We show the universe was reionized twice , first at z \sim 15 - 16 and second at z \sim 6 .
Such an outcome appears inevitable , when normalizing to two well determined observational measurements , namely , the epoch of the final cosmological reionization at z \sim 6 and the density fluctuations at z \sim 6 , which in turn are tightly constrained by Ly \alpha forest observations at z \sim 3 .
These two observations most importantly fix the product of star formation efficiency and ionizing photon escape fraction from galaxies at high redshift .
The only major assumption made is that the initial mass function of metal-free , Population III stars is top-heavy .

To the extent that the relative star formation efficiencies in gaseous minihalos with { H _ { 2 } } cooling and large halos with atomic cooling at high redshift are unknown , the primary source for the first reionization is still uncertain .
If star formation efficiency in minihalos is at least 10 % of that in large halos , then Pop III stars in the minihalos may be largely responsible for the first reionization ; otherwise , the first reionization will be attributable largely to Pop III stars in large halos .
In the former case , { H _ { 2 } } cooling in minihalos is necessarily efficient .
We show that gas in minihalos can be cooled efficiently by { H _ { 2 } } molecules and star formation can continue to take place largely unimpeded throughout the first reionization period , as long as gas is able to accumulate in them .
This comes about thanks to two new mechanisms for generating a high X-ray background during the Pop III era , put forth here , namely , X-ray emission from the cooling energy of Pop III supernova blast waves and from miniquasars powered by Pop III black holes .
Consequently , { H _ { 2 } } formation in the cores of minihalos is significantly induced to be able to counteract the destruction by Lyman-Werner photons produced by the same Pop III stars .
In addition , an important process for producing a large number of { H _ { 2 } } molecules in relic HII regions of Pop III galaxies , first pointed out by Ricotti , Gnedin , & Shull , is quantified here .
It is shown that { H _ { 2 } } molecules produced by this process may overwhelm the Lyman-Werner photons produced by stars in the same Pop III galaxies .
As a result , the Lyman-Werner background may never build up in the first place during the Pop III era .

The long cosmological reionization and reheating history is complex .
From z \sim 30 Pop III stars gradually heat up and ionize the intergalactic medium , completing the first reionization at z \sim 15 - 16 , followed by a brief period of \Delta z \sim 1 , during which the intergalactic medium stays completely ionized due to sustained ionizing photon emission from concomitant Pop III galaxies .
The transition from Pop III stars to Pop II stars at z \sim 13 suddenly reduces , by a factor of \sim 10 , ionizing photon emission rate , causing hydrogen to rapidly recombine , marking the second cosmological recombination .
From z \sim 13 to z = 6 , Compton cooling by the cosmic microwave background and photoheating by the stars self-regulate the Jeans mass and the star formation rate , giving rise to a mean temperature of the intergalactic medium maintained nearly at constant of \sim 10 ^ { 4 } ~ { } K. Meanwhile , recombination and photoionization balance one another such that the intergalactic medium stays largely ionized during this stage with n _ { HII } / n _ { H } \geq 0.6 .
Most of the star formation in this period occurs in large halos with dominant atomic line cooling .

We discuss a wide range of implications and possible tests for this new reionization picture .
In particular , the Thomson scattering optical depth is increased to 0.10 \pm 0.03 , compared to 0.027 for the case of only one rapid reionization at z = 6 .
Upcoming Microwave Anisotropy Probe observation of the polarization of the cosmic microwave background should be able to distinguish between these two scenarios .