Analytic spectrum of relic gravitational waves modified by neutrino free streaming and dark energy

We include the effect of neutrino free streaming into the spectrum of relic gravitational waves (RGWs) in the currently accelerating universe. For the realistic case of a varying fractional neutrino energy density and a non-vanishing derivative of mode function at the neutrino decoupling, the integro-differential equation of RGWs is solved by a perturbation method for the period from the neutrino decoupling to the matter-dominant stage. Incorporating it to the analytic solution of the whole history of expansion of the universe, the analytic solution of GRWs is obtained, evolving from the inflation up to the current acceleration. The resulting spectrum of GRWs covers the whole range of frequency $(10^{-19}\sim 10^{10})$Hz, and improves the previous results. It is found that the neutrino free-streaming causes a reduction of the spectral amplitude by $\sim 20$ in the range $(10^{-16}\sim 10^{-10})$ Hz, and leaves the other portion of the spectrum almost unchanged. This agrees with the earlier numerical calculations. Examination is made on the difference between the accelerating and non-accelerating models, and our analysis shows that the ratio of the spectral amplitude in accelerating $\Lambda$CDM model over that in CDM model is $\sim 0.7$, and within the various accelerating models of $\Omega_{\Lambda}> \Omega_m$ the spectral amplitude is proportional to $\Omega_m/\Omega_{\Lambda}$ for the whole range of frequency. Comparison with LIGO S5 Runs Sensitivity shows that RGWs are not yet detectable by the present LIGO, and in the future LISA may be able to detect RGWs in some inflationary models.Comment: 22 pages,12 figures, accepeted by PR

Detecting very-high-frequency relic gravitational waves by electromagnetic wave polarizations in a waveguide

The polarization vector (PV) of an electromagnetic wave (EW) will experience a rotation in a region of spacetime perturbed by gravitational waves (GWs). Based on this idea, Cruise's group has built an annular waveguide to detect GWs. We give detailed calculations of the rotations of the polarization vector of an EW caused by incident GWs from various directions and in various polarization states, and then analyze the accumulative effects on the polarization vector when the EW passes n cycles along the annular waveguide. We reexamine the feasibility and limitation of this method to detect GWs of high frequency around 100 MHz, in particular, the relic gravitational waves (RGWs). By comparing the spectrum of RGWs in the accelerating universe with the detector sensitivity of the current waveguide, it is found that the amplitude of the RGWs is too low to be detected by the waveguide detectors currently running. Possible ways of improvements on detection are discussed also.Comment: 18pages, 10 figures, accepted by ChJA

Modifications by QCD transition and e+e−e^+e^- annihilation on analytic spectrum of relic gravitational waves in accelerating universe

As predicted by quantum chromodynamics(QCD), around $T\sim 190$ MeV in the early universe, the QCD transition occurs during which the quarks are combined into the massive hadrons. This process reduces the effective relativistic degree of freedom, and causes a change in the expansion behavior of the universe. Similarly, the $e^+e^-$ annihilation occurred around $T\sim 0.5$ Mev has the same kind of effect. Besides, the dark energy also drives the present stage accelerating expansion. We study these combined effects on the relic gravitational waves (RGWs). In our treatment, the QCD transition and the $e^+e^-$ annihilation, each is respectively represented by a short period of expansion inserted into the radiation era. Incorporating these effects, the equation of RGWs is analytically solved for a spatially flat universe, evolving from the inflation up to the current acceleration, and the spectrum of RGWs is obtained, covering the whole range of frequency $>10^{-19}$ Hz. It is found that the QCD transition causes a reduction of the amplitude of RGWs by $\sim 20$ in the range $>10^{-9}$ Hz, and the $e^+e^-$ annihilation causes a reduction $\sim 10$ in the range $>10^{-12}$ Hz. In the presence of the dark energy, the combination of the QCD transition and the $e^+e^-$ annihilation, causes a larger reduction of the amplitude by $\sim 30$ for the range $>10^{-9}$ Hz, which covers the bands of operation of LIGO and LISA. By analysis, it is shown that RGWs will be difficult to detect by the present LIGO, but can be tested by LISA for certain inflationary models.Comment: 21 pages, 14 figures, to appear in PR

Inflation and squeezed quantum states

The inflationary cosmology is analyzed from the point of view of squeezed quantum states. As noted by Grishchuk and Sidorov, the amplification of quantum fluctuations into macroscopic perturbations which occurs during cosmic inflation is a process of quantum squeezing. We carefully develop the squeezed state formalism and derive the equations that govern the evolution of a gaussian initial state. We derive the power spectrum of density perturbations for a simple inflationary model and discuss its features. We conclude that the squeezed state formalism provides an interesting framework within which to study the amplification process, but,in disagreement with the claims of Grishchuk and Sidorov, that it does {\em not} provide us with any new physical results.Comment: 33 pages, one section added, significant revisions, 6 figures (in uuencoded file), Imperial/TP/92-93/2

Beclin 1-independent autophagy contributes to apoptosis in cortical neurons.

Neuronal autophagy is enhanced in many neurological conditions, such as cerebral ischemia and traumatic brain injury, but its role in associated neuronal death is controversial, especially under conditions of apoptosis. We therefore investigated the role of autophagy in the apoptosis of primary cortical neurons treated with the widely used and potent pro-apoptotic agent, staurosporine (STS). Even before apoptosis, STS enhanced autophagic flux, as shown by increases in autophagosomal (LC3-II level, LC3 punctate labeling) and lysosomal (cathepsin D, LAMP1, acid phosphatase, β-hexasominidase) markers. Inhibition of autophagy by 3-methyladenine, or by lentivirally-delivered shRNAs against Atg5 and Atg7, strongly reduced the STS-induced activation of caspase-3 and nuclear translocation of AIF, and gave partial protection against neuronal death. Pan-caspase inhibition with Q-VD-OPH likewise protected partially against neuronal death, but failed to affect autophagy. Combined inhibition of both autophagy and caspases gave strong synergistic neuroprotection. The autophagy contributing to apoptosis was Beclin 1-independent, as shown by the fact that Beclin 1 knockdown failed to reduce it but efficiently reduced rapamycin-induced autophagy. Moreover the Beclin 1 knockdown sensitized neurons to STS-induced apoptosis, indicating a cytoprotective role of Beclin 1 in cortical neurons. Caspase-3 activation and pyknosis induced by two other pro-apoptotic stimuli, MK801 and etoposide, were likewise found to be associated with Beclin 1-independent autophagy and reduced by the knockdown of Atg7 but not Beclin 1. In conclusion, Beclin 1-independent autophagy is an important contributor to both the caspase-dependent and -independent components of neuronal apoptosis and may be considered as an important therapeutic target in neural conditions involving apoptosis

Modified Amplitude of Gravitational Waves Spectrum

The spectrum of thermal gravitational waves is obtained by including the high frequency thermal gravitons created from extra-dimensional effect and is a new feature of the spectrum. The amplitude and spectral energy density of gravitational waves in thermal vacuum state are found enhanced. The amplitude of the waves get modified in the frequency range (10$^{-16}$ -10 $^{8}$ Hz) but the corresponding spectral energy density is less than the upper bound of various estimated results. With the addition of higher frequency thermal waves, the obtained spectral energy density of the wave in thermal vacuum state does not exceed the upper bound put by nucleosynthesis rate. The existence of cosmologically originated thermal gravitational waves due to extra dimension is not ruled out.Comment: 18 pages, 4 figures, to appear in Classical and Quantum Gravity. arXiv admin note: text overlap with arXiv:astro-ph/0503162, arXiv:astro-ph/0501329 by other author

The Response of Test Masses to Gravitational Waves in the Coordinates of a Local Observer

The response of laser interferometers to gravitational waves has been calculated in a number of different ways, particularly in the transverse-traceless and the local Lorentz gauges. At first sight, it would appear that these calculations lead to different results when the separation between the test masses becomes comparable to the wavelength of the gravitational wave. In this paper this discrepancy is resolved. We describe the response of free test masses to plane gravitational waves in the coordinate frame of a local observer and show that it acquires contributions from three different effects: the displacement of the test masses, the apparent change in the photon velocity, and the variation in the clock speed of the local observer, all of which are induced by the gravitational wave. Only when taken together do these three effects represent a quantity which is translationally invariant. This translationally-invariant quantity is identical to the response function calculated in the transverse-traceless gauge. We thus resolve the well-known discrepancy between the two coordinates systems, and show that the results found in the coordinate frame of a local observer are valid for large separation between the masses.Comment: 25 pages, 3 figures, Latex2

Revisit relic gravitational waves based on the latest CMB observations

According to the CMB observations, Mielczarek (\cite{Mielczarek}) evaluated the reheating temperature, which could help to determine the history of the Universe. In this paper, we recalculate the reheating temperature using the new data from WMAP 7 observations. Based on that, we list the approximate solutions of relic gravitational waves (RGWs) for various frequency bands. With the combination of the quantum normalization of RGWs when they are produced and the CMB observations, we obtain the relation between the tensor-to-scalar ratio $r$ and the inflation index $\beta$ for a given scalar spectral index $n_s$. As a comparison, the diagram $r-\beta$ in the slow-roll inflation model is also given. Thus, the observational limits of $r$ from CMB lead to the constraints on the value of $\beta$. Then, we illustrate the energy density spectrum of RGWs with the quantum normalization for different values of $r$ and the corresponding $\beta$. For comparison, the energy density spectra of RGWs with parameters based on slow-roll inflation are also discussed. We find that the values of $n_s$ affect the spectra of RGWs sensitively in the very high frequencies. Based on the current and planed gravitational wave detectors, we discuss the detectabilities of RGWs.Comment: 16 pages, 6 figures, accepted for publication in Class. Quantum Gra

Cosmological test of gravity with polarizations of stochastic gravitational waves around 0.1-1 Hz

In general relativity, a gravitational wave has two polarization modes (tensor mode), but it could have additional polarizations (scalar and vector modes) in the early stage of the universe, where the general relativity may not strictly hold and/or the effect of higher-dimensional gravity may become significant. In this paper, we discuss how to detect extra-polarization modes of stochastic gravitational wave background (GWB), and study the separability of each polarization using future space-based detectors such as BBO and DECIGO. We specifically consider two plausible setups of the spacecraft constellations consisting of two and four clusters, and estimate the sensitivity to each polarization mode of GWBs. We find that a separate detection of each polarization mode is rather sensitive to the geometric configuration and distance between clusters and that the clusters should be, in general, separated by an appropriate distance. This seriously degrades the signal sensitivity, however, for suitable conditions, space-based detector can separately detect scalar, vector and tensor modes of GWBs with energy density as low as ~10^-15.Comment: 16 pages, 11 figure

Physics of the interior of a spherical, charged black hole with a scalar field

We analyse the physics of nonlinear gravitational processes inside a spherical charged black hole perturbed by a self-gravitating massless scalar field. For this purpose we created an appropriate numerical code. Throughout the paper, in addition to investigation of the properties of the mathematical singularities where some curvature scalars are equal to infinity, we analyse the properties of the physical singularities where the Kretschmann curvature scalar is equal to the planckian value. Using a homogeneous approximation we analyse the properties of the spacetime near a spacelike singularity in spacetimes influenced by different matter contents namely a scalar field, pressureless dust and matter with ultrarelativistic isotropic pressure. We also carry out full nonlinear analyses of the scalar field and geometry of spacetime inside black holes by means of an appropriate numerical code with adaptive mesh refinement capabilities. We use this code to investigate the nonlinear effects of gravitational focusing, mass inflation, matter squeeze, and these effects dependence on the initial boundary conditions. It is demonstrated that the position of the physical singularity inside a black hole is quite different from the positions of the mathematical singularities. In the case of the existence of a strong outgoing flux of the scalar field inside a black hole it is possible to have the existence of two null singularities and one central $r=0$ singularity simultaneously