Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Towards a measurement of the spectral runnings   Single-field slow-roll inflation predicts a nearly scale-free power spectrum
of perturbations, as observed at the scales accessible to current cosmological
experiments. This spectrum is slightly red, showing a tilt $(1-n_s)\sim 0.04$.
A direct consequence of this tilt are nonvanishing runnings $\alpha_s=\mathrm d
n_s/\mathrm d\log k$, and $\beta_s=\mathrm d\alpha_s/\mathrm d\log k$, which in
the minimal inflationary scenario should reach absolute values of $10^{-3}$ and
$10^{-5}$, respectively. In this work we calculate how well future surveys can
measure these two runnings. We consider a Stage-4 (S4) CMB experiment and show
that it will be able to detect significant deviations from the inflationary
prediction for $\alpha_s$, although not for $\beta_s$. Adding to the S4 CMB
experiment the information from a WFIRST-like or a DESI-like survey improves
the sensitivity to the runnings by $\sim$ 20\%, and 30\%, respectively. A
spectroscopic survey with a billion objects, such as the SKA, will add enough
information to the S4 measurements to allow a detection of $\alpha_s=10^{-3}$,
required to probe the single-field slow-roll inflationary paradigm. We show
that only a very-futuristic interferometer targeting the dark ages will be
capable of measuring the minimal inflationary prediction for $\beta_s$. The
results of other probes, such as a stochastic background of gravitational waves
observable by LIGO, the Ly-$\alpha$ forest, and spectral distortions, are shown
for comparison. Finally, we study the claims that large values of $\beta_s$, if
extrapolated to the smallest scales, can produce primordial black holes of tens
of solar masses, which we show to be easily testable by the S4 CMB experiment.

12
The categories of this paper are: nucl-th
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
14
The categories of this paper are: math-ph