We place observational constraints on a coupling between dark energy and dark matter by using 71 Type Ia supernovae (SNe Ia) from the first year of the five-year Supernova Legacy Survey (SNLS), the cosmic microwave background (CMB) shift parameter from the three-year Wilkinson Microwave Anisotropy Probe (WMAP), and the baryon acoustic oscillation (BAO) peak found in the Sloan Digital Sky Survey (SDSS). The interactions we study are (i) constant coupling δ and (ii) varying coupling δ(z) that depends on a redshift z, both of which have simple parametrizations of the Hubble parameter to confront with observational data. We find that the combination of the three databases marginalized over a present dark energy density gives stringent constraints on the coupling, −0.08 < δ < 0.03 (95% CL) in the constant coupling model and −0.4 < δ 0 < 0.1 (95% CL) in the varying coupling model, where δ 0 is a present value. The uncoupled ΛCDM model (w X = −1 and δ = 0) still remains a good fit to the data, but the negative coupling (δ < 0) with the equation of state of dark energy w X < −1 is slightly favoured over the ΛCDM model. PACS number(s): 98.80.Es, 98.80.Cq

We present a phase-space analysis of cosmology containing multiple scalar fields with positive and negative exponential potentials. We show that there exist power-law multi-kineticpotential scaling solutions for sufficiently flat positive potentials or steep negative potentials. The former is the unique late-time attractor and the well-known assisted inflationary solution, but the later is never unstable in an expanding universe. Moreover, for steep negative potentials there exist a kinetic-dominated regime in which each solution is a late-time attractor. We briefly discuss the physical consequences of these results.

We discuss the realization of inflation and resulting cosmological perturbations in the low-energy effective string theory. In order to obtain nearly scale-invariant spectra of density perturbations and a suppressed tensor-to-scalar ratio, it is generally necessary that the dilaton field φ is effectively decoupled from gravity together with the existence of a slowly varying dilaton potential. We also study the effect of second-order corrections to the tree-level action which are the sum of a Gauss-Bonnet term coupled to φ and a kinetic term (∇φ) 4 . We find that it is possible to realize observationally supported spectra of scalar and tensor perturbations provided that the correction is dominated by the (∇φ) 4 term even in the absence of the dilaton potential. When the Gauss-Bonnet term is dominant, tensor perturbations exhibit violent negative instabilities on small-scales about a de Sitter background in spite of the fact that scale-invariant scalar perturbations can be achieved.

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