Large Curvature Perturbations Research Articles

Primordial perturbations from ultra-slow-roll single-field inflation with quantum loop effects

It is known that the single-field inflation with a transient ultra-slow-roll phase can produce a large curvature perturbation at small scales for the formation of primordial black holes. In our previous work, we have considered quantum loop corrections to the curvature perturbation and found that the growth of these small-scale modes would affect the curvature perturbation at large scales probed by cosmic microwave background observation. In this work, we will further derive the constraints on the growing modes in the transition between the slow-roll and the ultra-slow-roll phases under the effect of the loop corrections. Our results would help clarify the recent controversy on whether or not the primordial-black-hole formation from the single-field inflation is ruled out at one-loop level.

Stochastic dynamics of multi-waterfall hybrid inflation and formation of primordial black holes

We show that a hybrid inflation model with multiple waterfall fields can result in the formation of primordial black holes (PBHs) with an astrophysical size, by using an advanced algorithm to follow the stochastic dynamics of the waterfall fields. This is in contrast to the case with a single waterfall field, where the wavelength of density perturbations is usually too short to form PBHs of the astrophysical scale (or otherwise PBHs are overproduced and the model is ruled out) unless the inflaton potential is tuned. In particular, we demonstrate that PBHs with masses of order 1020 g can form after hybrid inflation consistently with other cosmological observations if the number of waterfall fields is about 5 for the case of instantaneous reheating. Observable gravitational waves are produced from the second-order effect of large curvature perturbations as well as from the dynamics of texture or global defects that form after the waterfall phase transition.

Primordial black holes and inflation from double-well potentials

We investigate the formation of large peaks in the inflationary curvature power spectrum from double-well potentials. In such scenarios, the initial CMB spectrum is created at large field values. Subsequently, the inflaton will cross one of the minima and will decelerate rapidly as it reaches the local maximum at the origin, either falling back or crossing it. During this final phase, a significant peak in the curvature power spectrum can be generated. Our analysis reveals that this class of models produces more pronounced peaks than most quasi-inflection point scenarios with less tuning for the model parameters. Finally, we construct an explicit theoretically motivated inflationary scenario that is consistent with the latest CMB observations and capable of generating sufficiently large curvature perturbations for primordial black holes.

Scalar induced gravitational waves from warm inflation

Stochastic gravitational waves can be induced from the primordial curvature perturbations generated during inflation, through scalar–tensor mode coupling at the second order of cosmological perturbation theory. Here we discuss a model of warm inflation in which large curvature perturbations are generated at the small scales because of inflaton dissipation. These overdense perturbations then collapse at later epoch to form primordial black holes, as was studied in our earlier work (Ref. Arya (2020)), and therefore may also act as a source to the second-order tensor perturbations. In this study, we calculate the spectrum of these secondary gravitational waves from our warm inflationary model. We find that our model leads to a generation of scalar induced gravitational waves (SIGW) over a frequency range ∼ ( 1 – 1 0 6 ) Hz. Further, we discuss the detection possibilities of these SIGWs, taking in account the sensitivity of different ongoing and future gravitational wave experiments.

Stochastic effects in axion inflation and primordial black hole formation

We revisit the model of axion inflation in the context of stochastic inflation and investigate the effects of the stochastic noises associated to the electromagnetic fields. Because of the parity violating interaction, one polarization of the gauge field is amplified inducing large curvature perturbation power spectrum. Taking into account the stochastic kicks arising from the short modes at the time of horizon crossing we obtain the corresponding Langevin equations for the long modes of the electromagnetic and axion fields. It is shown that a mean-reverting process governs the dynamics of the electromagnetic fields such that the tachyonic growth of the gauge fields is balanced by the diffusion forces. As the instability parameter grows towards the end of inflation, the large curvature perturbations induced from gauge field perturbations lead to copious production of small mass primordial black holes (PBHs). It is shown that the produced PBHs follow a Gaussian statistics. Imposing the observational constraints on PBHs formation relaxes the previous bounds on the instability parameter by about fifty percents.

Multiple field ultraslow-roll inflation: Primordial black holes from straight bulk and distorted boundary

We study a model of two-field ultra-slow-roll (USR) inflation bounded by a curve in the field space. Curvature perturbations and non-Gaussianities can be enhanced both during the USR phase and from the inhomogeneities at the boundary. We employ the full non-linear $\delta N$ formalism to calculate the probability distribution function (PDF) for curvature perturbation non-perturbatively and show that the non-linear effects can significantly enhance the abundance of the primordial black holes (PBHs). For large curvature perturbations, the PDF has a universal exponential tail, but for the intermediate values, the PDF -- and, therefore, the abundance of the PBHs -- depend sensitively on the geometry of the boundary.

Cosmic Coincidences of Primordial-Black-Hole Dark Matter.

If primordial black holes (PBHs) contribute more than 10% of the dark matter (DM) density, their energy density today is of the same order as that of the baryons. Such a cosmic coincidence might hint at a mutual origin for the formation scenario of PBHs and the baryon asymmetry of the Universe. Baryogenesis can be triggered by a sharp transition of the rolling rate of inflaton from slow-roll to (nearly) ultraslow-roll phases that produce large curvature perturbations for PBH formation in single-field inflationary models. We show that the baryogenesis requirement drives the PBH contribution to DM, along with the inferred PBH mass range, the resulting stochastic gravitational wave background frequency window, and the associated cosmic microwave background tensor-to-scalar ratio amplitude, into potentially observable regimes.

Primordial black holes from Gauss-Bonnet-corrected single field inflation

Primordial blackholes formed in the early Universe via gravitational collapse of over-dense regions may contribute a significant amount to the present dark matter relic density. Inflation provides a natural framework for the production mechanism of primordial blackholes. For example, single field inflation models with a fine-tuned scalar potential may exhibit a period of ultra-slow roll, during which the curvature perturbation may be enhanced to become seeds of the primordial blackholes formed as the corresponding scales reenter the horizon. In this work, we propose an alternative mechanism for the primordial blackhole formation. We consider a model in which a scalar field is coupled to the Gauss-Bonnet term and show that primordial blackholes may be seeded when a scalar potential term and the Gauss-Bonnet coupling term are nearly balanced. Large curvature perturbation in this model not only leads to the production of primordial blackholes but it also sources gravitational waves at the second order. We calculate the present density parameter of the gravitational waves and discuss the detectability of the signals by comparing them with sensitivity bounds of future gravitational wave experiments.

Primordial black holes and gravitational waves from parametric amplification of curvature perturbations

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 corresponding stochastic gravitational waves fall in the frequency band measurable for the pulsar timing array and the space-based gravitational wave detectors.

Primordial black holes for the LIGO events in the axionlike curvaton model

We revise primordial black hole (PBH) formation in the axion-like curvaton model and investigate whether PBHs formed in this model can be the origin of the gravtitational wave (GW) signals detected by the Advanced LIGO. In this model, small-scale curvature perturbations with large amplitude are generated, which is essential for PBH formation. On the other hand, large curvature perturbations also become a source of primordial GWs by their second-order effects. Severe constraints are imposed on such GWs by pulsar timing array (PTA) experiments. We also check the consistency of the model with these constraints. In this analysis, it is important to take into account the effect of non-Gaussianity, which is generated easily in the curvaton model. We see that, if there are non-Gaussianities, the fixed amount of PBHs can be produced with a smaller amplitude of the primordial power spectrum.

The Standard Model Higgs as the origin of the hot Big Bang

If the Standard Model (SM) Higgs is weakly coupled to the inflationary sector, the Higgs is expected to be universally in the form of a condensate towards the end of inflation. The Higgs decays rapidly after inflation - via non-perturbative effects - into an out-of-equilibrium distribution of SM species, which thermalize soon afterwards. If the post-inflationary equation of state of the universe is stiff, $w \simeq +1$, the SM species eventually dominate the total energy budget. This provides a natural origin for the relativistic thermal plasma of SM species, required for the onset of the `hot Big Bang' era. The viability of this scenario requires the inflationary Hubble scale $H_*$ to be lower than the instability scale for Higgs vacuum decay, the Higgs not to generate too large curvature perturbations at cosmological scales, and the SM dominance to occur before Big Bang Nucleosynthesis. We show that successful reheating into the SM can only be obtained in the presence of a non-minimal coupling to gravity $\xi \gtrsim 1$, with a reheating temperature of $T_{\rm RH} \gtrsim \mathcal{O}(10^{10})\xi^{3/2}(H_*/10^{14}{\rm GeV})^2~{\rm GeV}$.

Massive primordial black holes from hybrid inflation as dark matter and the seeds of galaxies

In this paper we present a new scenario where massive Primordial Black Holes (PBH) are produced from the collapse of large curvature perturbations generated during a mild waterfall phase of hybrid inflation. We determine the values of the inflaton potential parameters leading to a PBH mass spectrum peaking on planetary-like masses at matter-radiation equality and producing abundances comparable to those of Dark Matter today, while the matter power spectrum on scales probed by CMB anisotropies agrees with Planck data. These PBH could have acquired large stellar masses today, via merging, and the model passes both the constraints from CMB distortions and micro-lensing. This scenario is supported by Chandra observations of numerous BH candidates in the central region of Andromeda. Moreover, the tail of the PBH mass distribution could be responsible for the seeds of supermassive black holes at the center of galaxies, as well as for ultra-luminous X-rays sources. We find that our effective hybrid potential can originate e.g. from D-term inflation with a Fayet-Iliopoulos term of the order of the Planck scale but sub-planckian values of the inflaton field. Finally, we discuss the implications of quantum diffusion at the instability point of the potential, able to generate a swiss-cheese like structure of the Universe, eventually leading to apparent accelerated cosmic expansion.

Cosmological constraints on the curvaton web parameters

We consider the mixed inflaton-curvaton scenario in which quantum fluctuations of the curvaton field during inflation lead to a relatively large curvature perturbation spectrum at small scales. We use the model of chaotic inflation with quadratic potential including supergravity corrections leading to a large positive tilt in the power spectrum of the curvaton field. The model is characterized by the strongly inhomogeneous curvaton field in the Universe and large non-Gaussianity of curvature perturbations at small scales. We obtained the constraints on the model parameters considering the process of primordial black hole production in the radiation era.

Quantum phase of inflation

Inflation models can have an early phase of inflation where the evolution of the inflaton is driven by quantum fluctuations before entering the phase driven by the slope of the scalar field potential. For a Coleman-Weinberg potential this quantum phase lasts 10^{7-8} e-foldings. A long period of fluctuation driven growth of the inflation field can possibly take the inflaton past phi_*, the value of the field where our current horizon scale crosses the horizon; alternatively, even if the field does not cross phi_*, the inflaton could have high kinetic energy at the end of this phase. Therefore we study these issues in the context of different models of inflation. In scenarios where cosmological relevant scales leave during the quantum phase we obtain large curvature perturbations of O(10). We also apply our results to quadratic curvaton models and to quintessence models. In curvaton models we find that inflation must last longer than required to solve the horizon problem, that the curvaton models are incompatible with small field inflation models and that there may be too large non-gaussianity. A new phase of thermal fluctuation driven inflation is proposed, in which during inflation the inflaton evolution is governed by fluctuations from a sustained thermal radiation bath rather than by a scalar field potential.

Large curvature perturbations near horizon crossing in single-field inflation models

We consider the examples of single-field inflation models predicting large amplitudes of the curvature perturbation power spectrum at relatively small scales. It is shown that in models with an inflationary potential of double-well type the peaks in the power spectrum, having, in maximum, the amplitude ${\mathcal{P}}_{\mathcal{R}}\ensuremath{\sim}0.1$, can exist (if parameters of the potential are chosen appropriately). It is shown also that the spectrum amplitude of the same magnitude (at large $k$ values) is predicted in the model with the running mass potential, if the positive running, ${n}^{\ensuremath{'}}$, exists and is about 0.005 at cosmological scales. Estimates of the quantum diffusion effects during inflation in models with the running mass potential are given.

SUPPRESSING SUPER-HORIZON CURVATURE PERTURBATIONS?

We consider the possibility of suppressing super-horizon curvature perturbations after the end of the ordinary slow-roll inflationary stage. This is the opposite of the curvaton limit. We assume that large curvature perturbations are created by the inflaton and investigate if they can be diluted or suppressed by a second very homogeneous field which starts to dominate the energy density of the universe shortly after the end of inflation. We show explicit that the gravitational sourcing of inhomogeneities from the more inhomogeneous fluid to the more homogeneous fluid makes the suppression difficult if not impossible to achieve.