Radial oscillations and tidal Love numbers of dark energy stars
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Radial oscillations and tidal Love numbers of dark energy stars Grigorios Panotopoulos1,a , Ángel Rincón2,b , Ilídio Lopes1,c 1 Centro de Astrofísica e Gravitação, Departamento de Física, Instituto Superior Técnico-IST, Universidade
de Lisboa-UL, Av. Rovisco Pais, 1049-001 Lisbon, Portugal
2 Instituto de Física, Pontificia Universidad Católica de Valparaíso, Avenida Brasil 2950, Casilla 4059,
Valparaíso, Chile Received: 20 August 2020 / Accepted: 16 October 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract We investigate the properties of relativistic stars made of dark energy. We model stellar structure assuming (1) isotropic perfect fluid and (2) a dark energy inspired equation of state, the generalized equation of state of Chaplygin gas, as we will be calling it. The mass-to-radius profiles, the tidal Love numbers as well as the ten lowest radial oscillation modes are computed. Causality, stability and energy conditions are also discussed.
1 Introduction The origin and nature of dark energy (DE), the fluid component that currently accelerates the Universe [1–3], is one of the biggest mysteries and challenges in modern theoretical Cosmology. It is well known that Einstein’s general relativity (GR) [4] with radiation and matter only cannot lead to accelerating solutions. A positive cosmological constant [5] is the simplest, most economical model in a very good agreement with a great deal of current observational data. The CDM model (concordance model), based on cold dark matter and a positive cosmological constant, however, suffers from the cosmological constant problem [6,7]. Furthermore, regarding the value of the Hubble constant H0 , there is nowadays a tension between high red-shift CMB data and local measurements at low red-shift data, see e.g. [8–12]. The value of the Hubble constant extracted by the PLANCK Collaboration [13,14], H0 = (67−68) km/(Mpc sec), is found to be lower than the value obtained by local measurements, H0 = (73−74) km/(Mpc sec) [15,16]. This tension might call for new physics [17,18]. For those reasons, several alternatives to the CDM model have been proposed and studied over the years. Generically speaking, all dark energy (DE) models fall into two broad classes; namely either a modified theory of gravity is assumed, providing correction terms to GR at cosmological scales, or a new dynamical degree of freedom with an equation of state parameter w < −1/3 must be introduced. In the first class of models (geometrical DE),
a e-mail: [email protected] (corresponding author) b e-mail: [email protected] c e-mail: [email protected]
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one finds, for instance, f (R) theories of gravity [19–22], brane-world models [23–25] and scalar-tensor theories of gravity [26–29], while in the second class (dynamical DE) one finds models such as quintessence [30], phantom [31], quintom [32], tachyonic [33] or k-essence [34].
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