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On Number of Nflation Fields

Iftikhar Ahmad, Yun-Song Piao, Cong-Feng Qiao

TL;DR

The paper analyzes Nflation, where many massive scalar fields drive inflation, and shows that increasing the number of fields $N$ can eliminate the slow-roll region. By comparing the total classical field motion to quantum fluctuations, the authors derive a bound that, for massive fields, scales as $N \lesssim M_p^2/\bar{m}^2$ (with $\bar{m}$ the average mass). This bound is shown to hold both for equal-mass ensembles and for a Marčenko–Pastur mass spectrum, while a $\phi^4$-type potential does not impose such a bound. The result aligns with black-hole physics expectations and places a gravitational cutoff on how many fields can participate in inflation, with implications for string-inspired multi-field scenarios and the viability of Nflation in the observable universe.

Abstract

We study the Nflation model, in which a collection of massive scalar fields drive the inflation simultaneously. We find, when the number of fields is larger than the square of ratio of the Planck scale $M_p$ to the average value $\bar m$ of fields masses, the slow roll inflation region will disappear. This suggests that in order to make Nflation responsible for our observable universe, the number of fields driving the Nflation must be bounded by the above ratio. This result is also consistent with recent arguments from black hole physics.

On Number of Nflation Fields

TL;DR

The paper analyzes Nflation, where many massive scalar fields drive inflation, and shows that increasing the number of fields can eliminate the slow-roll region. By comparing the total classical field motion to quantum fluctuations, the authors derive a bound that, for massive fields, scales as (with the average mass). This bound is shown to hold both for equal-mass ensembles and for a Marčenko–Pastur mass spectrum, while a -type potential does not impose such a bound. The result aligns with black-hole physics expectations and places a gravitational cutoff on how many fields can participate in inflation, with implications for string-inspired multi-field scenarios and the viability of Nflation in the observable universe.

Abstract

We study the Nflation model, in which a collection of massive scalar fields drive the inflation simultaneously. We find, when the number of fields is larger than the square of ratio of the Planck scale to the average value of fields masses, the slow roll inflation region will disappear. This suggests that in order to make Nflation responsible for our observable universe, the number of fields driving the Nflation must be bounded by the above ratio. This result is also consistent with recent arguments from black hole physics.

Paper Structure

This paper contains 6 sections, 24 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Bound for $N$ of Nflation
  3. The case with equal masses
  4. The case with mass distribution following Mar$\check{c}$enko-Pastur law
  5. The case of Nflation with $\phi^4$ fields
  6. Summary and Discussion

Figures (3)

  • Figure 1: The figure of $\log$ change of the end point of slow roll inflation and the critical point separating the slow roll inflation region and eternal inflation region with respect to the number $N$ of fields in Nflation model with massive fields, in which $m =10^{-6}M_p$ is taken. Three regions separated by both lines have been pointed out in figure. We can see that when $N\sim 10^{12}$, the slow roll inflation region disappears.
  • Figure 2: The figures of $f_1(t,\beta)$ and $f_2(t,\beta)$ with respect to $c$ with different $\beta$. The average mass $\bar{m}=10^{-6}M_p$ is taken.
  • Figure 3: The figure of $\log$ change of the end point of slow roll inflation and the critical point separating the slow roll inflation region and eternal inflation region with respect to the number $N$ of fields in Nflation model with $\phi^4$ fields, in which $\lambda =10^{-12}$ is taken. Three regions separated by both lines have been pointed out in figure. We can see that both lines are parallel, thus there is not the bound for $N$.