After the release of the PLANCK data, it is evident that inflationary paradigm has stood the test of time. Even though, it is difficult to realise inflationary paradigm in a particle physics model as the present observations have ruled out the simplest quartic and quadratic inflationary potentials, which generically arise in particle physics. We would show that such simplest inflationary potentials can evade discrepancies with observations, if the inflaton field is assisted by another scalar during inflation. Moreover, unlike other multifield models, our model yields no isocurvature perturbations and negligible non-Gaussianity, making it more compatible with the present data. Above all, our model can also be realised in the framework of SUGRA.

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)

Many inflating spacetimes are likely to violate the weak energy condition, a key assumption of singularity theorems. Here we offer a simple kinematical argument, requiring no energy condition, that a cosmological model which is inflating--or just expanding sufficiently fast--must be incomplete in null and timelike past directions. Specifically, we obtain a bound on the integral of the Hubble parameter over a past-directed timelike or null geodesic. Thus inflationary models require physics other than inflation to describe the past boundary of the inflating region of spacetime.

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Abstract. I summarize the arguments that strongly suggest that our universe is the product of inflation. The mechanisms that lead to eternal inflation in both new and chaotic models are described. Although the infinity of pocket universes produced by eternal inflation are unobservable, it is argued that eternal inflation has real consequences in terms of the way that predictions are extracted from theoretical models. The ambiguities in defining probabilities in eternally inflating spacetimes are reviewed, with emphasis on the youngness paradox that results from a synchronous gauge regularization technique. Although inflation is generically eternal into the future, it is not eternal into the past: it can be proven under reasonable assumptions that the inflating region must be incomplete in past directions, so some physics other than inflation is needed to describe the past boundary of the inflating region.

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