Chaotic Inflation Research Articles

Slow-roll inflation in f(R,T) gravity with a RT mixing term

We consider slow-roll inflationary models in a class of modified theories of gravity which contains non-minimal curvature-inflaton couplings, i.e., the $f(R,T)$ gravity, where $R$ is the Ricci scalar and $T$ is the trace of the inflaton energy-momentum tensor. On top of the minimally coupled $T$ that has been widely investigated in the literature, we further include a $RT$ mixing term in the theory. This mixing term introduces non-minimal derivative couplings and plays an important role in inflationary dynamics. Taking chaotic and natural inflation as examples, we find that the predictions for spectral tilt and the tensor-to-scalar ratio are sensitive to the existence of the $RT$ mixing term. In particular, by turning on this mixing term, it is possible to bring chaotic and natural inflation into better agreement with observational data.

Large field polynomial inflation: parameter space, predictions and (double) eternal nature

Simple monomial inflationary scenarios have been ruled out by recent observations. In this work we revisit the next simplest scenario, a single-field model where the scalar potential is a polynomial of degree four which features a concave “almost” saddle point. We focus on trans-Planckian field values. We reparametrize the potential, which greatly simplifies the procedure for finding acceptbale model parameters. This allows for the first comprehensive scan of parameter space consistent with recent Planck and BICEP/Keck 2018 measurements. Even for trans-Planckian field values the tensor-to-scalar ratio r can be as small as \U0001d4aa(10-8), but the model can also saturate the current upper bound. In contrast to the small-field version of this model, radiative stability does not lead to strong constraints on the parameters of the inflaton potential. For very large field values the potential can be approximated by the quartic term; as well known, this allows eternal inflation even for field energy well below the reduced Planck mass M Pl, with Hubble parameter H ∼ 10-2 M Pl. More interestingly, we find a region of parameter space that even supports two phases of eternal inflation. The second epoch only occurs if the slope at the would-be saddle point is very small, and has H ∼ 10-5 M Pl; it can only be realized if r ∼ 10-2, within the sensitivity range of next-generation CMB observations.

Black hole production, eternal inflation, and information in quasi-de Sitter space

When the slow-roll parameter ϵ H is smaller than H 2/M Pl 2, the quantum fluctuations of the inflaton after the horizon crossing are large enough to realize eternal inflation. Whereas they do not generate a sufficient amount of density fluctuation of the inflaton to produce the black hole in quasi-de Sitter space, they can also generate the sizeable density fluctuation of the radiation when the number of degrees of freedom increases rapidly in time, as predicted by the distance conjecture. We argue that the condition that the density fluctuation of the radiation is not large enough to produce the black hole until the end of inflation is equivalent to the no eternal inflation condition. When the radiation emitted by the horizon does not produce the black hole, even if the number of degrees of freedom increases in time, the information paradox does not arise for ϵ H larger than 10-7 (H 2/M Pl 2) and time scale shorter than 104 (M Pl/H 2). Regardless of the presence of the information paradox, a static observer cannot retrieve a sufficient amount of information, which is consistent with the complementarity.

Inflationary Cosmology with Rotation and Chaotic Inflation

Inflationary Cosmology with Rotation and Chaotic Inflation

Quantitative theory for spikes and bubbles in the Richtmyer-Meshkov instability at arbitrary density ratios

It is well known that Goncharov's theory based on Layzer's approach for the Richtmyer-Meshkov instability provides good predictions for bubbles, but could give qualitatively incorrect predictions for spikes. This leads to the belief that Layzer's approach is not applicable to spikes. We show that, by incorporating the distinctive behaviors of spikes and bubbles properly, Layzer's approach is actually applicable to both spikes and bubbles, and can provide accurate predictions for both spikes and bubbles, for systems with arbitrary density ratios, and for the entire evolution process of unstable fingers.

Small cosmological constant from a peculiar inflaton potential

We propose a novel scenario to explain the small cosmological constant (CC) by a finely tuned inflaton potential. The tuned shape is stable under radiative corrections, and our setup is technically natural. The peculiar po- tential approximately satisfies the following conditions: the inflation is eternal if CC is positive, and not eternal if CC is negative. By introducing a slowly varying CC from a positive value to a negative value, the dominant volume of the Universe after the inflation turns out to have a vanishingly small CC. The scenario does not require eternal inflation but the e-folding number is exponentially large and the inflation scale should be low enough. The scenario can have a consistent thermal history, but the present equation of state of the Universe is predicted to differ from the prediction of the {\Lambda}CDM model. A concrete model with a light scalar field is studied.

Healing the cosmological constant problem during inflation through a unified quasi-quintessence matter field

We heal the cosmological constant problem by means of a cancellation mechanism that adopts a phase transition during which quantum fluctuations are eliminated. To this purpose, we propose that a generalized scalar (dark) matter field with a non-vanishing pressure term can remove the vacuum energy contribution, if its corresponding thermodynamics is written in terms of a quasi-quintessence representation. In such a picture, pressure differs from quintessence as it shows a zero kinetic contribution. Using this field, we investigate a metastable transition phase, in which the Universe naturally passes through an inflationary phase. To reach this target, we single out a double exponential potential, describing the metastable inflationary dynamics by considering suitable boundaries and thermodynamic conditions. We analyze stability investigating saddle, stable and unstable points and we thus predict a chaotic inflation that mimics the Starobinsky exponential potential. Consequently, the role of the proposed dark matter field is investigated throughout the overall Universe evolution. To do so, we provide a physical explanation on unifying the dark sector with inflation by healing the cosmological constant problem.

Rejuvenating the hope of a swampland consistent inflated multiverse with tachyonic inflation in the high-energy RS-II braneworld

The swampland conjectures from string theory have had some really interesting implications on cosmology, in particular on inflationary models. Some models of inflation have been shown to be incompatible with these criteria while some have been shown to be severely fine-tuned, with most of these problems arising in single field inflationary models in a General relativistic cosmology. Recent works have although optimistically shown that single field models in more general cosmologies can be consistent with these conjectures and hence there is an optimism that not all such models lie in the swampland. However, a paradigm of inflation which has been shown to not be perfectly okay with the conjectures is eternal inflation. So in this work, we discuss tachyonic inflation in the high-energy RS-II Braneworld scenario in the context of the swampland conjectures while also considering the possibility of swampland consistent eternal inflation. We show that our concerned regime evades all the prominent swampland issues for single field inflation being virtually unscathed. After this, we show that the main conflicts of eternal inflation with the swampland can easily be resolved in the considered tachyonic scenario and in particular, we also discuss the exciting prospect of a Generalized Uncertainty Principle facilitating the notion of Swampland consistent eternal inflation. Our work as a whole reignites the possibility that there can be a swampland (and possibly, quantum gravitationally) consistent picture of a “Multiverse”.

Quantitative theory for spikes and bubbles in the Richtmyer−Meshkov instability at arbitrary density ratios in three dimensions

It is known that conducting numerical simulations and experiments for the shock-induced Richtmyer–Meshkov instability in three dimensions is much more difficult and time-consuming than that in two dimensions. Therefore, theories can play a more important role in the study of three-dimensional Richtmyer–Meshkov instability. We present analytical formulas for predicting the behavior of growth rate and amplitude of fingers at the unstable Richtmyer–Meshkov interface. Our theory is for both spikes and bubbles, for the arbitrary density ratio between the two fluids, and for the entire development process from early to late times.

Double inflation via non-minimally coupled spectator

We argue that double inflation may occur when a spectator field is non-minimally coupled to gravity. As a concrete example, we study a two-field inflationary model where the initial spectator field is non-minimally coupled to gravity while the initial inflaton field is minimally coupled. The non-minimal coupling results in the growth of the spectator field which, in turn, drives the second stage of inflation in a significant region of parameter space. The isocurvature fluctuations originating from the spectator field source adiabatic ones, and hence the spectator non-minimal coupling can modify the inflationary predictions for the spectral index and the tensor-to-scalar ratio even though the initial inflaton field is minimally coupled to gravity. We explicitly show that quadratic chaotic inflation can become viable by the introduction of the spectator non-minimal coupling.

Hubble selection of the weak scale from QCD quantum critical point

There is growing evidence that the small weak scale may be related to self-organized criticality. In this regard, we note that if the strange quark were lighter, the QCD phase transition could have been first order, possibly exhibiting quantum critical points at zero temperature as a function of the Higgs vacuum expectation value $v_h$ smaller than (but near) the weak scale. We show that these quantum critical points allow a dynamical selection of the observed weak scale, via quantum-dominated stochastic evolutions of the value of $v_h$ during eternal inflation. Although the values of $v_h$ in different Hubble patches are described by a probability distribution in the multiverse, inflationary quantum dynamics ensures that the peak of the distribution evolves toward critical points (self-organized criticality), driven mainly by the largest Hubble expansion rate there -- the Hubble selection of the universe. To this end, we first explore the quantum critical points of the three-flavor QCD linear sigma model, parametrized by $v_h$ at zero temperature, and we present a relaxion model for the weak scale. Among the patches that have reached reheating, it results in a sharp probability distribution of $v_h$ near the observed weak scale, which is critical not to the crossover at $v_h=0$ but to the sharp transition at ${\sim}\Lambda_{\rm QCD}$.

How Generic Is Eternal Inflation?

Everlasting inflation has far-reaching implications for cosmology and the standing of self-localizing inferences made by observers, which have been subjects of renewed interest in light of the growing acceptance of theory landscapes and the attendant anthropic arguments. Under what assumptions and to what extent does inflation generically produce an eternal “multiverse,” without fine-tuning with respect to measures over the space of inflationary cosmologies driven by a single minimally coupled scalar field? We address this and related questions with numerical simulations of inflationary dynamics across populations of randomly generated inflation models, instantiating a few particular simply-defined measures.

Early-time measure in eternal inflation

In a situation like eternal inflation, where our data is replicated at infinitely-many other space-time events, it is necessary to make a prior assumption about our location to extract predictions. The principle of mediocrity entails that we live at asymptotic late times, when the occupational probabilities of vacua has settled to a near-equilibrium distribution. In this paper we further develop the idea that we instead exist during the approach to equilibrium, much earlier than the exponentially-long mixing time. In this case we are most likely to reside in vacua that are easily accessed dynamically. Using first-passage statistics, we prove that vacua that maximize their space-time volume at early times have: 1. maximal ever-hitting probability; 2. minimal mean first-passage time; and 3. minimal decay rate. These requirements are succinctly captured by an early-time measure. The idea that we live at early times is a predictive guiding principle, with many phenomenological implications. First, our vacuum should lie deep in a funneled region, akin to folding energy landscapes of proteins. Second, optimal landscape regions are characterized by relatively short-lived vacua, with lifetime of order the de Sitter Page time. For our vacuum, this lifetime is ∼ 10130 years, which is consistent with the Standard Model estimate due to Higgs metastability. Third, the measure favors vacua with small, positive vacuum energy. This can address the cosmological constant problem, provided there are sufficiently many vacua in the entire ensemble of funnels. As a concrete example, we study the Bousso-Polchinski lattice of flux vacua, and find that the early-time measure favors lattices with the fewest number of flux dimensions. This favors compactifications with a large hierarchy between the lightest modulus and all other Kähler and complex structure moduli.

Non-minimally assisted chaotic inflation

Conventional wisdom says that a chaotic inflation model with a power-law potential is ruled out by the recent Planck-BICEP/Keck results. We find, however, that the model can be assisted by a non-minimally coupled scalar field and still provides a successful inflation. Considering a power-law chaotic inflation model of the type V ∼ φn with n = {2, 4/3, 1, 2/3, 1/3}, we show that n = 1/3 (n = {2/3, 1/3}) may be revived with the help of the quadratic (quartic) non-minimal coupling of the assistant field to gravity.

Generalizing the constant-roll condition in scalar inflation

In this work, we generalize the constant-roll condition for minimally coupled canonical scalar field inflation. Particularly, we shall assume that the scalar field satisfies the condition [Formula: see text], and we derive the field equations under this assumption. We call the framework extended constant-roll framework. Accordingly, we calculate the inflationary indices and the corresponding observational indices of inflation. In order to demonstrate the inflationary viability, we choose three potentials that are problematic in the context of slow-roll dynamics, namely, chaotic, linear power-law and exponential inflation, and by choosing a simple power-law form for the smooth function [Formula: see text], we show that in the extended constant-roll framework, the models are compatible with the latest 2018 Planck constraints on inflation. We also justify appropriately why we called this new framework extended constant-roll framework, and we show that the condition [Formula: see text] is equivalent to the condition [Formula: see text], with the latter condition being a simple generalization of the constant-roll condition. Finally, we examine an interesting physical situation, in which a general extended constant-roll scalar field model is required to satisfy the cosmological tracker condition used in quintessence models. In contrast to the slow-roll and ordinary constant-roll cases, in which case the tracker condition is not compatible with neither the slow-roll or the ordinary constant-roll conditions, the extended constant-roll condition can be compatible with the tracker condition. This feature leads to a new inflationary phenomenological framework, the essential features of which we develop in brief. The main feature of the new theoretical framework is that the function [Formula: see text] and the potential [Formula: see text] are no longer free to choose, but these are directly functionally related.

APPLYING THE LOCAL MARTINGALE THEORY OF BUBBLES TO CRYPTOCURRENCIES

Cryptocurrencies provide a natural setting to test for the existence of price bubbles using the local martingale theory of bubbles because cryptocurrencies have no cash flows. Using a robust statistical algorithm, we test for price bubbles in eight cryptocurrencies, Bitcoin (BTC), Litecoin (LTC), Ethereum (ETH), Ripple (XRP), Bitcoin Cash (BCH), EOS (EOS), Monero (XMR), and Zcash (ZEC), from 1 January 2019 to 17 July 2019. The statistical test first estimates the cryptocurrencies’ volatilities as a function of the price level. Then, these estimates are extrapolated over the positive real line using power functions. Finally, these power functions underly a sequence of hypothesis tests for price bubbles that control for both Type I and Type II errors. Five of the eight currencies (BTC, BCH, EOS, XMR, ZEC) exhibit price bubbles, LTC does not, and the evidence for ETH and XRP is inconclusive. The paper provides strong evidence for the prevalence of bubbles in cryptocurrencies.

Carroll Symmetry, Dark Energy and Inflation

Carroll symmetry arises from Poincaré symmetry upon taking the limit of vanishing speed of light. We determine the constraints on the energy-momentum tensor implied by Carroll symmetry and show that for energy-momentum tensors of perfect fluid form, these imply an equation of state E+P=0 for energy density plus pressure. Therefore Carroll symmetry might be relevant for dark energy and inflation. In the Carroll limit, the Hubble radius goes to zero and outside it recessional velocities are naturally large compared to the speed of light. The de Sitter group of isometries, after the limit, becomes the conformal group in Euclidean flat space. We also study the Carroll limit of chaotic inflation, and show that the scalar field is naturally driven to have an equation of state with w = − 1. Finally we show that the freeze-out of scalar perturbations in the two point function at horizon crossing is a consequence of Carroll symmetry. To make the paper self-contained, we include a brief pedagogical review of Carroll symmetry, Carroll particles and Carroll field theories that contains some new material as well. In particular we show, using an expansion around speed of light going to zero, that for scalar and Maxwell type theories one can take two different Carroll limits at the level of the action. In the Maxwell case these correspond to the electric and magnetic limit. For point particles we show that there are two types of Carroll particles: those that cannot move in space and particles that cannot stand still.

Investigation of unsteady cryogenic cavitating flow and induced noise around a three-dimensional hydrofoil

In this paper, the Large Eddy Simulation (LES) combined with the Schnerr–Sauer cavitation model and the permeable Ffowcs Williams–Hawkings (FW-Hpds) acoustic analogy approach are introduced to study the unsteady cavitation behaviors and the radiated noise characteristics of the transient liquid nitrogen (LN2) cavitating flow around a NACA66 (National Advisory Committee for Aeronautics) hydrofoil. Satisfactory agreement is obtained between the numerical predictions and experimental measurements. The cavitation noise is predicted based on the sound radiation theory for spherical bubbles and compared with the sound pressure levels of non-cavitating flow from the FW-Hpds equation. It is found that the cavity volume acceleration is directly responsible for driving the generation of cavitation noise, and the sound pressure caused by the development of LN2 cavitation is shown to vary with the periodic pulsing cavity volume evolution, indicating a strong link between cavity evolutions and radiated noises. The transient cavitation structures of the sheet and cloud cavitation are well captured, and the evolution features of the cavities and vortex structures are analyzed in detail. The collapse of the detached small cloud cavity downstream is the main mechanism for generating intense acoustic impulses for both sheet and cloud cavitation. While the strong interaction between the re-entrant jet and the main flow results in violent pressure fluctuations, and thus produces instantaneous extreme dipole noise, which accounts for another distinctive mechanism to induce intense acoustic impulses for cloud cavitation, the presented study provides a deep understanding of the nature of cavitation-dominated noise for cryogenic cavitating flow.

Implication of the swampland distance conjecture on the Cohen–Kaplan–Nelson bound in de Sitter space

The Cohen–Kaplan–Nelson (CKN) bound formulates the condition that black hole is not produced by the low energy effective field theory dynamics. In de Sitter space it also constrains the maximal size of the matter distribution to be smaller than the cosmological horizon determined by black hole. On the other hand, the swampland distance conjecture (SDC) predicts that de Sitter space becomes unstable by the descent of the low energy degrees of freedom from UV. This results in the rapid increase in the energy inside the cosmological horizon, the distribution of which can be constrained by the CKN bound. We study the CKN bound in de Sitter space in detail and point out that when compared with the slow-roll in the inflation, the bound on the slow-roll parameter which forbids the eternal inflation is obtained.

The effect of surface tension on the color Doppler ultrasound twinkling artifact

Imaging crystalline structures with Doppler ultrasound can produce a rapid color shift, termed the twinkling artifact, that can assist in diagnosing pathological mineralizations such as kidney stones, heterotopic ossification, gout, and breast microcalcifications. Twinkling is theorized to arise from scattering off surface crevice microbubbles, which are affected by the surface tension between the bubble and surrounding medium. In this study, we evaluated the effect of surface tension on twinkling in pure crystals. Cholesterol, calcium phosphate, and uric acid crystals were grown in vitro (n = 5 each) and imaged with a Philips/ATL L7-4 transducer and Vantage-128 research ultrasound system. Crystals were imaged in water while varying surfactant concentration (0%–4%) leading to surface tensions that ranged from 45–72 mN/m. Surface tension of the solution was determined by measuring the contact angle of 0.1-mL droplet on an acrylic sheet exposed to air. As the concentration of surfactant increased, twinkling was found to decrease by ∼20% for cholesterol and calcium phosphate and ∼10% for uric acid. These results continue to support the crevice bubble theory of twinkling and suggest the importance of surface tension when evaluating minerals with the twinkling artifact. [Work supported by NSF-CAREER-1943937 and NSF-GRFP-DGE1255832.]