The Imprint of Gravitational Waves on the Cosmic Microwave Background

Long-wavelength gravitational waves can induce significant temperature anisotropy in the cosmic microwave background. Distinguishing this from anisotropy induced by energy density fluctuations is critical for testing inflationary cosmology and theories of large-scale structure formation. We describe full radiative transport calculations of the two contributions and show that they differ dramatically at angular scales below a few degrees. We show how anisotropy experiments probing large- and small-angular scales can combine to distinguish the imprint due to gravitational waves.Comment: 11 pages, Penn Preprint-UPR-

Can inflationary models of cosmic perturbations evade the secondary oscillation test?

We consider the consequences of an observed Cosmic Microwave Background (CMB) temperature anisotropy spectrum containing no secondary oscillations. While such a spectrum is generally considered to be a robust signature of active structure formation, we show that such a spectrum {\em can} be produced by (very unusual) inflationary models or other passive evolution models. However, we show that for all these passive models the characteristic oscillations would show up in other observable spectra. Our work shows that when CMB polarization and matter power spectra are taken into account secondary oscillations are indeed a signature of even these very exotic passive models. We construct a measure of the observability of secondary oscillations in a given experiment, and show that even with foregrounds both the MAP and \pk satellites should be able to distinguish between models with and without oscillations. Thus we conclude that inflationary and other passive models can {\em not} evade the secondary oscillation test.Comment: Final version accepted for publication in PRD. Minor improvements have been made to the discussion and new data has been included. The conclusions are unchagne

Limits on the gravity wave contribution to microwave anisotropies

We present limits on the fraction of large angle microwave anisotropies which could come from tensor perturbations. We use the COBE results as well as smaller scale CMB observations, measurements of galaxy correlations, abundances of galaxy clusters, and Lyman alpha absorption cloud statistics. Our aim is to provide conservative limits on the tensor-to-scalar ratio for standard inflationary models. For power-law inflation, for example, we find T/S<0.52 at 95% confidence, with a similar constraint for phi^p potentials. However, for models with tensor amplitude unrelated to the scalar spectral index it is still currently possible to have T/S>1.Comment: 23 pages, 7 figures, accepted for publication in Phys. Rev. D. Calculations extended to blue spectral index, Fig. 6 added, discussion of results expande

On the degree of scale invariance of inflationary perturbations

Many, if not most, inflationary models predict the power-law index of the spectrum of density perturbations is close to one, though not precisely equal to one, |n-1| \sim O(0.1), implying that the spectrum of density perturbations is nearly, but not exactly, scale invariant. Some models allow n to be significantly less than one (n \sim 0.7); a spectral index significantly greater than one is more difficult to achieve. We show that n \approx 1 is a consequence of the slow-roll conditions for inflation and ``naturalness,'' and thus is a generic prediction of inflation. We discuss what is required to deviate significantly from scale invariance, and then show, by explicit construction, the existence of smooth potentials that satisfy all the conditions for successful inflation and give $n$ as large as 2.Comment: 7 pages, 2 figures, submitted to Phys. Rev.

The Formation of Cosmic Structures in a Light Gravitino Dominated Universe

We analyse the formation of cosmic structures in models where the dark matter is dominated by light gravitinos with mass of $100$ eV -- 1 keV, as predicted by gauge-mediated supersymmetry (SUSY) breaking models. After evaluating the number of degrees of freedom at the gravitinos decoupling ($g_*$), we compute the transfer function for matter fluctuations and show that gravitinos behave like warm dark matter (WDM) with free-streaming scale comparable to the galaxy mass scale. We consider different low-density variants of the WDM model, both with and without cosmological constant, and compare the predictions on the abundances of neutral hydrogen within high-redshift damped Ly--$\alpha$ systems and on the number density of local galaxy clusters with the corresponding observational constraints. We find that none of the models satisfies both constraints at the same time, unless a rather small $\Omega_0$ value (\mincir 0.4) and a rather large Hubble parameter (\magcir 0.9) is assumed. Furthermore, in a model with warm + hot dark matter, with hot component provided by massive neutrinos, the strong suppression of fluctuation on scales of \sim 1\hm precludes the formation of high-redshift objects, when the low--$z$ cluster abundance is required. We conclude that all different variants of a light gravitino DM dominated model show strong difficulties for what concerns cosmic structure formation. This gives a severe cosmological constraint on the gauge-mediated SUSY breaking scheme.Comment: 28 pages,Latex, submitted for publication to Phys.Rev.

Is cosmology consistent?

We perform a detailed analysis of the latest CMB measurements (including BOOMERaNG, DASI, Maxima and CBI), both alone and jointly with other cosmological data sets involving, e.g., galaxy clustering and the Lyman Alpha Forest. We first address the question of whether the CMB data are internally consistent once calibration and beam uncertainties are taken into account, performing a series of statistical tests. With a few minor caveats, our answer is yes, and we compress all data into a single set of 24 bandpowers with associated covariance matrix and window functions. We then compute joint constraints on the 11 parameters of the ``standard'' adiabatic inflationary cosmological model. Out best fit model passes a series of physical consistency checks and agrees with essentially all currently available cosmological data. In addition to sharp constraints on the cosmic matter budget in good agreement with those of the BOOMERaNG, DASI and Maxima teams, we obtain a heaviest neutrino mass range 0.04-4.2 eV and the sharpest constraints to date on gravity waves which (together with preference for a slight red-tilt) favors ``small-field'' inflation models.Comment: Replaced to match accepted PRD version. 14 pages, 12 figs. Tiny changes due to smaller DASI & Maxima calibration errors. Expanded neutrino and tensor discussion, added refs, typos fixed. Combined CMB data, window and covariance matrix at http://www.hep.upenn.edu/~max/consistent.html or from [email protected]

Constraining the Power Spectrum using Clusters

(Shortened Abstract). We analyze a redshift sample of Abell/ACO clusters and compare them with numerical simulations based on the truncated Zel'dovich approximation (TZA), for a list of eleven dark matter (DM) models. For each model we run several realizations, on which we estimate cosmic variance effects. We analyse correlation statistics, the probability density function, and supercluster properties from percolation analysis. As a general result, we find that the distribution of galaxy clusters provides a constraint only on the shape of the power spectrum, but not on its amplitude: a shape parameter 0.18 < \Gamma < 0.25 and an effective spectral index at 20Mpc/h in the range [-1.1,-0.9] are required by the Abell/ACO data. In order to obtain complementary constraints on the spectrum amplitude, we consider the cluster abundance as estimated using the Press--Schechter approach, whose reliability is explicitly tested against N--body simulations. We conclude that, of the cosmological models considered here, the only viable models are either Cold+Hot DM ones with \Omega_\nu = [0.2-0.3], better if shared between two massive neutrinos, and flat low-density CDM models with \Omega_0 = [0.3-0.5].Comment: 37 pages, Latex file, 9 figures; New Astronomy, in pres

STATIONARY SOLUTIONS IN BRANS-DICKE STOCHASTIC INFLATIONARY COSMOLOGY

In Brans-Dicke theory the Universe becomes divided after inflation into many exponentially large domains with different values of the effective gravitational constant. Such a process can be described by diffusion equations for the probability of finding a certain value of the inflaton and dilaton fields in a physical volume of the Universe. For a typical chaotic inflation potential, the solutions for the probability distribution never become stationary but grow forever towards larger values of the fields. We show here that a non-minimal conformal coupling of the inflaton to the curvature scalar, as well as radiative corrections to the effective potential, may provide a dynamical cutoff and generate stationary solutions. We also analyze the possibility of large nonperturbative jumps of the fluctuating inflaton scalar field, which was recently revealed in the context of the Einstein theory. We find that in the Brans--Dicke theory the amplitude of such jumps is strongly suppressed.Comment: 19 pages, LaTe

Estimating the tensor-to-scalar ratio and the effect of residual foreground contamination

We consider future balloon-borne and ground-based suborbital experiments designed to search for inflationary gravitational waves, and investigate the impact of residual foregrounds that remain in the estimated cosmic microwave background maps. This is achieved by propagating foreground modelling uncertainties from the component separation, under the assumption of a spatially uniform foreground frequency scaling, through to the power spectrum estimates, and up to measurement of the tensor to scalar ratio in the parameter estimation step. We characterize the error covariance due to subtracted foregrounds, and find it to be subdominant compared to instrumental noise and sample variance in our simulated data analysis. We model the unsubtracted residual foreground contribution using a two-parameter power law and show that marginalization over these foreground parameters is effective in accounting for a bias due to excess foreground power at low $\ell$. We conclude that, at least in the suborbital experimental setups we have simulated, foreground errors may be modeled and propagated up to parameter estimation with only a slight degradation of the target sensitivity of these experiments derived neglecting the presence of the foregrounds.Comment: 19 pages, 12 figures, accepted for publication in JCA

Turbulent Thermalization

We study, analytically and with lattice simulations, the decay of coherent field oscillations and the subsequent thermalization of the resulting stochastic classical wave-field. The problem of reheating of the Universe after inflation constitutes our prime motivation and application of the results. We identify three different stages of these processes. During the initial stage of ``parametric resonance'', only a small fraction of the initial inflaton energy is transferred to fluctuations in the physically relevant case of sufficiently large couplings. A major fraction is transfered in the prompt regime of driven turbulence. The subsequent long stage of thermalization classifies as free turbulence. During the turbulent stages, the evolution of particle distribution functions is self-similar. We show that wave kinetic theory successfully describes the late stages of our lattice calculation. Our analytical results are general and give estimates of reheating time and temperature in terms of coupling constants and initial inflaton amplitude.Comment: 27 pages, 13 figure