A universe containing a coupled scalar field would have different dynamical evolution compared to uncoupled cases. Significant differences are expected to emerge during matter dominated era, where scalar field density mimics how matter density evolves, by becoming subdominant. Analysis of the dynamics was investigated both analytically and numerically through phase plane method, and we obtained two attractor solutions which are compatible to a late time cosmic acceleration as the ending of matter dominated era. Ordinary scalar field triggers an acceleration with stable attractor solution which converges to ωϕ = ωeff ≈ −1. Whereas, phantom scalar field allows negative values for its own energy (ωeff ˂ −1 and Ωϕ ˂ 0); however this is not stable, therefore it will be caught by attractor solution which is stable to ωϕ = ωeff ≈ −1. In addition, we found cosmological parameters generated from both analytical and numerical calculations, i.e. ωϕ , Ωϕ and ωeff , by assuming a flat universe. The existence of a coupling constant Q between scalar field and matter induces different structure growth compared to uncoupled cases and standard cold dark matter (CDM) model. During matter dominated era, ordinary scalar field induces growth of structures so that it becomes faster than the standard model does, whereas phantom scalar field slows down the growth of structures. During scalar field dominated era (far in the future), we obtained that formed structures or density contrasts will decay in a similar way as in uncoupled cases, whereas following phantom scenario, the decay of formed structures occurs faster and more significant. This result is associated to background dynamics which shows that big rip will be the relevant fate of our universe.

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We performed an investigation of the possibility of constraining the dark energy models such as w-cold dark matter, holographic dark energy, and Ricci dark energy, using a special type of Einstein ring system, called as double-source plane (DSP) lensing system. We found that DSP lensing system only gives a good constraint of the model parameters. We also found that the method highly complimentary to cosmic microwave background measurement for each model.

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In this paper, we reconstruct matter power spectrum of a cosmological model in which coupled scalar field acts as dark energy. The coupled scalar field (CSF) dark energy we propose here is a generalized model of quintessence, k-essence or phantom coupled to dark matter (non-baryonic matter) via a coupling constant. The existence of coupling between dark energy and matter allows energy to transfer between them, which may give rise to different observational signatures, especially at perturbation level, including matter power spectrum. In this work, through analytical exploration we studied that possible signature in matter power spectrum that maybe induced by this mode.