Constraining Isocurvature Fluctuations with the Planck Surveyor

A second generation of satellite experiments, MAP [1] and Planck [2], will soon provide highly detailed temperature maps of the cosmic microwave background (CMB). From the measured spectrum of temperature fluctuations one may infer the properties of the cosmic fluid, such as its density or the rate by which it comoves with the expansion of the Universe, and thus determine most cosmological parameters to an accuracy of a few percent [3–5]. In addition, the spectrum of temperature fluctuations allows us to study and constrain physics at very small distance scales, corresponding to energies much higher than can be achieved in any particle accelerator in the foreseeable future. This is so because the features on the temperature map depend on the nature of the primordial density fluctuation. Cosmic inflation is currently the most popular explanation for the origin of the primordial perturbations, and it typically predicts a near scale invariant spectrum with Gaussian fluctuations. The perturbations are adiabatic with the number density proportional to entropy density so that δ(n/s) = 0. This is so because the quantum fluctuations of the field responsible for inflation, called the inflaton, give directly rise to perturbations in the energy density of the inflaton field. However, the inflaton may not be the only field which is subject to quantum fluctuations during inflation. In fact, any effectively massless scalar field will fluctuate by virtue of the nearly constant energy density of the inflation era with a root mean square amplitude H/(2π), where H is the Hubble parameter during inflation. Such fluctuations will contribute to the perturbations in the microwave background. They may be adiabatic, in which case it is difficult to entangle their effect from the inflaton fluctuations. The other possibility is isocurvature fluctuations, which are fluctuations in the number rather than the energy density so that δ(n/s) 6= 0. Examples of particle physics models giving rise to isocurvature fluctuations include axions [6,7], inflation with more than one inflaton field [8], and supersymmetric theories with flat directions in the potential [9]. Isocurvature perturbations [10,11] in a given particle species have δρ = 0 with the overdensities balanced by perturbations in other particle species, such as radiation. At the last scattering surface (LSS) the compensation for the isocurvature perturbations can be maintained only for scales larger than the horizon, effectively generating extra power to photon perturbations at small angular multipoles l. As a consequence, the spectrum of isocurvature perturbations differs a great deal from adiabatic perturbations, and a purely isocurvature cold dark matter (CDM) perturbation spectrum is in fact already ruled out [12] on the basis of COBE normalization and σ8, the amplitude of the rms mass fluctuations in an 8h−1 Mpc−1 sphere. (There are suggestions that a decaying CDM model could sustain purely isocurvature perturbations [13]; however, such models are not motivated from particle physics point of view). A small isocurvature contribution might, however, be beneficial in the sense that it could help to improve the fit to the power spectrum in Ω0 = 1 CDM models with a cosmological constant [14,6]. The simplest possibility is that there is a single CDM which has both adiabatic and isocurvature perturbations. An example of such a situation is obtained in supersymmetric models with the so-called Affleck-Dine (AD) fields [15], which also provide a basis for baryogenesis. The AD fields are superpositions of squark and slepton fields corresponding to the flat directions. During inflation they will fluctuate along the flat directions forming a condensate. They are complex fields and, in the currently favoured D-term inflation models [16], is effectively massless during inflation. The condensate does not correspond to the state of lowest energy but fragments into non-topological solitons [17], which carry baryonic (and sometimes leptonic) number [18] and are called B-balls