at very high energies. In this paper we investigate the impact on the CMB bispectrum of higher spin fields which are long-lived on super-Hubble scales, e.g. partially massless higher spin fields. We show that distinctive statistical anisotropic signals on the CMB three-point correlator are induced and we investigate their detectability.

On the Magnetic Evolution in Friedmann Universes and the Question of Cosmic Magnetogenesis

We analyse the evolution of primordial magnetic fields in spatially flat Friedmann universes and reconsider the belief that, after inflation, these fields decay adiabatically on all scales. Without abandoning classical electromagnetism or standard cosmology, we demonstrate that this is not necessarily the case for superhorizon-sized magnetic fields. The underlying reason for this is causality, which confines the post-inflationary process of electric-current formation, electric-field elimination and magnetic-flux freezing within the horizon. As a result, the adiabatic magnetic decay is not a priori guaranteed on super-Hubble scales. Instead, after inflation, large-scale magnetic fields obey a power-law solution, where one of the modes drops at a rate slower than the adiabatic. Whether this slowly decaying mode can dominate and dictate the post-inflationary magnetic evolution depends on the initial conditions. These are determined by the evolution of the field during inflation and by the nature of the transition from the de Sitter phase to the reheating era and then to the subsequent epochs of radiation and dust. We discuss two alternative and complementary scenarios to illustrate the role and the implications of the initial conditions for cosmic magnetogenesis. Our main claim is that magnetic fields can be superadiabatically amplified after inflation, as long as they remain outside the horizon. This means that inflation-produced fields can reach astrophysically relevant residual strengths without breaking away from standard physics. Moreover, using the same causality arguments, one can constrain (or in some cases assist) the non-conventional scenarios of primordial magnetogenesis that amplify their fields during inflation. Finally, we show that our results extend naturally to the marginally open and the marginally closed Friedmann universes.

Cosmological perturbations on the phantom brane

We obtain a closed system of equations for scalar perturbations in a multi-component braneworld. Our braneworld possesses a phantom-like equation of state at late times, weff < −1, but no big-rip future singularity. In addition to matter and radiation, the braneworld possesses a new effective degree of freedom—the `Weyl fluid' or `dark radiation'. Setting initial conditions on super-Hubble spatial scales at the epoch of radiation domination, we evolve perturbations of radiation, pressureless matter and the Weyl fluid until the present epoch. We observe a gradual decrease in the amplitude of the Weyl-fluid perturbations after Hubble-radius crossing, which results in a negligible effect of the Weyl fluid on the evolution of matter perturbations on spatial scales relevant for structure formation. Consequently, the quasi-static approximation of Koyama and Maartens provides a good fit to the exact results during the matter-dominated epoch. We find that the late-time growth of density perturbations on the brane proceeds at a faster rate than in ΛCDM. Additionally, the gravitational potentials Φ and Ψ evolve differently on the brane than in ΛCDM, for which Φ = Ψ. On the brane, by contrast, the ratio Φ/Ψ exceeds unity during the late matter-dominated epoch (z ≲ 50). These features emerge as smoking gun tests of phantom brane cosmology and allow predictions of this scenario to be tested against observations of galaxy clustering and large-scale structure.

Conservation of ζ with radiative corrections from heavy field

In this paper, we address a possible impact of radiative corrections from a heavy scalar field χ on the curvature perturbation ζ. Integrating out χ, we derive the effective action for ζ, which includes the loop corrections of the heavy field χ. When the mass of χ is much larger than the Hubble scale H, the loop corrections of χ only yield a local contribution to the effective action and hence the effective action simply gives an action for ζ in a single field model, where, as is widely known, ζ is conserved in time after the Hubble crossing time. Meanwhile, when the mass of χ is comparable to H, the loop corrections of χ can give a non-local contribution to the effective action. Because of the non-local contribution from χ, in general, ζ may not be conserved, even if the classical background trajectory is determined only by the evolution of the inflaton. In this paper, we derive the condition that ζ is conserved in time in the presence of the radiative corrections from χ. Namely, we show that when the dilatation invariance, which is a part of the diffeomorphism invariance, is preserved at the quantum level, the loop corrections of the massive field χ do not disturb the constant evolution of ζ at super Hubble scales. In this discussion, we show the Ward-Takahashi identity for the dilatation invariance, which yields a consistency relation for the correlation functions of the massive field χ.

Quantum discord of cosmic inflation: Can we show that CMB anisotropies are of quantum-mechanical origin?

We investigate the quantumness of primordial cosmological fluctuations and its detectability. The quantum discord of inflationary perturbations is calculated for an arbitrary splitting of the system, and shown to be very large on super-Hubble scales. This entails the presence of large quantum correlations, due to the entangled production of particles with opposite momentums during inflation. To determine how this is reflected at the observational level, we study whether quantum correlators can be reproduced by a non-discordant state, i.e. a state with vanishing discord that contains classical correlations only. We demonstrate that this can be done for the power spectrum, the price to pay being twofold: first, large errors in other two-point correlation functions and second, the presence of intrinsic non-Gaussianity. The detectability of these two features remains to be determined but could possibly rule out a non-discordant description of the cosmic microwave background. If one abandons the idea that perturbations should be modeled by quantum mechanics and wants to use a classical stochastic formalism instead, we show that any two-point correlators on super-Hubble scales can be exactly reproduced regardless of the squeezing of the system. The latter becomes important only for higher-order correlation functions that can be accurately reproduced only in the strong squeezing regime.