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A large number of dark energy and modified gravity models lead to the same expansion history of the Universe, hence, making it difficult to distinguish them from observations. To make the calculations transparent, we consider f (R) gravity with a pressureless matter without making any assumption about the form of f (R). Using the late-time expansion history realizations constructed by Shafieloo et al [1], we explicitly show for any f (R) model that the Bardeen potentials Ψ and Φ evolve differently. For an arbitrary f (R) model that leads to late-time accelerated expansion, we explicitly show that |Ψ + Φ| and its time-derivative evolves differently than the ΛCDM model at lower redshifts. We show that the Ψ/Φ has significant deviation from unity for larger wavenumbers. We discuss the implications of the results for the cosmological observations. * josephpj@iitb.ac.in † shanki@phy.iitb.ac.in arXiv:1904.07608v2 [astro-ph.CO] 30 Sep 2019 Providing a fundamental understanding of the late-time accelerated expansion of the Universe is one of the most challenging problems in cosmology. GR alone can not explain the late-time acceleration of the Universe with ordinary matter or radiation. The presence of an exotic matter source energy referred to as dark energy can explain the late-time accelerated expansion [11-15]. The most straightforward candidate for the dark energy (DE) is the cosmological constant Λ [16-19]. However, the estimated value of Λ from observations shows that it is many orders smaller than the vacuum energy density predicted by particle physics [16, 17]. The cosmological constant does not change with the evolution of the Universe. However, in models like Quintessence, K-essence, Phantom models, Chameleon scalar fields dark energy changes with time [12]. An alternative to dark energy is the modified gravity (MG) model, where the late-time acceleration is due to the large-scale modifications to GR. Several modified gravity models, like f (R), Braneworld and Galileon models, have been proposed as the possible explanation for the late-time accelerated expansion of the universe [20-23]. Among the modified gravity models, f (R) models (where f is an arbitrary function of the Ricci scalar R) are popular owing to the simplicity of the dynamical equations. Also, f (R) models do not suffer from Oströgradsky instability [24].Naturally, many phenomenological f (R) models that are consistent with local gravity tests and have stable late-time de Sitter point have been proposed [25][26][27][28][29]. These models also suffer from fine-tuning problem as like the cosmological constant. In other words, one needs to tune the threshold value of the Ricci scalar R 0 to obtain the observed late-time acceleration.As mentioned above, many different f (R) models with fine-tuning can account for the