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Register a new userPhantom expansion with non-linear Schr{o}dinger-type formulation of scalar field cosmology
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We describe non-flat standard Friedmann cosmology of canonical scalar field with barotropic fluid in form of non-linear Schr{o}dinger-type (NLS) formulation in which all cosmological dynamical quantities are expressed in term of Schr{o}dinger quantities as similar to those in time-independent quantum mechanics. We assume the expansion to be superfast, i.e. phantom expansion. We report all Schr{o}dinger-analogous quantities to scalar field cosmology. Effective equation of state coefficient is analyzed and illustrated. We show that in a non-flat universe, there is no fixed $w_{rm eff}$ value for the phantom divide. In a non-flat universe, even $w_{rm eff} > -1$, the expansion can be phantom. Moreover, in open universe, phantom expansion can happen even with $w_{rm eff} > 0$. We also report scalar field exact solutions within frameworks of the Friedmann formulation and the NLS formulation in non-flat universe cases.
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Aspects of non-linear Schr{o}dinger-type (NLS) formulation of scalar (phantom) field cosmology on slow-roll, acceleration, WKB approximation and Big Rip singularity are presented. Slow-roll parameters for the curvature and barotropic density terms are introduced. We reexpress all slow-roll parameters, slow-roll conditions and acceleration condition in NLS form. WKB approximation in the NLS formulation is also discussed when simplifying to linear case. Most of the Schr{o}dinger potentials in NLS formulation are very slowly-varying, hence WKB approximation is valid in the ranges. In the NLS form of Big Rip singularity, two quantities are infinity in stead of three. We also found that approaching the Big Rip, $w_{rm eff}to -1 + {2}/{3q}$, $(q<0)$ which is the same as effective phantom equation of state in the flat case.
We study the dynamics of a phantom scalar field dark energy interacting with dark matter in loop quantum cosmology (LQC). Two kinds of coupling of the form $alpha{rho_m}{dotphi}$ (case I) and $3beta H (rho_phi +rho_m)$ (case II) between the phantom energy and dark matter are examined with the potential for the phantom field taken to be exponential. For both kinds of interactions, we find that the future singularity appearing in the standard FRW cosmology can be avoided by loop quantum gravity effects. In case II, if the phantom field is initially rolling down the potential, the loop quantum effect has no influence on the cosmic late time evolution and the universe will accelerate forever with a constant energy ratio between the dark energy and dark matter.
We consider rotating wormhole solutions supported by a complex phantom scalar field with a quartic self-interaction, where the phantom field induces the rotation of the spacetime. The solutions are regular and asymptotically flat. A subset of solutions describing static but not spherically symmetric wormholes is also obtained.
A $p$-adic Schr{o}dinger-type operator $D^{alpha}+V_Y$ is studied. $D^{alpha}$ ($alpha>0$) is the operator of fractional differentiation and $V_Y=sum_{i,j=1}^nb_{ij}<delta_{x_j}, cdot>delta_{x_i}$ $(b_{ij}inmathbb{C})$ is a singular potential containing the Dirac delta functions $delta_{x}$ concentrated on points ${x_1,...,x_n}$ of the field of $p$-adic numbers $mathbb{Q}_p$. It is shown that such a problem is well-posed for $alpha>1/2$ and the singular perturbation $V_Y$ is form-bounded for $alpha>1$. In the latter case, the spectral analysis of $eta$-self-adjoint operator realizations of $D^{alpha}+V_Y$ in $L_2(mathbb{Q}_p)$ is carried out.
Massive scalar fields provide excellent dark matter candidates, whose dynamics are often explored analytically and numerically using nonrelativistic Schr{o}dinger-Poisson (SP) equations in a cosmological context. In this paper, starting from the nonlinear and fully relativistic Klein-Gordon-Einstein (KGE) equations in an expanding universe, we provide a systematic framework for deriving the SP equations, as well as relativistic corrections to them, by integrating out `fast modes and including nonlinear metric and matter contributions. We provide explicit equations for the leading-order relativistic corrections, which provide insight into deviations from the SP equations as the system approaches the relativistic regime. Upon including the leading-order corrections, our equations are applicable beyond the domain of validity of the SP system, and are simpler to use than the full KGE case in some contexts. As a concrete application, we calculate the mass-radius relationship of solitons in scalar dark matter and accurately capture the deviations of this relationship from the SP system towards the KGE one.
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