We review the relation between the inflationary potential and the spectra of density (scalar) perturbations and gravitational waves (tensor perturbations) produced, with particular emphasis on the possibility of reconstructing the inflaton potential from observations. The spectra provide a potentially powerful test of the inflationary hypothesis; they are not independent but instead are linked by consistency relations reflecting their origin from a single inflationary potential. To lowest-order in a perturbation expansion there is a single, now familiar, relation between the tensor spectral index and the relative amplitude of the spectra. We demonstrate that there is an infinite hierarchy of such consistency equations, though observational difficulties suggest only the first is ever likely to be useful. We also note that since observations are expected to yield much better information on the scalars than on the tensors, it is likely to be the next-order version of this consistency equation which will be appropriate, not the lowest-order one. If inflation passes the consistency test, one can then confidently use the remaining observational information to constrain the inflationary potential, and we survey the general perturbative scheme for carrying out this procedure. Explicit expressions valid to next-lowest order in the expansion are presented. We then briefly assess the prospects for future observations reaching the quality required, and consider simulated data sets motivated by this outlook.

We demonstrate how the properties of the attractor solutions of exponential potentials can lead to models of quintessence with the currently observationally favored equation of state. Moreover, we show that these properties hold for a wide range of initial conditions and for natural values of model parameters.PACS number͑s͒: 98.80.Cq

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We address the important issue of stabilizing the dilaton in the context of superstring cosmology. Scalar potentials which arise out of gaugino condensates in string models are generally exponential in nature. In a cosmological setting this allows for the existence of quasiscaling solutions, in which the energy density of the scalar field can, for a period, become a fixed fraction of the background density, due to the friction of the background expansion. Eventually the field can be trapped in the minimum of its potential as it leaves the scaling regime. We investigate this possibility in various gaugino condensation models and show that stable solutions for the dilaton are far more common than one would have naively thought. ͓S0556-2821͑98͒01320-4͔

A well-known problem of the ΛCDM model is the tension between the relatively high level of clustering, as quantified by the parameter σ8, found in cosmic microwave background experiments and the smaller one obtained from large-scale observations in the late Universe. In this paper we show that coupled quintessence, i.e. a single dark energy scalar field conformally coupled to dark matter through a constant coupling, can solve this problem if the background is taken to be identical to the ΛCDM one. We show that two competing effects arise. On one hand, the additional scalar force is attractive, and is therefore expected to increase the clustering. On the other, in order to obtain the same background as ΛCDM, coupled quintessence must have a smaller amount of dark matter near the present epoch. We show that the second effect is dominating today and leads to an overall slower growth. Comparing to redshift distortion data, we find that coupled quintessence with ΛCDM background solves the tension between early and late clustering.We find for the coupling β and for σ8 the best fit values |β| = 0.079 +0.059 −0.067 and σ8 = 0.818 +0.115 −0.088 . These values also fit the lensing data from the KiDS-450 survey. We also estimate that the future missions SKA and Euclid will constrain β with an error of ± 1.5 × 10 −3 and for σ8 of ± 1.8 × 10 −3 at 1σ level.