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Register a new userVersatile parametrization of the perturbation growth rate on the phantom brane
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We derive an analytical expression for the growth rate of matter density perturbations on the phantom brane (which is the normal branch of the Dvali-Gabadadze-Porrati model). This model is characterized by a phantomlike effective equation of state for dark energy at the present epoch. It agrees very well with observations. We demonstrate that the traditional parametrization $f=Omega_m^gamma$ with a quasiconstant growth index $gamma$ is not successful in this case. Based on a power series expansion at large redshifts, we propose a different parametrization for this model: $f=Omega_m^gammaleft(1+frac{b}{ell H}right)^beta$, where $beta$ and $b$ are constants. Our numerical simulations demonstrate that this new parametrization describes the growth rate with great accuracy - the maximum error being $leq 0.1%$ for parameter values consistent with observations.
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In [Schmidt PRD 80 123003 (2009)], the author suggested that dynamical dark energy (DDE) propagating on the phantom brane could mimick $Lambda$CDM. Schmidt went on to derive a phenomenological expression for $rho_{rm DE}$ which could achieve this. We demonstrate that while Schmidts central premise is correct, the expression for $rho_{rm DE}$ derived in Schmidt (2009) is flawed. We derive the correct expression for $rho_{rm DE}$ which leads to $Lambda$CDM-like expansion on the phantom brane. We also show that DDE on the brane can be associated with a Quintessence field and derive a closed form expression for its potential $V(phi)$. Interestingly the $alpha$-attractor based potential $V(phi) propto coth^2{lambdaphi}$ makes braneworld expansion resemble $Lambda$CDM. However the two models can easily be distinguished on the basis of density perturbations which grow at different rates on the braneworld and in $Lambda$CDM.
In this paper we investigate the so called phantom barrier crossing issue in a cosmological model based in the scalar-tensor theory with non-minimal derivative coupling to the Einsteins tensor. Special attention will be paid to the physical bounds on the squared sound speed. The numeric results are geometrically illustrated by means of a qualitative procedure of analysis that is based on the mapping of the orbits in the phase plane onto the surfaces that represent physical quantities in the extended phase space, that is: the phase plane complemented with an additional dimension relative to the given physical parameter. We find that the cosmological model based in the non-minimal derivative coupling theory -- this includes both the quintessence and the pure derivative coupling cases -- has serious causality problems related with superluminal propagation of the scalar and tensor perturbations. Even more disturbing is the finding that, despite that the underlying theory is free of the Ostrogradsky instability, the corresponding cosmological model is plagued by the Laplacian (classical) instability related with negative squared sound speed. This instability leads to an uncontrollable growth of the energy density of the perturbations that is inversely proportional to their wavelength. We show that independent of the self-interaction potential, for the positive coupling the tensor perturbations propagate superluminally, while for the negative coupling a Laplacian instability arises. This latter instability invalidates the possibility for the model to describe the primordial inflation.
Using Leavers continue fraction and time domain method, we investigate the wave dynamics of phantom scalar perturbation in the background of Schwarzschild black hole. We find that the presence of the negative kinetic energy terms modifies the standard results in quasinormal spectrums and late-time behaviors of the scalar perturbations. The phantom scalar perturbation in the late-time evolution will grow with an exponential rate.
Using Leavers continue fraction and time domain method, we study the wave dynamics of phantom scalar perturbation in a Schwarzschild black string spacetime. We find that the quasinormal modes contain the imprint from the wavenumber $k$ of the fifth dimension. The late-time behaviors are dominated by the difference between the wavenumber $k$ and the mass $mu$ of the phantom scalar perturbation. For $k<mu$, the phantom scalar perturbation in the late-time evolution grows with an exponential rate as in the four-dimensional Schwarzschild black hole spacetime. While, for $k=mu$, the late-time behavior has the same form as that of the massless scalar field perturbation in the background of a black hole. Furthermore, for $k>mu$, the late-time evolution of phantom scalar perturbation is dominated by a decaying tail with an oscillation which is consistent with that of the usual massive scalar field. Thus, the Schwarzschild black string is unstable only against the phantom scalar perturbations which satisfy the wavelength $lambda>2pi/mu$. These information can help us know more about the wave dynamics of phantom scalar perturbation and the properties of black string.
We investigate the role of bulk viscous pressure on the warm inflationary modified Chaplygin gas in brane-world framework in the presence of standard scalar field. We assume the intermediate inflationary scenario in strong dissipative regime and constructed the inflaton, potential, entropy density, slow-roll parameters, scalar and tensor power spectra, scalar spectral index and tensor-to-scalar ratio. We develop various trajectories such as $n_s - N$, $n_s - r$ and $n_s - alpha_s$ (where $n_s$ is the spectral index, $alpha_s$ is the running of spectral index, $N$ is the number of e-folds and $r$ is tensor-to-scalar ratio) for variable as well as constant dissipation and bulk viscous coefficients at high dissipative regime. It is interesting to remark here that our results of these parameters are compatible with recent observational data such as WMAP $7+9$, BICEP$2$ and Planck data.
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