Configurational entropy in f ( T ) gravity
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Configurational entropy in f (T ) gravity Snehasish Bhattacharjeea Department of Astronomy, Osmania University, Hyderabad 500007, India Received: 23 June 2020 / Accepted: 16 September 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The evolution of the configurational entropy of the universe relies on the growth rate of density fluctuations and on the Hubble parameter. In this work, I present the evolution of configurational entropy for the power law f (T ) gravity model of the form f (T ) = ζ (−T )b , Ω P0 and b a free parameter. From the analysis, I report that the where, ζ = (6H02 )(1−s) 2s−1 configurational entropy in f (T ) gravity is negative and decreases with increasing scale factor and therefore, consistent with an accelerating universe. The decrease in configurational entropy is the highest when b vanishes since the effect of dark energy is maximum when b = 0. Additionally, I find that as the parameter b increases, the growth rate, growing mode and the matter density parameter evolve slowly, whereas the Hubble parameter evolves rapidly. The rapid evolution of the Hubble parameter in conjunction with the growth rate for the b = 0 may provide an explanation for the large dissipation of configurational entropy.
1 Introduction Predictions of ΛCDM cosmological model have been tremendously successful in describing the universe at all length scales [1,2] by incorporating dark matter and dark energy [3,4] where dark matter is responsible for providing the additional gravitational pull to keep the galaxies and clusters from flying apart while dark energy is responsible for fueling the acceleration of the universe at the largest scales. Nonetheless, after numerous attempts to detect these dark components, their identity remains elusive and their presence unconfirmed. The other problem that gravely compromises the efficiency of the “standard” cosmological model is the so-termed Hubble tension, where the value of H0 obtained from CMB anisotropies differs significantly from the one obtained from local observations [5–8]. In this spirit, extended theories of gravity have been formulated in which the gravitational sector of the field equations is altered keeping the matter-energy sector unchanged. In this work, I am going to work with teleparallel f (T ) gravity where f (T ) represents any arbitrary function of torsion scalar T . Teleparallel gravity theories are formulated through the Weitzenböck connection [9,10] which is curvature-less and satisfy the metricity condition [11]. For f (T ) = T , the dynamical equations produced for a Lagrangian consisting only of only T are identical to the ones obtained from GR differing only by a boundary term B and is termed Teleparallel equivalent of general relativity (TEGR) [11]. Teleparallel gravity has been reported to yield encouraging results in various cosmological scenarios [9,12,13,16–
a e-mail: [email protected] (corresponding author)
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