Cosmic Microwave Background Observations as a Way to Discriminate Among Inflation Models

The upcoming satellite missions MAP and Planck will measure the spectrum of fluctuations in the Cosmic Microwave Background with unprecedented accuracy. We discuss the prospect of using these observations to distinguish among proposed models of inflationary cosmology.Comment: To appear in the proceedings of the XXXIIIrd Rencontres de Moriond, "Fundamental Parameters in Cosmology", 17-24 January, Les Arcs, France. 6 Pages, 2 figures, uses moriond.st

Latest inflation model constraints from cosmic microwave background measurements

In this addendum to Phys.Rev. D74 (2006) 023502, we present an update of cosmological constraints on single-field inflation in light of the Wilkinson Microwave Ansiotropy Probe satellite mission five-year results (WMAP5). We find that the cosmic microwave background data are quite consistent with a Harrison-Zel'dovich primordial spectrum with no running and zero tensor amplitude. We find that the three main conclusions of our analysis of the WMAP three-year data (WMAP3) are consistent with the WMAP5 data: (1) the Harrison--Zel'dovich model is within the 95% confidence level contours; (2) there is no evidence for running of the spectral index of scalar perturbations; (3) From the WMAP 5 data alone, potentials of the form $V \propto \phi^p$ are consistent with the data for $p = 2$, and are ruled out for $p = 4$. Furthermore, consistent with our WMAP3 analysis, we find no evidence for primordial tensor perturbations, this time with a 95% confidence upper limit of $r < 0.4$ for the WMAP5 data alone, and $r < 0.35$ for the WMAP5 data taken in combination with the Arcminute Cosmology Bolometer Array (ACBAR).Comment: 8 pages, 4 figures. V2: matches version accepted by PR

WMAPping inflationary physics

We extract parameters relevant for distinguishing among single-field inflation models from the Wilkinson Microwave Anisotropy Probe (WMAP) data set, and from a combination of the WMAP data and seven other Cosmic Microwave Background (CMB) experiments. We use only CMB data and perform a likelihood analysis over a grid of models including the full error covariance matrix. We find that a model with a scale-invariant scalar power spectrum ($n=1$), no tensor contribution, and no running of the spectral index, is within the 1-$\sigma$ contours of both data sets. We then apply the Monte Carlo reconstruction technique to both data sets to generate an ensemble of inflationary potentials consistent with observations. None of the three basic classes of inflation models (small-field, large-field, and hybrid) are completely ruled out, although hybrid models are favored by the best-fit region. The reconstruction process indicates that a wide variety of smooth potentials for the inflaton are consistent with the data, implying that the first-year WMAP result is still too crude to constrain significantly either the height or the shape of the inflaton potential. In particular, the lack of evidence for tensor fluctuations makes it impossible to constrain the energy scale of inflation. Nonetheless, the data rule out a large portion of the available parameter space for inflation. For instance, we find that potentials of the form $V = \lambda \phi^4$ are ruled out to $3\sigma$ by the combined data set, but not by the WMAP data taken alone.Comment: 22 pages, 13 figures. Higher resolution figures available at http://home.fnal.gov/~rocky/Mapping

Slow roll in simple non-canonical inflation

We consider inflation using a class of non-canonical Lagrangians for which the modification to the kinetic term depends on the field, but not its derivatives. We generalize the standard Hubble slow roll expansion to the non-canonical case and derive expressions for observables in terms of the generalized slow roll parameters. We apply the general results to the illustrative case of ``Slinky'' inflation, which has a simple, exactly solvable, non-canonical representation. However, when transformed into a canonical basis, Slinky inflation consists of a field oscillating on a multi-valued potential. We calculate the power spectrum of curvature perturbations for Slinky inflation directly in the non-canonical basis, and show that the spectrum is approximately a power law on large scales, with a ``blue'' power spectrum. On small scales, the power spectrum exhibits strong oscillatory behavior. This is an example of a model in which the widely used solution of Garriga and Mukhanov gives the wrong answer for the power spectrum.Comment: 9 pages, LaTeX, four figures. (V2: minor changes to text. Version submitted to JCAP.

New Solutions of the Inflationary Flow Equations

The inflationary flow equations are a frequently used method of surveying the space of inflationary models. In these applications the infinite hierarchy of differential equations is truncated in a way which has been shown to be equivalent to restricting the set of models considered to those characterized by polynomial inflaton potentials. This paper explores a different method of solving the flow equations, which does not truncate the hierarchy and in consequence covers a much wider class of models while retaining the practical usability of the standard approach.Comment: References added, and a couple of comment

Three-Dimensional Mapping of Mineral Densities in Carious Dentin: Theory and Method

X-ray tomographic microscopy (XTM), a three-dimensional X-ray imaging technique, has been used to quantitatively map mineral concentrations in carious dentin. Data analysis from the XTM study indicates that variations in the mineral concentration surrounding the caries can be imaged in three dimensions with a spatial resolution that is sufficient to detect calcified and enlarged tubule spaces in the lesion. A three-dimensional image of the subsurface lesion indicates that lesion penetration is along the direction of the tubules. The mineral concentration in the uninfected dentin was measured by the XTM to be 1.29 ± 0.14 g/cm3 based upon the tabulated X-ray attenuation coefficients for apatite. This value is in excellent agreement with averaged estimates for the mineral concentration in dentin (1.4 g/cm3). Furthermore, the mineral concentration determined using XTM varies from 2.25 g/cm3 in the remineralized dentin to as low as 0.55 ± 0.17 g/cm3 in the demineralized tissue. The high concentration of mineral in the remineralized region suggests that organic matter is lost and mineral is deposited at some time during the caries process