The living ring-opening metathesis polymerization of 5-{[n-[(4'-methoxy-4-biphenylyl)oxy]alkyl]carbonyl}bicyclo[2.2.1]hept-2-ene (1-n, n = 2-8) by Mo(CH-t-Bu)(NAr)(0-t-Bu)2 (Ar = M-CeHj-i-Prj) is described. Polymers with degrees of polymerization from 5 to 100 and narrow molecular weight distributions (MJMn = 1.05-1.24) were obtained in high yield. All polymers exhibit an enantiotropic nematic mesophase. Glass transition and isotropization temperatures increase with increasing molecular weight and become independent at approximately 30-50 repeat units. The change in enthalpy of isotropization is relatively independent of molecular weight. Using polymer blends, it was shown that polydispersity has no effect on either the transition temperatures or the temperature range of isotropization. Isotropization alternates in an odd-even manner up to spacer lengths of n = 6 and then levels off.

We studied the cosmological constraints on Galileon gravity obtained from observational data of the growth rate of matter density perturbations, the supernovae Ia (SN Ia), the cosmic microwave background (CMB), and baryon acoustic oscillations (BAO). For the same value of the energy density parameter of matter Ω m,0 , the growth rate f in Galileon models is enhanced relative to the ΛCDM case, because of an increase in Newton's constant. The smaller the Ω m,0 , the more the growth rate is suppressed. Therefore, the best fit value of Ω m,0 in the Galileon model, based only on the growth rate data, is quite small. This is incompatible with the value of Ω m,0 obtained from the combination of SN Ia, CMB, and BAO data. On the other hand, in the ΛCDM model, the values of Ω m,0 obtained from different observational data sets are consistent. In the analysis presented in this paper, we found that the Galileon model is less compatible with observations than the ΛCDM model. This result seems to be qualitatively the same in most of the generalized Galileon models in which Newton's constant is enhanced.

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Aims. An attempt is made to constrain the values of the cosmological parameters together with the galaxy merging factor η on the basis of a comparison between the observed galaxy number counts vs. their apparent magnitudes relation (N−m relation) with those theoretically constructed for the universe with a time-decaying cosmological term Λ. Methods. We assume that the galaxy number density evolution can be represented sufficiently well by a function of the redshift z of the formThree variations of the cosmological term with time τ are considered, (1)with a being the scale factor, and (3) Λ ∝ H n with H the Hubble parameter. The optimum ranges for the decaying parameters (l, m, and n), the density parameters Ω Λ,0 and Ω m,0 , as well as T mg (the timescale for the merger of a pair of galaxies) and the redshift z mg for the first onset of galaxy merger are sought based on statistical analysis using likelihood functions given by χ 2 evaluations. Results. In the case of the type I models, for instance, we find that l = 0.75 +0.14 −0.07 . As a consistency check, we have also carried out computations of the cosmic microwave background radiation (CMBR) spectrum, and have made comparisons with WMAP measurements. We found that it is necessary to somewhat modify the parameter values obtained above on account of the high sensitivity of η to the value of T mg . The final model that was found to account for both the observed N−m relation and the WMAP measurements of the CMBR spectrum is as follows: z mg = 3.0, T mg = 0.2 Gyr, l = 0.04, Ω Λ,0 = 0.77, η = 2.2269. The age of this model universe is 14.6 Gyr, which is still sufficiently high to cope with the "new" cosmic age problem.

We investigate the observational constraints on the oscillating scalar field model using data from type Ia supernovae, cosmic microwave background anisotropies, and baryon acoustic oscillations. According to a Fourier analysis, the galaxy number count $N$ from redshift $z$ data indicates that galaxies have preferred periodic redshift spacings. We fix the mass of the scalar field as $m_\phi=3.2\times 10^{-31}h$ ${\rm eV}$ such that the scalar field model can account for the redshift spacings, and we constrain the other basic parameters by comparing the model with accurate observational data. We obtain the following constraints: $\Omega_{m,0}=0.28\pm 0.03$ (95% C.L.), $\Omega_{\phi,0} < 0.035$ (95% C.L.), $\xi > -158$ (95% C.L.) (in the range $\xi \le 0$). The best fit values of the energy density parameter of the scalar field and the coupling constant are $\Omega_{\phi,0}= 0.01$ and $\xi= -25$, respectively. The value of $\Omega_{\phi,0}$ is close to but not equal to $0$. Hence, in the scalar field model, the amplitude of the galaxy number count cannot be large. However, because the best fit values of $\Omega_{\phi,0}$ and $\xi$ are not $0$, the scalar field model has the possibility of accounting for the periodic structure in the $N$--$z$ relation of galaxies. The variation of the effective gravitational constant in the scalar field model is not inconsistent with the bound from observation.Comment: 9 pages, 11 figures, 1 table, Accepted for publication in Physical Review