Cosmological parameter estimation and the spectral index from inflation

Accurate estimation of cosmological parameters from microwave background anisotropies requires high-accuracy understanding of the cosmological model. Normally, a power-law spectrum of density perturbations is assumed, in which case the spectral index $n$ can be measured to around $\pm 0.004$ using microwave anisotropy satellites such as MAP and Planck. However, inflationary models generically predict that the spectral index $n$ of the density perturbation spectrum will be scale-dependent. We carry out a detailed investigation of the measurability of this scale dependence by Planck, including the influence of polarization on the parameter estimation. We also estimate the increase in the uncertainty in all other parameters if the scale dependence has to be included. This increase applies even if the scale dependence is too small to be measured unless it is assumed absent, but is shown to be a small effect. We study the implications for inflation models, beginning with a brief examination of the generic slow-roll inflation situation, and then move to a detailed examination of a recently-devised hybrid inflation model for which the scale dependence of $n$ may be observable.Comment: 6 pages LaTeX file with one figure incorporated (uses mn.sty and epsf). Important modifications to result

Inflaton potential reconstruction without slow-roll

We describe a method of obtaining the inflationary potential from observations which does not use the slow-roll approximation. Rather, the microwave anisotropy spectrum is obtained directly from a parametrized potential numerically, with no approximation beyond linear perturbation theory. This permits unbiased estimation of the parameters describing the potential, as well as providing the full error covariance matrix. We illustrate the typical uncertainties obtained using the Fisher information matrix technique, studying the $\lambda \phi^4$ potential in detail as a concrete example

Higher order corrections to primordial spectra from cosmological inflation

We calculate power spectra of cosmological perturbations at high accuracy for two classes of inflation models. We classify the models according to the behaviour of the Hubble distance during inflation. Our approximation works if the Hubble distance can be approximated either to be a constant or to grow linearly with cosmic time. Many popular inflationary models can be described in this way, e.g., chaotic inflation with a monomial potential, power-law inflation and inflation at a maximum. Our scheme of approximation does not rely on a slow-roll expansion. Thus we can make accurate predictions for some of the models with large slow-roll parameters.Comment: 13 pages, 1 figure; section on consistency relations of inflation added; accepted by Physics Letters

Distribution of particles which produces a "smart" material

If $A_q(\beta, \alpha, k)$ is the scattering amplitude, corresponding to a potential $q\in L^2(D)$, where $D\subset\R^3$ is a bounded domain, and $e^{ik\alpha \cdot x}$ is the incident plane wave, then we call the radiation pattern the function $A(\beta):=A_q(\beta, \alpha, k)$, where the unit vector $\alpha$, the incident direction, is fixed, and $k>0$, the wavenumber, is fixed. It is shown that any function $f(\beta)\in L^2(S^2)$, where $S^2$ is the unit sphere in $\R^3$, can be approximated with any desired accuracy by a radiation pattern: $||f(\beta)-A(\beta)||_{L^2(S^2)}<\epsilon$, where $\epsilon>0$ is an arbitrary small fixed number. The potential $q$, corresponding to $A(\beta)$, depends on $f$ and $\epsilon$, and can be calculated analytically. There is a one-to-one correspondence between the above potential and the density of the number of small acoustically soft particles $D_m\subset D$, $1\leq m\leq M$, distributed in an a priori given bounded domain $D\subset\R^3$. The geometrical shape of a small particle $D_m$ is arbitrary, the boundary $S_m$ of $D_m$ is Lipschitz uniformly with respect to $m$. The wave number $k$ and the direction $\alpha$ of the incident upon $D$ plane wave are fixed.It is shown that a suitable distribution of the above particles in $D$ can produce the scattering amplitude $A(\alpha',\alpha)$, $\alpha',\alpha\in S^2$, at a fixed $k>0$, arbitrarily close in the norm of $L^2(S^2\times S^2)$ to an arbitrary given scattering amplitude $f(\alpha',\alpha)$, corresponding to a real-valued potential $q\in L^2(D)$.Comment: corrected typo

The 73 S ribosome of Neurospora crassa is the native mitochondrial ribosome

The effect of the inclusion of EDTA and of heparin, in media used in the isolation of mitochondria, on the mitochindrial previous termribosomenext term has been investigated. 1. 1. Mitochondria isolated from previous termNeurospora crassanext term in the presence of EDTA contain only a single type of monomeric previous termribosome, viz. 73next term S. 2. 2. Mitochondria isolated in the presence of Mg2+ contain both 79-S and previous term73next term-S monomeric previous termribosomes.next term The heterogeneity of the previous termribosomesnext term was demonstrated by (a) ultracentrifugation on sucrose gradients, (b) electron microscopy, (c) immunoprecipitation with antibodies against mitochondrial previous term73next term-S and 79-S cytoplasmic previous termribosomes,next term (d) gel electrophoresis of high and low molecular weight RNAs. 3. 3. Inclusion of heparin in all media used for the isolation of mitochondria and previous termribosomesnext term resulted in (a) dissociation of previous term73next term-S mitochondrial previous termribosomesnext term into 50-S and 37-S subunits; (b) stabilization of 79-S cytoplasmic previous termribosomes;next term (c) in the case of mitochondria isolated in the presence of Mg2+ containing both previous term73next term-S and 79-S previous termribosomes,next term heparin causes the selective dissociation of the previous term73next term S monosome to yield previous termribosomesnext term containing only a single monomeric previous termribosomenext term type, viz. 79 S. 4. 4. It is concluded that (a) the 79-S previous termribosomesnext term present in mitochondria isolated in the presence of Mg2+ are contaminating cytoplasmic previous termribosomes,next term (b) the previous term73next term-S previous termribosomesnext term are the real functional mitochondrial previous termribosomes of Neurospora crassanext term

Revisiting the calculations of inflationary perturbations

We present a new approximation scheme that allows us to increase the accuracy of analytical predictions of the power spectra of inflationary perturbations for two specific classes of inflationary models. Among these models are chaotic inflation with a monomial potential, power-law inflation and natural inflation (inflation at a maximum). After reviewing the established first order results we calculate the amplitudes and spectral indices for these classes of models at higher orders in the slow-roll parameters for scalar and tensorial perturbations.Comment: Extended version of the talk to be published in the proceedings of the Mexican Meeting on Exact Solutions and Scalar Fields in Gravity. Mexico, 1-6 October, 200

Developing a tool for obtaining maternal skinfold thickness measurements and assessing inter-observer variability among pregnant women who are overweight and obese

Extent: 6p.Background: It is estimated that between 34% and 50% of Australian women entering pregnancy are overweight and obese, which is associated with an increased risk in complications for both the woman and her infant. Current tools used in clinical and research practice for measuring body composition include body mass index (BMI), waist circumference and bioimpedance analysis. Not all of these measures are applicable for use during pregnancy due to a lack of differentiation between maternal and fetal contributions. While skinfold thickness measurement (SFTM) is increasingly being used in pregnancy, there is limited data and a lack of a standard tool for its use in overweight and obese pregnant women. Methods: We developed a standard tool for evaluating SFTM among women with a BMI ≥ 25 kg/m2. Forty-nine women were measured as part of a prospective cohort study nested within a multicentre randomised controlled trial (The LIMIT Randomised Controlled Trial). Two blinded observers each performed 2 skinfold measurements on the biceps, triceps and subscapular of each woman. Intraclass correlation coefficients (ICC) and standard error of measurement (SEM) were used to analyse SFTM, body fat percentage (BF%) and inter-observer variability. Results: The ICC for inter-observer variability in measurements were considered moderate for biceps SFTM (ICC = 0.56) and triceps SFTM (ICC = 0.51); good for subscapular SFTM (ICC = 0.71) and BF% (ICC = 0.74); and excellent for arm circumference (ICC = 0.97). The standard error of measurements ranged from 0.53 cm for arm circumference to 3.58 mm for the subscapular SFTM. Conclusion: Our findings indicate that arm circumference and biceps, triceps and subscapular SFTM can be reliably obtained from overweight and obese pregnant women to calculate BF%, using multiple observers, and can be used in a research setting.Lavern M Kannieappan, Andrea R Deussen, Rosalie M Grivell, Lisa Yelland and Jodie M Dod

Inflation and the cosmic microwave background

I give a status report and outlook concerning the use of the cosmic microwave background anisotropies to constrain the inflationary cosmology, and stress its crucial role as an underlying paradigm for the estimation of cosmological parameters.Comment: 8 pages LaTeX file, with two figures incorporated using epsf. To appear, proceedings of `The non-sleeping universe', Porto (Astrophysics and Space Science