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Chain Inflation in the Landscape: "Bubble Bubble Toil and Trouble"

Katherine Freese, Douglas Spolyar

TL;DR

This paper introduces Chain Inflation, a framework where a large number of coupled scalar fields tunnel through a multidimensional potential landscape, yielding many small inflationary steps that cumulatively exceed 60 e-folds. Reheating is achieved via inter-field couplings that catalyze subsequent tunneling, avoiding the fine-tuning typical of slow-roll models and accommodating energy scales from 10 MeV to 10^16 GeV. The authors develop a toy model with identical parameters and extend it to generalized couplings and multiple chains, arguing that the chain progression is robust and generic, provided sufficient long-lived false vacua and natural couplings exist. They discuss variants and critical issues, notably density fluctuations and moving beyond the thin-wall approximation, outlining directions for future work to establish the full phenomenological viability of chain inflation.

Abstract

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 highest energy bowl to another bowl of lower energy, and so on until it reaches the zero energy ground state. Such a scenario can be motivated by the many vacua in the stringy landscape, and our model can apply to other multidimensional potentials. The ''graceful exit'' 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 and succeeds for natural couplings and parameters. Chain inflation succeeds for a wide variety of energy scales -- for potentials ranging from 10MeV scale inflation to $10^{16}$ GeV scale inflation.

Chain Inflation in the Landscape: "Bubble Bubble Toil and Trouble"

TL;DR

This paper introduces Chain Inflation, a framework where a large number of coupled scalar fields tunnel through a multidimensional potential landscape, yielding many small inflationary steps that cumulatively exceed 60 e-folds. Reheating is achieved via inter-field couplings that catalyze subsequent tunneling, avoiding the fine-tuning typical of slow-roll models and accommodating energy scales from 10 MeV to 10^16 GeV. The authors develop a toy model with identical parameters and extend it to generalized couplings and multiple chains, arguing that the chain progression is robust and generic, provided sufficient long-lived false vacua and natural couplings exist. They discuss variants and critical issues, notably density fluctuations and moving beyond the thin-wall approximation, outlining directions for future work to establish the full phenomenological viability of chain inflation.

Abstract

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 highest energy bowl to another bowl of lower energy, and so on until it reaches the zero energy ground state. Such a scenario can be motivated by the many vacua in the stringy landscape, and our model can apply to other multidimensional potentials. The ''graceful exit'' 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 and succeeds for natural couplings and parameters. Chain inflation succeeds for a wide variety of energy scales -- for potentials ranging from 10MeV scale inflation to GeV scale inflation.

Paper Structure

This paper contains 24 sections, 55 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Review of Tunneling in Double Well Potential and Old Inflation
  3. Double Field Inflation: Time-Dependent Nucleation Rate
  4. Chain Inflation
  5. Simplest Model: Single Chain in which all fields have the same parameters:
  6. The First Field
  7. Example
  8. Caveat
  9. Issues: Would the Path skip a Link in the Chain?
  10. Generalizing the Model
  11. Arbitrary parameters, a number of chains
  12. More general interactions
  13. Thermal Activation
  14. Mixing Rollers and Tunnelers
  15. Variants
  16. ...and 9 more sections

Figures (3)

  • Figure 1: Potential energy density of tunneling field $\phi$ as a function of field strength. The energy difference $\epsilon$ between the false vacuum (at $\phi_1=-a$) and the true vacuum (at $\phi_+ = +a$) provides the vacuum energy density for inflation.
  • Figure 2: The probability of any point remaining in the false vacuum for old inflation (dotted line) and Chain Inflation (solid line). While the transition from slow to rapid nucleation (large to small $p(t)$ is too gradual for old inflation, it is virtually a step function for Chain Inflation, which can thus easily percolate and reheat.
  • Figure 3: The four bowls (minima) in the multidimensional potential for two fields $\phi_1$ and $\phi_2$ for the case of identical parameters for the fields. Energy differences between bowls are labeled in the figure. The length of the arrows gives a rough indication of the amplitude of the ratio of (the energy difference to distance$^4$) between any two bowls. This quantity determines the tunneling rate. The system chooses the path with the longest arrow, since its tunneling rate is the highest.