Determining the Equation of State of the Expanding Universe Using a New Independent Variable

To determine the equation of state of the universe, we propose to use a new independent variable $R\equiv (H_0/c)(d_L(z)/(1+z))$, where $H_0$ and $d_L(z)$ are the present Hubble parameter and the luminosity distance, respectively. For the flat universe suggested from the observation of the anisotropy of cosmic microwave background, the density and the pressure are expressed as $\rho/\rho_0=4(df/dR)^2/f^6$ and $p/\rho_0=-4/3(d^2f/dR^2)/f^5$ where $\rho_0$ is the present density and $f(R)=1/\sqrt{1+z(R)}$. In $(R, f)$ plane the sign as well as the strength of the pressure is in proportion to the curvature of the curve $f(R)$. We propose to adopt a Pade-like expression of $f(R)=1/\sqrt{u}$ with $u\equiv 1+\sum\limits_{n=1}^{N}u_nR^n$. For flat $\Lambda$ model the expansion up to N=7 has at most an error $< 0.2$ for $z < 1.7$ and any value of $\Lambda$. We also propose a general method to determine the equation of state of the universe which has $N-1$ free parameters. If the number of parameters are smaller than $N-1$, there is a consistency check of the equation of state so that we may confirm or refute each model.Comment: 12 pages, to be published in the Astrophysical Journa

A Null Test of the Cosmological Constant

We provide a consistency relation between cosmological observables in general relativity with the cosmological constant. Breaking of this relation at any redshift would imply the breakdown of the hypothesis of the cosmological constant as an explanation of the current acceleration of the universe.Comment: 5 pages, 1 figure, references added, to be published in Prog.Theor.Phy

The Luminosity Distance, the Equation of State, and the Geometry of the Universe

The second derivative of the luminosity distance with respect to the redshift is written in terms of the deceleration parameter $q_0$. We point out that the third derivative contains the information regarding the sound speed of cosmic matter as well as the curvature of the universe. We restrict physically possible parameter ranges of the coefficients. It is found that there is a relation between the coefficients in a flat universe model with matter such that $c_{s0}(1+w_{\rm x0})=0$ ($c_{s0}$ is the total sound speed of the matter component and $w_{\rm x0}$=$p_{\rm x0}/\rho_{\rm x0}$).Comment: 5 pages + 1 figure, one reference added, Prog.Theor.Phys. in pres

Cosmology with x-matter

Motivated by the possibility of $H_0t_0 > 1$ where $H_0$ and $t_0$ are the Hubble parameter and the age of the universe, respectively, we investigate the cosmology including x-matter. x-matter is expressed by the equation of state $p_x=w_0\rho_{x0} + c_s^2(\rho_x-\rho_{x0})$, where $p_x$, $\rho_x$ and $\rho_{x0}$ are the pressure, the density of x-matter and the density at present, respectively. $w_0$ and $c_s^2$ are functions of $\rho_x$ in general. x-matter has the most general form of the equation of state which is characterized by 1)violation of strong energy condition at present for $w_0 < -1/3$ ; 2) locally stable (i.e. $c_s^2\geq 0$); 3)causality is guaranteed ($c_s\leq 1$). Considering the case that $w_0$ and $c_s^2$ are constants, we find that there is a large parameter space of $(w_0,c_s^2,\Omega_{x0})$ in which the model universe is consistent with the age of the universe and the observations of distant Type I supernovae.Comment: minor changes, 4 pages, 6 figures, accepted for publication as a Letter in MNRA

Microwave Background Anisotropies in Primeval Isocurvature Baryon Models: Constraints on the Cosmological Parameters

We have performed the most comprehensive predictions of the temperature fluctuations \dtt in the primeval isocurvature baryon models to see whether or not the models are consistent with the recent data on the cosmic microwave background anisotropies. More specifically, we computed the \dtt corresponding to the experimental set-up by the South-Pole and the Owens Valley experiments as well as the COBE satellite. The amplitudes of the predicted \dtt are normalized by means of the COBE 10$^\circ$ data. The resulting constraints on the models are presented on $n - \Omega_b$ plane in the case of $\lambda_0=1-\Omega_b$ (flat models) and $\lambda_0=0$ (open models), where $n$ is the primordial spectral index of entropy fluctuations and $\Omega_b$ is the present baryon density parameter. Our results imply that the PIB models cannot be reconciled with the current observations for any reasonable set of cosmological parameters.Comment: 10pages and 4figures compressed uuencoded postscript (with figures), UTAP-93-16

Observational tests of x-matter models

We study gravitational lensing statistics, matter power spectra and the angular power spectra of the cosmic microwave background (CMB) radiation in x-matter models. We adopt an equation-of-state of x-matter which can express a wide range of matter from the pressureless dust to the cosmological constant. A new ingredient in this model is the sound speed of the x-component in addition to the equation-of-state $w_0=p_{x0}/\rho_{x0}$. Except for the cosmological constant case, the perturbations of x-matter itself are considered. Our primary interest is in the effect of non-zero sound speed on the structure formation and the CMB spectra. It is found that there exist parameter ranges where x-matter models are consistent with all current observations. The x-matter generally leaves imprints in the CMB anisotropy and the matter power spectrum, which should be detectable in future observations.Comment: minor changes, 10 pages+14 figures, MNRAS in pres

Determining the Equation of State of the Expanding Universe: Inverse Problem in Cosmology

Even if the luminosity distance as a function of redshift is obtained accurately using, for example, Type Ia supernovae, the equation of state of the Universe cannot be determined uniquely but depends on one free parameter $\Omega_{k0} ={k}/(a_0^2H_0^2)$, where $a_0$ and $H_0$ are the present scale factor and the Hubble parameter, respectively. This degeneracy might be resolved if, for example, the time variations of the redshift of quasars are measured as proposed recently by Loeb. Therefore the equation of state of the Universe (or the metric of the universe) might be determined without any theoretical assumption on the matter content of the Universe in future.Comment: 5 pages, accepted for publication in MNRA

Numerical analysis of voltage-controlled magnetization switching operation in magnetic-topological-insulator-based devices

We theoretically investigate influences of electronic circuit delay, noise and temperature on write-error-rate (WER) in voltage-controlled magnetization switching operation of a magnetic-topological-insulator-based (MTI) device by means of the micromagnetic simulation. This device realizes magnetization switching via spin-orbit torque(SOT) and voltage-controlled magnetic anisotropy (VCMA) which originate from 2D-Dirac electronic structure. We reveal that the device operation is extremely robust against circuit delay and signal-to-noise ratio. We demonstrate that the WER on the order of approximately $10^{-4}$ or below is achieved around room temperature due to steep change in VCMA. Also, we show that the larger SOT improves thermal stability factor. This study provides a next perspective for developing voltage-driven spintronic devices with ultra-low power consumption.Comment: 6 pages, 5 figure

Tibial condylar valgus osteotomy (TCVO) for osteoarthritis of the knee: 5-year clinical and radiological results

According to one line of thought only propositions can be part of one’s evidence, since only propositions can serve the central functions of our ordinary concept of evidence. Ram Neta has challenged this argument. In this paper I respond to Neta’s challenge