Fluctuations in the New Inflationary Universe

Abstract

The spectrum of density perturbations is calculated in the new-inflationary-universe scenario. The main source is the quantum fluctuations of the Higgs field, which lead to fluctuations in the time at which the false vacuum energy is released. The value of bp/p on any given length scale l, at the time when the Hubble radius » l, is estimated. This quantity is nearly scale invariant (as desired), but is unfortunately about 10' times too large. PACS numbers: 98.80. Bp, 12.10.En, 98.50.Eb, 98.80.DrThe inflationary-universe scenario was proposed by one of us' as a possible solution to the horizon, flatness, and monopole problems. In this scenario the universe supercools by many orders of magnitude below the critical temperature of a grand unified theory (GUT) phase transition, and in the process it exponentially expands by an enormous factor. The original version required that eventually the bubbles of the new phase would coalesce to fill the space uniformly. It was pointed out in the original paper, however, that under plausible assumptions this requirement is not fulfilled. Further studies" have shown that there is no apparent way to achieve a smooth coalescence of bubbles in the aftermath of inflation.The hopes for the inflationary universe brightened considerably when Linde and Albrecht and Steinhardt' proposed an alternative ending which avoids the problems described above. In this new inflationary universe, " the entire observed universe emerges from a single bubble or fluctuation. While a generic potential would lead to bubbles with far too little entropy to comprise the observed universe, ' these authors showed that with a Coleman-Weinberg potential' it is very plausible that a single bubble or fluctuation can undergo enough inflation to avoid this problem. The universe expands exponentially as the Higgs field p slowly ' rolls" down the potential, and the energy is then rapidly thermalized when p begins to oscillate about its minimum.In this paper we will examine the consequences of the quantum fluctuations of the scalar field p which occur during the era of exponential expansion. We will follow the evolution of these fluctuations through the time at which galactic scales come within the Hubble radius (at about 10' sec), and we will estimate the energy density fluctuations Dpi'p at that time. According to Harrison and Zeldovich' this number should be about 10 ', and roughly independent of scale. We find that the new inflationary universe leads to a 5p/p which is roughly independent of scale, but with a magnitude of = 50. Thus, it appears that a further modification of this scenario is necessary in order to make it workable.For concreteness we will deal with an SU (5)

Inflaton fluctuations in the presence of cosmological defects

“…which reproduces the well-known scale-invariant power spectrum of de Sitter quantum fluctuations [10][11][12]. The second term is the first order correction,…”

Dynamical supersymmetric inflation

“…During inflation, quantum fluctuations on small scales are quickly redshifted to scales much larger than the horizon size, where they are "frozen" as perturbations in the background metric [15][16][17][18]. Metric perturbations at the surface of last scattering are observable as temperature anisotropy in the CMB, which was first detected by the Cosmic Background Explorer (COBE) satellite.…”

Oscillations during inflation and the cosmological density perturbations

“…In the inflationary picture, primordial density and gravity-wave fluctuations are created from quantum fluctuations "redshifted" out of the horizon, where they are "frozen" as perturbations in the background metric [2,3,4,5,6]. Metric perturbations at the surface of last scattering are observable as temperature anisotropy in the CMB.…”