Testing Inflation: A Bootstrap Approach

We note that the essential idea of inflation, that the Universe underwent a brief period of accelerated expansion followed by a long period of decelerated expansion, can be encapsulated in a “closure condition” which relates the amount of accelerated expansion during inflation to the amount of decelerated expansion afterward. We present a protocol for systematically testing the validity of this condition observationally.

Figure 1

First and second bootstrap tests: The first test is satisfied for $r$ and $n_s$ corresponding to the open white circle for efficient reheating; the circle becomes a short arc (dotted) if one includes the uncertainty in the “reheating epoch” (parameterized by $\Delta N$). The second test is passed if $r$ and $n_s$ lie anywhere along the solid black curve or, allowing for the uncertainty in $\Delta N$, the black curve plus shaded region.

Figure 2

The third bootstrap relation constrains ($r$, $n_s$, ${\alpha }_s$) to lie on a curve, as shown, assuming efficient reheating ($\Delta N=0$); including this uncertainty extends each curve downward (towards more easily observable values of ${\alpha }_s$) into a strip of finite thickness. Note that these curves include values of ($r$, $n_s$) that fail the first two bootstrap tests.