Observations have confirmed the accelerated expansion of the universe. The accelerated

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Dynamical models for dark energy are an alternative to the cosmological constant. It is important to investigate properties of perturbations in these models and go beyond the smooth FRLW cosmology. This allows us to distinguish different dark energy models with the same expansion history. For this, one often needs the potential for a particular expansion history. We study how such potentials can be reconstructed obtaining closed formulae for potential or reducing the problem to quadrature. We consider three classes of models here: tachyons, quintessence, and, interacting dark energy. We present results for constant w and the CPL parameterization. The method given here can be generalized to any arbitrary form of w(z).

We study evolution of perturbations in dark matter and dark energy for spherical collapse using a completely self consistent, relativistic approach. We study tachyon models of dark energy using the approach outlined in Rajvanshi and Bagla (2018). We work with models that are allowed by current observations. We find that as with quintessence models allowed by observations, dark energy perturbations do not affect evolution of perturbations in dark matter in a significant manner. Perturbations in dark energy remain small for such models. We then take two different Lagrangians for dark energy: tachyon and quintessence models, reconstruct potentials to have same expansion history and then compare if two can be distinguished in the nonlinear regime. Any variations we find are only due to a different Lagrangian density, and allow a comparison of different classes of models in a fair manner. We find that dark matter perturbations carry no imprint of the class of dark energy models for the same expansion history: this is significant in that we can work with any convenient model to study clustering of dark matter. We find that the evolution of dark energy perturbations carries an imprint of the class of models and dark energy perturbations grow differently in tachyon models and quintessence models for the same expansion history. However, the difference between these diminishes for (1 + w) ≪ 1 and hence prospects for differentiating between models using characteristics of perturbations are limited in our Universe.

Bimetric gravity is an interesting alternative to standard GR given its potential to provide a concrete theoretical framework for a ghost-free massive gravity theory. Here we investigate a class of Bimetric gravity models for their cosmological implications. We study the background expansion as well as the growth of matter perturbations at linear and second order. We use low-redshift observations from SnIa (Pantheon+ and SH0ES), Baryon Acoustic Oscillations (BAO), the growth ($$f\sigma _{8}$$ f σ 8 ) measurements and the measurement from Megamaser Cosmology Project to constrain the Bimetric model. We find that the Bimetric models are consistent with the present data alongside the $$\Lambda $$ Λ CDM model. We reconstructed the “ effective dark energy equation of state”($$\omega _{de}$$ ω de ) and “Skewness”($$S_{3}$$ S 3 ) parameters for the Bimetric model from the observational constraints and show that the current low-redshift data allow significant deviations in $$\omega _{de}$$ ω de and $$S_{3}$$ S 3 parameters with respect to the $$\Lambda $$ Λ CDM behaviour. We also look at the ISW effect via galaxy-temperature correlations and find that the best fit Bimetric model behaves similarly to $$\Lambda $$ Λ CDM in this regard.