Reconstructing emission from pre-reionization sources with cosmic
  infrared background fluctuation measurements by the JWST
  We present new methodology to use cosmic infrared background (CIB)
fluctuations to probe sources at 10<z<30 from a JWST/NIRCam configuration that
will isolate known galaxies to 28 AB mag at 0.5--5 micron. At present
significant mutually consistent source-subtracted CIB fluctuations have been
identified in the Spitzer and Akari data at 2--5 micron, but we demonstrate
internal inconsistencies at shorter wavelengths in the recent CIBER data. We
evaluate CIB contributions from remaining galaxies and show that the bulk of
the high-z sources will be in the confusion noise of the NIRCam beam, requiring
CIB studies. The accurate measurement of the angular spectrum of the
fluctuations and probing the dependence of its clustering component on the
remaining shot noise power would discriminate between the various currently
proposed models for their origin and probe the flux distribution of its
sources. We show that the contribution to CIB fluctuations from remaining
galaxies is large at visible wavelengths for the current instruments precluding
probing the putative Lyman-break of the CIB fluctuations. We demonstrate that
with the proposed JWST configuration such measurements will enable probing the
Lyman break. We develop a Lyman-break tomography method to use the NIRCam
wavelength coverage to identify or constrain, via the adjacent two-band
subtraction, the history of emissions over 10<z<30 as the Universe comes out of
the 'Dark Ages'. We apply the proposed tomography to the current Spitzer/IRAC
measurements at 3.6 and 4.5 micron, to find that it already leads to
interestingly low upper limit on emissions at z>30.
