Chain Inflation Research Articles

Natural Chain Inflation

In Chain Inflation the universe tunnels along a series of false vacua of ever-decreasing energy. The main goal of this paper is to embed Chain Inflation in high energy fundamental physics. We begin by illustrating a simple effective formalism for calculating Cosmic Microwave Background (CMB) observables in Chain Inflation. Density perturbations seeding the anisotropies emerge from the probabilistic nature of tunneling (rather than from quantum fluctuations of the inflation). To obtain the correct normalization of the scalar power spectrum and the scalar spectral index, we find an upper limit on the scale of inflation at horizon crossing of CMB scales, V⁎1/4<1012 GeV. We then provide an explicit realization of chain inflation, in which the inflaton is identified with an axion in supergravity. The axion enjoys a perturbative shift symmetry which is broken to a discrete remnant by instantons. The model, which we dub ‘natural chain inflation’ satisfies all cosmological constraints and can be embedded into a standard ΛCDM cosmology. Our work provides a major step towards the ultraviolet completion of chain inflation in string theory.

Global Supply Chain Pressures, International Trade, and Inflation

Global Supply Chain Pressures, International Trade, and Inflation

Power spectrum of density perturbations in chain inflation

Chain Inflation is an alternative to slow roll inflation in which the universe undergoes a series of transitions between different vacua. The density perturbations (studied in this paper) are seeded by the probabilistic nature of tunneling rather than quantum fluctuations of the inflaton. We find the scalar power spectrum of chain inflation and show that it is fully consistent with a $\Lambda$CDM cosmology. In agreement with some of the previous literature (and disagreement with others), we show that $10^4$ phase transitions per e-fold are required in order to agree with the amplitude of Cosmic Microwave Background anisotropies within the observed range of scales. Interestingly, the amplitude of perturbations constrains chain inflation to a regime of highly unstable de Sitter spaces, which may be favorable from a quantum gravity perspective since the Swampland Conjecture on Trans-Planckian Censorship is automatically satisfied. We provide new analytic estimates for the bounce action and the tunneling rate in periodic potentials which replace the thin-wall approximation in the regime of fast tunneling. Finally, we study model implications and derive an upper limit of $\sim 10^{10}$ GeV on the axion decay constant in viable chain inflation with axions.

Chain inflation reconsidered

We investigate density perturbations in the chain inflation scenario, where the inflaton undergoes successive tunneling transitions along one field direction. First we show that when the bubble walls associated with such a phase transition meet, they induce the next phase transition and continue to propagate as phase interfaces. Then we present an analytical calculation of the density fluctuations and an estimate of non-Gaussianities such as fNL, which we find to be small (of order 1). To get the right amplitude for the power spectrum, there have to be 108 phase transitions per Hubble time, a significant model building challenge. We find that working models of chain inflation must be rather strongly coupled, and thus have a very limited range of validity as effective field theories. We discuss generalizations to the multiple field case, the curvaton scenario, and noncanonical kinetic terms.

Observing the structure of the landscape with the CMB experiments

Assuming that inflation happened through a series of tunneling in the string theory landscape, it is argued that one can determine the structure of vacua using precise measurements of the scalar spectral index and tensor perturbations at large scales. It is shown that for a vacuum structure where the energy gap between the minima is constant, i.e. ϵi = imf4, one obtains the scalar spectral index, ns, to be ≃ 0.9687, for the modes that exit the horizon 60 e-folds before the end of inflation. Alternatively, for a vacuum structure in which the energy gap increases linearly with the vacuum index, i.e. ϵi = ½i2mf4, ns turns out to be ≃ 0.9614. Both these two models are motivated within the string theory landscape using flux-compactification and their predictions for scalar spectral index are compatible with WMAP results. For both these two models, the results for the scalar spectral index turn out to be independent of mf. Nonetheless, assuming that inflation started at Planckian energies and that there had been successful thermalization at each step, one can constrain mf < 2.6069 × 10−5mP and mf < 6.5396 × 10−7mP in these two models, respectively. Violation of the single-field consistency relation between the tensor and scalar spectra is another prediction of chain inflation models. This corresponds to having a smaller tensor/scalar ratio at large scales in comparison with the slow-roll counterparts. Similar to slow-roll inflation, it is argued that one can reconstruct the vacuum structure using the CMB experiments.

Slow nucleation rates in chain inflation with QCD axions or monodromy

The previous proposal (by two of us) of chain inflation with the QCD axion is shown to fail. The proposal involved a series of fast tunneling events, yet here it is shown that tunneling is too slow. We calculate the bubble nucleation rates for phase transitions in the thick wall limit, approximating the barrier by a triangle. A similar problem arises in realization of chain inflation in the string landscape that uses series of minima along the monodromy staircase around the conifold point. The basic problem is that the minima of the potential are too far apart to allow rapid enough tunneling in these two models. We entertain the possibility of overcoming this problem by modifying the gravity sector to a Brans-Dicke theory. However, one would need extremely small values for the Brans-Dicke parameter in the early universe. Many successful alternatives exist, including other axions (with mass scales not set by QCD) or potentials with comparable heights and widths that do not suffer from the problem of slow tunneling and provide successful candidates for chain inflation.

Chain inflation and the imprint of fundamental physics in the CMBR

In this work we investigate characteristic modifications of thespectrum of cosmological perturbations and the spectral index due to chain inflation.We find two types of effects. First, modifications of the spectral index depending on interactionsbetween radiation and the vacuum, and on features of the effectivevacuum potential of the underlying fundamental theory. Second,a modulation of the spectrum signaling new physics due to bubble nucleation. Thiseffect is similar to those oftransplanckian physics.Measurements of such signatures could provide a wealth of information on thefundamental physics at the basis of inflation.

Chain inflation revisited

This paper represents an in-depth treatment of the chain inflation scenario. We fullydetermine the evolution of the universe in the model, the conditions necessary in order tohave a successful inflationary period, and the matching with the observational resultsregarding the cosmological perturbations. We study in great detail, and in general, thedynamics of the background, as well as the mechanism of generation of the perturbations.We also find an explicit formula for the spectrum of adiabatic perturbations. Our resultsprove that chain inflation is a viable model for solving the horizon, entropy and flatnessproblems of standard cosmology and for generating the right amount of adiabaticcosmological perturbations. The results are radically different from those found in previousworks on the subject. Finally, we argue that there is a natural way to embed chain inflationinto flux compactified string theory. We discuss the details of the implementation and howto fit observations.

Inflationary non-Gaussianity from thermal fluctuations

We calculate the contribution of fluctuations with a thermal origin to the inflationarynon-Gaussianity. We find that even a small component of radiation can lead to a largenon-Gaussianity. We show that this thermal non-Gaussianity always has positivefNL. We illustrate our result in the chain inflation model and the very weakly dissipative warminflation model. We show that is general in such models. If we allow a modified equation of state,or some decoupling effects, a large thermal non-Gaussianity of orderfNL>5 oreven fNL∼100 can be produced. We also show that the power spectrum of chain inflationshould have a thermal origin. In the appendix, we give a clarification on thedifferent conventions used in the literature related to the calculation offNL.

Simplified chain inflation

We propose a simplified chain inflation model and calculate the primordial power spectra ofthe scalar and tensor fluctuations. The spectral index and the tensor–scalar ratio arerespectively 0.972 and 0.089, which are consistent with present cosmological observations.

Density perturbations in chain inflation

We consider the model of ‘chain inflation,’ in which the period of inflation in our universetook the form of a long sequence of quantum tunnelling events. We find that in thesimplest such scenario, in which the tunnelling processes are uniform, approximately104 vacua per e-folding of inflation are required in order for the density perturbations producedto be of an acceptable size. We arrive at this conclusion through a combination of analyticand numerical techniques, which could also serve as starting points for calculations withmore general sets of assumptions.

Inflating with the QCD axion

We show that the QCD axion can drive inflation via a series of tunneling events. For axion models with a softly broken ${Z}_{N}$ symmetry, the axion potential has a series of $N$ local minima and may be modeled by a tilted cosine. Chain inflation results along this tilted cosine: the field tunnels from an initial minimum near the top of the potential through a series of ever lower minima to the bottom. This results in sufficient inflation and reheating. QCD axions, potentially detectable in current searches, may thus simultaneously solve problems in particle physics and provide inflation.

Chain inflation in the landscape: ‘bubble bubble toil and trouble’

In the model of chain inflation, a sequential chain of coupled scalar fields drives inflation.We consider a multidimensional potential with a large number of bowls, or local minima,separated by energy barriers: inflation takes place as the system tunnels from the highestenergy bowl to another bowl of lower energy, and so on until it reaches the zero-energyground state. Such a scenario can be motivated by the many vacua in the stringylandscape, and our model can apply to other multidimensional potentials. The ‘gracefulexit’ problem of old inflation is resolved since reheating is easily achieved at each stage.Coupling between the fields is crucial to the scenario. The model is quite generic andsucceeds for natural couplings and parameters. Chain inflation succeeds for a widevariety of energy scales—for potentials ranging from 10 MeV scale inflation to1016 GeV scale inflation.