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We study the conditions under which simple relations between the inflaton couplings and CMB observables can be established. The crucial criterion is to avoid feedback effects during reheating, which tend to introduce a complicated dependence of the CMB observables on a large number of microphysical parameters that prohibits the derivation of meaningful constraints on any individual one of them. We find that the inflaton coupling can be measured with cosmological data when the effective potential during reheating can be approximated by a parabola, and when the coupling constants are smaller than an upper bound that it determined by the ratios between the inflaton mass and the Planck mass or the scale of inflation. The power at which these ratios appear is determined by the power at which the inflaton appears in a given interaction term, and the value of the upper bound is largely independent of the type of produced particle. Our results show that next generation CMB observatories may be able to constrain the inflaton couplings for various types of interactions, providing an important clue to understand how a given model of inflation may be embedded into a more fundamental microphysical theory of nature.
We place functional constraints on the shape of the inflaton potential from the cosmic microwave background through a variant of the generalized slow roll approximation that allows large amplitude, rapidly changing deviations from scale-free conditions. Employing a principal component decomposition of the source function G~3(V/V)^2 - 2V/V and keeping only those measured to better than 10% results in 5 nearly independent Gaussian constraints that maybe used to test any single-field inflationary model where such deviations are expected. The first component implies < 3% variations at the 100 Mpc scale. One component shows a 95% CL preference for deviations around the 300 Mpc scale at the ~10% level but the global significance is reduced considering the 5 components examined. This deviation also requires a change in the cold dark matter density which in a flat LCDM model is disfavored by current supernova and Hubble constant data and can be tested with future polarization or high multipole temperature data. Its impact resembles a local running of the tilt from multipoles 30-800 but is only marginally consistent with a constant running beyond this range. For this analysis, we have implemented a ~40x faster WMAP7 likelihood method which we have made publicly available.
We present a method to measure the small-scale matter power spectrum using high-resolution measurements of the gravitational lensing of the Cosmic Microwave Background (CMB). To determine whether small-scale structure today is suppressed on scales below 10 kiloparsecs (corresponding to M < 10^9 M_sun), one needs to probe CMB-lensing modes out to L ~ 35,000, requiring a CMB experiment with about 20 arcsecond resolution or better. We show that a CMB survey covering 4,000 square degrees of sky, with an instrumental sensitivity of 0.5 uK-arcmin at 18 arcsecond resolution, could distinguish between cold dark matter and an alternative, such as 1 keV warm dark matter or 10^(-22) eV fuzzy dark matter with about 4-sigma significance. A survey of the same resolution with 0.1 uK-arcmin noise could distinguish between cold dark matter and these alternatives at better than 20-sigma significance; such high-significance measurements may also allow one to distinguish between a suppression of power due to either baryonic effects or the particle nature of dark matter, since each impacts the shape of the lensing power spectrum differently. CMB temperature maps yield higher signal-to-noise than polarization maps in this small-scale regime; thus, systematic effects, such as from extragalactic astrophysical foregrounds, need to be carefully considered. However, these systematic concerns can likely be mitigated with known techniques. Next-generation CMB lensing may thus provide a robust and powerful method of measuring the small-scale matter power spectrum.
The next generation of CMB experiments (CMB Stage-4) will produce a Sunyaev-Zeldovich (SZ) cluster catalog containing $sim10^{5}$ objects, two orders of magnitudes more than currently available. In this paper, we discuss the detectability of the polarized signal generated by scattering of the CMB quadrupole on the cluster electron gas using this catalog. We discuss the possibility of using this signal to measure the relationship between cluster optical depth and mass. We find that the area of observation of S4 maximizes the signal-to-noise (S/N) on the polarized signal but that this S/N is extremely small for an individual cluster, of order 0.5% for a typical cluster in our catalog, the main source of noise being the residual primordial E-mode signal. However, we find that the signal could be detected using the full cluster catalog and that the significance of the result will increase linearly with the size of the CMB S4 telescope mirror.
We point out that there is a high-frequency tail of the stochastic inflationary gravitational wave background that scales as $f^{-1/2}$ with frequency $f$. This contribution comes from the graviton vacuum fluctuation amplified by the inflaton coherent oscillation during the reheating stage. It contains information on inflaton properties such as the inflaton mass as well as the thermal history of the early Universe.
We propose a new way to implement an inflationary prior to a cosmological dataset that incorporates the inflationary observables at arbitrary order. This approach employs an exponential form for the Hubble parameter $H(phi)$ without taking the slow-roll approximation. At lowest non-trivial order, this $H(phi)$ has the unique property that it is the solution to the brachistochrone problem for inflation.