Density perturbation in an interacting holographic dark energy model

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Density perturbation in an interacting holographic dark energy model Srijita Sinhaa , Narayan Banerjeeb IISER Kolkata, Mohanpur Campus, Mohanpur, Nadia 741246, India Received: 28 February 2020 / Accepted: 23 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020

Abstract The present work deals with the evolution of the density contrasts for a cosmological model where along with the standard cold dark matter (CDM), the present Universe also contains holographic dark energy (HDE). The HDE is allowed to interact with the CDM. The equations for the density contrasts are integrated numerically. It is found that irrespective of the presence of an interaction, the matter perturbation has growing modes. The HDE is also found to have growth of perturbation, so very much like the CDM, HDE can also cluster. The interesting point to note is that the density contrast corresponding to HDE has a peak at a recent past and is decaying at the present epoch.

1 Introduction Ever since the discovery through the luminosity versus redshift surveys [1–3], that the Universe at the present epoch is expanding with an acceleration, there has been a proliferation of proposals of a “dark energy” that gravitates in the wrong way. A cosmological constant  appears to be a very competent candidate although not a clear winner because of the insurmountable discrepancy between the observational requirement and the theoretically predicted value. A scalar field with a suitable potential, called a quintessence, is arguably the close second. There are excellent reviews that summarise the list of candidates and their strength and weakness [4–7]. Among the quintessence models, some may evolve in a way such that the equation of state parameter of the dark energy attains a value less that −1 at the present epoch or in a finite future [8]. Such models are called “quintom” models as they evolve to mimic a phantom model. Several representative models of quintom cosmology can also be found in [9–11]. Moreover, this dark energy model can yield important cosmological applications, namely, it may avoid the big bang singularity if applied to the very early Universe. This result can be found in [12,13]. For a more detail theoretical and observational implications, we refer to the work of Cai et al [14]. Another most talked about form of dark energy is the so-called holographic dark energy (HDE) based on the holographic principle in quantum gravity theory [15]. The holographic principle, following the ’t Hooft conjecture [16], that the information contained in a volume can be ascertained with the knowledge about the degrees of freedom residing on its boundary

a e-mail: [email protected] b e-mail: [email protected] (corresponding author)

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actually stems from Bekenstein’s idea that the entropy of a black hole is related to its area [17]. Based on the holographic principle, one of the characteristic features of the HDE is