Cosmic microwave background constraints on cosmological models with large-scale isotropy breaking

Several anomalies appear to be present in the large-angle cosmic microwave background (CMB) anisotropy maps of WMAP, including the alignment of large-scale multipoles. Models in which isotropy is spontaneously broken (e.g., by a scalar field) have been proposed as explanations for these anomalies, as have models in which a preferred direction is imposed during inflation. We examine models inspired by these, in which isotropy is broken by a multiplicative factor with dipole and/or quadrupole terms. We evaluate the evidence provided by the multipole alignment using a Bayesian framework, finding that the evidence in favor of the model is generally weak. We also compute approximate changes in estimated cosmological parameters in the broken-isotropy models. Only the overall normalization of the power spectrum is modified significantly.Comment: Accepted for publication in Phys. Rev.

Chaotic Inflation with Time-Variable Space Dimensions

Assuming the space dimension is not constant but decreases during the expansion of the Universe, we study chaotic inflation with the potential $m^2\phi^2/2$. Our investigations are based on a model Universe with variable space dimensions. We write down field equations in the slow-roll approximation, and define slow-roll parameters by assuming the number of space dimensions decreases continuously as the Universe expands. The dynamical character of the space dimension shifts the initial and final value of the inflaton field to larger values. We obtain an upper limit for the space dimension at the Planck length. This result is in agreement with previous works for the effective time variation of the Newtonian gravitational constant in a model Universe with variable space dimensions.Comment: 19 pages, To be published in Int.J.Mod.Phys.D. Minor changes to match accepted versio

Observational constraints on the spectral index of the cosmological curvature perturbation

We evaluate the observational constraints on the spectral index $n$, in the context of the $\Lambda$CDM hypothesis which represents the simplest viable cosmology. We first take $n$ to be practically scale-independent. Ignoring reionization, we find at a nominal 2-$\sigma$ level $n\simeq 1.0 \pm 0.1$. If we make the more realisitic assumption that reionization occurs when a fraction $f\sim 10^{-5}$ to 1 of the matter has collapsed, the 2-$\sigma$ lower bound is unchanged while the 1-$\sigma$ bound rises slightly. These constraints are compared with the prediction of various inflation models. Then we investigate the two-parameter scale-dependent spectral index, predicted by running-mass inflation models, and find that present data allow significant scale-dependence of $n$, which occurs in a physically reasonable regime of parameter space.Comment: ReVTeX, 15 pages, 5 figures and 3 tables, uses epsf.sty Improved treatment of reionization and small bug fixed in the constant n case; more convenient parameterization and better treatment of the n dependence in the CMB anisotropy for the running mass case; conclusions basically unchanged; references adde

Detectability of Microwave Background Polarization

[NOTE: Previous versions of this paper (both on astro-ph and published in Phys. Rev. D) contain results that are in error. The power spectra C_l were normalized incorrectly by a factor of 2 pi. All observing times in detector-years in those versions are too large by a factor of 2 pi. The main place these numbers appear is on the vertical axes of Figures 4 and 5. Note that because all calculations were based on the same power spectra, all conclusions pertaining to comparisons of different techniques remain unchanged. This error has been corrected in the present version of the paper. An erratum is being sent to Phys. Rev. D. I apologize for the error.] Using a Fisher-matrix formalism, we calculate the required sensitivities and observing times for an experiment to measure the amplitudes of both E and B components as a function of sky coverage, taking full account of the fact that the two components cannot be perfectly separated in an incomplete sky map. We also present a simple approximation scheme that accounts for mixing of E and B components in computing predicted errors in the E-component power spectrum amplitude. In an experiment with small sky coverage, mixing of the two components increases the difficulty of detecting the subdominant B component by a factor of two or more in observing time; however, for larger survey sizes the effect of mixing is less pronounced. Surprisingly, mixing of E and B components can enhance the detectability of the E component by increasing the effective number of independent modes that probe this componentComment: Previous versions of this paper contained results that were in error. The present version on astro-ph has been corrected, and an erratum is being submitted. See abstract for detail

Frequentist Estimation of Cosmological Parameters from the MAXIMA-1 Cosmic Microwave Background Anisotropy Data

We use a frequentist statistical approach to set confidence intervals on the values of cosmological parameters using the MAXIMA-1 and COBE measurements of the angular power spectrum of the cosmic microwave background. We define a $\Delta \chi^{2}$ statistic, simulate the measurements of MAXIMA-1 and COBE, determine the probability distribution of the statistic, and use it and the data to set confidence intervals on several cosmological parameters. We compare the frequentist confidence intervals to Bayesian credible regions. The frequentist and Bayesian approaches give best estimates for the parameters that agree within 15%, and confidence interval-widths that agree within 30%. The results also suggest that a frequentist analysis gives slightly broader confidence intervals than a Bayesian analysis. The frequentist analysis gives values of \Omega=0.89{+0.26\atop -0.19}, \Omega_{\rm B}h^2=0.026{+0.020\atop -0.011} and n=1.02{+0.31\atop -0.10}, and the Bayesian analysis gives values of \Omega=0.98{+0.14\atop -0.19}, \Omega_{\rm B}h^2=0.0.029{+0.015\atop-0.010}, and $n=1.18{+0.10\atop -0.23}$, all at the 95% confidence level.Comment: 10 pages, 9 Postscript figures, changes made to reflect published versio

Preheating in Supersymmetric Hybrid Inflation

We study preheating in a general class of supersymmetric hybrid inflation model. Supersymmetry leads to only one coupling constant in the potential and thus only one natural frequency of oscillation for the homogeneous fields, whose classical evolution consequently differs from that of a general (non-supersymmetric) hybrid model. We emphasise the importance of mixing effects in these models which can significantly change the rate of production of particles. We perform a general study of the rate of production of the particles associated with the homogeneous fields, and show how preheating is efficient in producing these quanta. Preheating of other particle species will be model dependent, and in order to investigate this we consider a realistic working model of supersymmetric hybrid inflation which solves the strong-CP problem via an approximate Peccei-Quinn symmetry, which was proposed by us previously. We study axion production in this model and show that properly taking into account the mixing between the fields suppresses the axion production, yet enhances the production of other particles. Finally we demonstrate the importance of backreaction effects in this model which have the effect of shutting off axion production, leaving the axion safely within experimental bounds.Comment: 37 pages, Latex, 11 eps figures, 14 ps (colour) figure

How Anisotropic is our Universe?

Large-scale cosmic microwave background anisotropies in homogeneous, globally anisotropic cosmologies are investigated. We perform a statistical analysis in which the four-year data from the Cosmic Background Explorer satellite is searched for the specific anisotropy patterns predicted by these models and thereby set definitive upper limits on the amount of shear, $(\sigma/H)_0$ and vorticity, $(\omega/H)_0$, which are orders of magnitude stronger than previous constraints. We comment on how these results might impact our understanding of primordial global anisotropy.Comment: 12 pages (1 figure), uses RevTex and psfig, submitted to PR

Inverting the Sachs-Wolfe Formula: an Inverse Problem Arising in Early-Universe Cosmology

The (ordinary) Sachs-Wolfe effect relates primordial matter perturbations to the temperature variations $\delta T/T$ in the cosmic microwave background radiation; $\delta T/T$ can be observed in all directions around us. A standard but idealised model of this effect leads to an infinite set of moment-like equations: the integral of $P(k) j_\ell^2(ky)$ with respect to k ($0<k<\infty$) is equal to a given constant, $C_\ell$, for $\ell=0,1,2,...$. Here, P is the power spectrum of the primordial density variations, $j_\ell$ is a spherical Bessel function and y is a positive constant. It is shown how to solve these equations exactly for ~$P(k)$. The same solution can be recovered, in principle, if the first ~m equations are discarded. Comparisons with classical moment problems (where $j_\ell^2(ky)$ is replaced by $k^\ell$) are made.Comment: In Press Inverse Problems 1999, 15 pages, 0 figures, Late

Measuring the cosmological lepton asymmetry through the CMB anisotropy

A large lepton asymmetry in the Universe is still a viable possibility and leads to many interesting phenomena such as gauge symmetry nonrestoration at high temperature. We show that a large lepton asymmetry changes the predicted cosmic microwave background (CMB) anisotropy and that any degeneracy in the relic neutrino sea will be measured to a precision of 1% or better when the CMB anisotropy is measured at the accuracy expected to result from the planned satellite missions MAP and Planck. In fact, the current measurements already put an upper limit on the lepton asymmetry of the Universe which is stronger than the one coming from considerations of primordial nucleosynthesis and structure formation.Comment: 4 pagex LaTex, 1 color postscript figure, uses epsf. Version submitted to PRL. (Bug in code fixed, new figure, conclusions unchanged