Nonlinear power spectrum in the presence of massive neutrinos: perturbation theory approach, galaxy bias and parameter forecasts

Future or ongoing galaxy redshift surveys can put stringent constraints on neutrinos masses via the high-precision measurements of galaxy power spectrum, when combined with cosmic microwave background (CMB) information. In this paper we develop a method to model galaxy power spectrum in the weakly nonlinear regime for a mixed dark matter (CDM plus finite-mass neutrinos) model, based on perturbation theory (PT) whose validity is well tested by simulations for a CDM model. In doing this we carefully study various aspects of the nonlinear clustering and then arrive at a useful approximation allowing for a quick computation of the nonlinear power spectrum as in the CDM case. The nonlinear galaxy bias is also included in a self-consistent manner within the PT framework. Thus the use of our PT model can give a more robust understanding of the measured galaxy power spectrum as well as allow for higher sensitivity to neutrino masses due to the gain of Fourier modes beyond the linear regime. Based on the Fisher matrix formalism, we find that BOSS or Stage-III type survey, when combined with Planck CMB information, gives a precision of total neutrino mass constraint, sigma(m_nu,tot) 0.1eV, while Stage-IV type survey may achieve sigma(m_nu,tot) 0.05eV, i.e. more than a 1-sigma detection of neutrino masses. We also discuss possible systematic errors on dark energy parameters caused by the neutrino mass uncertainty. The significant correlation between neutrino mass and dark energy parameters is found, if the information on power spectrum amplitude is included. More importantly, for Stage-IV type survey, a best-fit dark energy model may be biased and falsely away from the underlying true model by more than the 1-sigma statistical errors, if neutrino mass is ignored in the model fitting.Comment: 33 pages, 11 figure

On the Approximation in the Hermitian Treatment of Dyson Boson Expansion Theory

We discuss about the Hermitian treatment of Dyson-type boson expansion theory. We show that the basic assumption of the conventional treatment does not hold in general and the method is only approximately valid. We also show that the approximation is the same order as that of truncation of the expansion usually done in the Hermitian type boson expansion theory.Comment: 18 page, no figur

Neutrino Mass Constraint from the Sloan Digital Sky Survey Power Spectrum of Luminous Red Galaxies and Perturbation Theory

We compare the model power spectrum, computed based on perturbation theory, with the power spectrum of luminous red galaxies (LRG) measured from the Sloan Digital Sky Survey Data Release 7 catalog, assuming a flat, cold dark matter-dominated cosmology. The model includes the effects of massive neutrinos, nonlinear matter clustering and nonlinear, scale-dependent galaxy bias in a self-consistent manner. We first test the accuracy of the perturbation theory model by comparing the model predictions with the halo power spectrum in real- and redshift-space, measured from 70 simulation realizations for a cold dark matter model without massive neutrinos. We show that the perturbation theory model with bias parameters being properly adjusted can fairly well reproduce the simulation results. As a result, the best-fit parameters obtained from the hypothetical parameter fitting recover, within statistical uncertainties, the input cosmological parameters in simulations, including an upper bound on neutrino mass, if the power spectrum information up to k ≃ 0.15 hMpc-1 is used. However, for the redshift-space power spectrum, the best-fit cosmological parameters show a sizable bias from the input values if using the information up to k ≃ 0.2 hMpc-1, probably due to nonlinear redshift distortion effect. Given these tests, we decided, as a conservative choice, to use the LRG power spectrum up to k=0.1 hMpc-1 in order to minimize possible unknown nonlinearity effects. In combination with the recent results from Wilkinson Microwave Background Anisotropy Probe (WMAP), we derive a robust upper bound on the sum of neutrino masses, given as ∑ mν ≤ 0. 81eV (95% C.L.), marginalized over other parameters including nonlinear bias parameters and dark energy equation of state parameter. The upper bound is only slightly improved to ∑ mν ≤ 0.80eV if including the LRG spectrum up to k = 0.2 hMpc-1, due to severe parameter degeneracies, although the constraint may be biased as discussed above. The neutrino mass limit is improved by a factor of 1.85 compared to the limit from the WMAP5 alone, ∑ mν ≤ 1.5eV

OPTICAL QPSK SIGNAL QUALITY DEGRADATION DUE TO PHASE ERROR OF PUMP LIGHT

The influence of pump phase error on phase-sensitive optical amplifier (PSA) repeaters and the waveform degradation due to chromatic dispersion and fiber nonlinearities in the optical multi-relay transmission of quadrature phase-shift keying phase-conjugated twin waves are considered theoretically. First, the influence of noise from the pump phase error, optical local oscillator, receiver, and the amplified spontaneous-emission (ASE) in PSA repeaters is investigated with the assumption that transmission fibers are linear lossy channels. The bit-error rate (BER) is estimated as a function of the signal-to-noise ratio, and the relationship between the number of transmission relays and the fiber launch power is clarified. Waveform degradation due to chromatic dispersion and the optical fiber nonlinearities in transmission fibers are investigated with the noiseless condition, and the maximum repeatable number as a function of the fiber launch power is calculated. Finally, we show the relationship among the maximum repeatable number, standard deviation of pump phase error in PSA repeaters, and the fiber launch power to clarify the optimum transmission condition with consideration of the noise and the waveform degradation

Impact of Massive Neutrinos on the Nonlinear Matter Power Spectrum

We present the first attempt to analytically study the nonlinear matter power spectrum for a mixed dark matter model containing neutrinos of total mass ~0.1eV, based on cosmological perturbation theory. The suppression in the power spectrum amplitudes due to massive neutrinos is enhanced in the weakly nonlinear regime. We demonstrate that, thanks to this enhanced effect, the use of such a nonlinear model may enable a precision of σ(mν,tot) ~ 0. 07eV in constraining the total neutrino mass for the planned galaxy redshift survey, a factor of 2 improvement compared to the linear regime