Can the universe afford inflation?

Cosmic inflation is envisioned as the “most likely” start for the observed universe. To give substance to this claim, a framework is needed in which inflation can compete with other scenarios and the relative likelihood of all scenarios can be quantified. The most concrete scheme to date for performing such a comparison shows inflation to be strongly disfavored. We analyze the source of this failure for inflation and present an alternative calculation, based on more traditional semiclassical methods, that results in inflation being exponentially favored. We argue that reconciling the two contrasting approaches presents interesting fundamental challenges, and is likely to have a major impact on ideas about the early universe.

Figure 1

The values of $F_I+F_O$ (top three curves) and $\widehat{F}$ (the highly overlapping bottom curves) as a function of the rescaled mass parameter ${\psi }_S$ over the range ${10}^{-10}<{\psi }_S<{\psi }_{cr}$. The three values of the pair ($m_I/m_P$,$\lambda$) shown here are given by (0.5, 33.5), (0.1, 838), and (0.05, 3350) in order of increasing ${\psi }_{cr}$. The main point of this figure is that $F_I+F_O\gg \widehat{F}$ for all relevant values of ${\psi }_S$ and for any realistic value of $\lambda$. More detailed features of this plot are discussed in the text.