The precision of slow-roll predictions for the CMBR anisotropies

Inflationary predictions for the anisotropy of the cosmic microwave background radiation (CMBR) are often based on the slow-roll approximation. We study the precision with which the multipole moments of the temperature two-point correlation function can be predicted by means of the slow-roll approximation. We ask whether this precision is good enough for the forthcoming high precision observations by means of the MAP and Planck satellites. The error in the multipole moments due to the slow-roll approximation is demonstrated to be bigger than the error in the power spectrum. For power-law inflation with $n_S=0.9$ the error from the leading order slow-roll approximation is $\approx 5$ for the amplitudes and $\approx 20$ for the quadrupoles. For the next-to-leading order the errors are within a few percent. The errors increase with $|n_S - 1|$. To obtain a precision of 1% it is necessary, but in general not sufficient, to use the next-to-leading order. In the case of power-law inflation this precision is obtained for the spectral indices if $|n_S - 1| < 0.02$ and for the quadrupoles if $|n_S - 1| < 0.15$ only. The errors in the higher multipoles are even larger than those for the quadrupole, e.g. $\approx 15$ for l=100, with $n_S = 0.9$ at the next-to-leading order. We find that the accuracy of the slow-roll approximation may be improved by shifting the pivot scale of the primordial spectrum (the scale at which the slow-roll parameters are fixed) into the regime of acoustic oscillations. Nevertheless, the slow-roll approximation cannot be improved beyond the next-to-leading order in the slow-roll parameters.Comment: 3 important additions: 1. discussion of higher multipoles, 2. comparison of error from the slow-roll approximation with the error from the cosmic variance, 3. suggestion for improvement of slow-roll approximation; two figures and a table added; 15 pages, 14 figures, RevTeX; accepted for publication in Phys. Rev.

Solving Stochastic Inflation for Arbitrary Potentials

A perturbative method for solving the Langevin equation of inflationary cosmology in presence of backreaction is presented. In the Gaussian approximation, the method permits an explicit calculation of the probability distribution of the inflaton field for an arbitrary potential, with or without the volume effects taken into account. The perturbative method is then applied to various concrete models namely large field, small field, hybrid and running mass inflation. New results on the stochastic behavior of the inflaton field in those models are obtained. In particular, it is confirmed that the stochastic effects can be important in new inflation while it is demonstrated they are negligible in (vacuum dominated) hybrid inflation. The case of stochastic running mass inflation is discussed in some details and it is argued that quantum effects blur the distinction between the four classical versions of this model. It is also shown that the self-reproducing regime is likely to be important in this case.Comment: 17 pages, 9 figure

Moduli Fields as Quintessence and the Chameleon

We consider models where moduli fields are not stabilized and play the role of quintessence. In order to evade gravitational tests, we investigate the possibility that moduli behave as chameleon fields. We find that, for realistic moduli superpotentials, the chameleon effect is not strong enough, implying that moduli quintessence models are gravitationally ruled out. More generally, we state a no-go theorem for quintessence in supergravity whereby models either behave like a pure cosmological constant or violate gravitational testsComment: 11 pages, 1 figur

High Energy Physics and Quintessence

It is shown that any realistic model of quintessence should be based on Supergravity (SUGRA) since the value of the quintessence field on the attractor is approximately the Planck mass. Under very general assumptions, the typical shape of a SUGRA tracking potential is derived. Cosmological implications are investigated. In particular, it is demonstrated that, generically, the equation of state parameter is driven to a value close to -1 in agreement with recent observations.Comment: 4 pages, 2 figures. Contribution to the Proceedings of Moriond 2000 "Energy Densities in the Universe", Les Arcs, France, January 22-29 200

Quintessence and the accelerating universe

Observations seem to indicate that our universe is presently accelerating due to the presence of dark energy. Quintessence represents a possible way to model the dark energy. In these proceedings, we briefly review its main properties.Comment: 4 pages, 3 figures. Invited talk given by J. Martin at the Sf2a meeting (June 24-29, 2002, Paris