# The Measure for the Multiverse and the Probability for Inflation

## TL;DR

This paper develops a measure for evaluating the likelihood of inflationary scenarios in cosmology, revealing that prolonged inflation is exponentially suppressed, while some alternative models are not affected.

## Contribution

It introduces a new measure for the multiverse and calculates the probabilities of different inflationary models lasting for many e-folds.

## Key findings

- Probability of single-field inflation lasting N e-folds is suppressed by exp(-3N)
- Multi-field inflation probability is suppressed by exp(-3nN)
- Non-inflationary models like cyclic models are not suppressed

## Abstract

We investigate the measure problem in the framework of inflationary cosmology. The measure of the history space is constructed and applied to inflation models. Using this measure, it is shown that the probability for the generalized single field slow roll inflation to last for $N$ e-folds is suppressed by a factor $\exp(-3N)$, and the probability for the generalized $n$-field slow roll inflation is suppressed by a much larger factor $\exp(-3nN)$. Some non-inflationary models such as the cyclic model do not suffer from this difficulty.