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Register a new userAnalytic Spectra of CMB Anisotropies and Polarization Generated by Relic Gravitational Waves with Modification due to Neutrino Free-Streaming
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We present an analytical calculation of the spectra of CMB anisotropies and polarizations generated by relic gravitational waves (RGWs). As a substantial extension to the previous studies, three new ingredients are included in this work. Firstly, the analytic $C_l^{TT}$ and $C_l^{TE}$ are given; especially the latter can be useful to extract signal of RGWs from the observed data in the zero multipole method. Secondly, a fitting formula of the decaying factor on small scales is given, coming from the visibility function around the photon decoupling. Thirdly, the impacts by the neutrino free-streaming (NFS) is examined, a process that occurred in the early universe and leaves observable imprints on CMB via RGWs. It is found that the analytic $C_l^{TT}$ and $C_l^{TE}$ have profiles agreeing with the numeric ones, except that $C^{TT}_l$ in a range $l le 10$ and the $1^{st}$ trough of $C_l^{TE}$ around $l sim 75$ have some deviations. With the new damping factor, the analytic $C^{EE}_l$ and $C^{BB}_l$ match with the numeric ones with the maximum errors only $sim 3%$ up to the first three peaks for $lle 600$, improving the previous studies substantially. The correspondence of the positions of peaks of $C^{XX}_l$ and those of RGWs are also demonstrated explicitly. We also find that NFS reduces the amplitudes of $C^{XX}_l$ by $(20% sim 35%)$ for $lsimeq(100sim 600)$ and shifts slightly their peaks to smaller angles. Detailed analyses show that the zero multipoles $l_0$, where $C_l^{TE}$ crosses 0, are shifted to larger values by NFS. This shifting effect is as important as those causedby different inflation models and different baryon fractions.
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We present an approximate, analytical calculation of the reionized spectra $C_l^{XX}$ of cosmic microwave background radiation (CMB) anisotropies and polarizations generated by relic gravitational waves (RGWs). Three simple models of reionization are explored, whose visibility functions are fitted by gaussian type of functions as approximations. We have derived the analytical polarization $beta_l$ and temperature anisotropies $alpha_l$, both consisting of two terms proportional to RGWs at the decoupling and at the reionization as well. The explicit dependence of $beta_l$ and $alpha_l$ upon the reionization time $eta_r$, the duration $Deltaeta_r$, and the optical depth $kappa_r$ are demonstrated. Moreover, $beta_l$ and $alpha_l$ contain $kappa_r$ in different coefficients, and the polarization spectra $C_l^{EE}$ are $C_l^{BB}$ are more sensitive probes of reionization than $C_l^{TT}$. These results facilitate examination of the reionization effects, in particular, the degeneracies of $kappa_r$ with the normalization amplitude and with the initial spectral index of RGWs. It is also found that reionization also causes a $kappa_r$-dependent shift $Delta lsim 20$ of the zero multipole $l_0$ of $C_l^{TE}$, an effect that should be included in order to detect the traces of RGWs. Compared with numerical results, the analytical $C_l^{XX}$ as approximation have the limitation. For the primary peaks in the range $lsimeq (30, 600)$, the error is $le 3%$ in three models. In the range $l < 20$ for the reionization bumps, the error is $le 15%$ for $C_l^{EE}$ and $C_l^{BB}$ in the two extended reionization models, and $C_l^{TT}$ and $C_l^{TE}$ have much larger departures for $l<10$. The bumps in the sudden reionization model are too low.
We discuss the polarization signature of primordial gravitational waves imprinted in cosmic microwave background (CMB) anisotropies. The high-energy physics motivated by superstring theory or M-theory generically yield parity violating terms, which may produce a circularly polarized gravitational wave background (GWB) during inflation. In contrast to the standard prediction of inflation with un-polarized GWB, circularly polarized GWB generates non-vanishing TB and EB-mode power spectra of CMB anisotropies. We evaluate the TB and EB-mode power spectra taking into account the secondary effects and investigate the dependence of cosmological parameters. We then discuss current constraints on the circularly polarized GWB from large angular scales (l < 16) of the three year WMAP data. Prospects for future CMB experiments are also investigated based on a Monte Carlo analysis of parameter estimation, showing that the circular polarization degree, varepsilon, which is the asymmetry of the tensor power spectra between right- and left-handed modes normalized by the total amplitude, can be measured down to |varepsilon| 0.35(r/0.05)^{-0.6}.
Searching for the signal of primordial gravitational waves in the B-modes (BB) power spectrum is one of the key scientific aims of the cosmic microwave background (CMB) polarization experiments. However, this could be easily contaminated by several foreground issues, such as the thermal dust emission. In this paper we study another mechanism, the cosmic birefringence, which can be introduced by a CPT-violating interaction between CMB photons and an external scalar field. Such kind of interaction could give rise to the rotation of the linear polarization state of CMB photons, and consequently induce the CMB BB power spectrum, which could mimic the signal of primordial gravitational waves at large scales. With the recent polarization data of BICEP2 and the joint analysis data of BICEP2/Keck Array and Planck, we perform a global fitting analysis on constraining the tensor-to-scalar ratio $r$ by considering the polarization rotation angle which can be separated into a background isotropic part and a small anisotropic part. Since the data of BICEP2 and Keck Array experiments have already been corrected by using the self-calibration method, here we mainly focus on the effects from the anisotropies of CMB polarization rotation angle. We find that including the anisotropies in the analysis could slightly weaken the constraints on $r$, when using current CMB polarization measurements. We also simulate the mock CMB data with the BICEP3-like sensitivity. Very interestingly, we find that if the effects of the anisotropic polarization rotation angle can not be taken into account properly in the analysis, the constraints on $r$ will be dramatically biased. This implies that we need to break the degeneracy between the anisotropies of the CMB polarization rotation angle and the CMB primordial tensor perturbations, in order to measure the signal of primordial gravitational waves accurately.
We calculate the secondary anisotropies in the CMB produced by inhomogeneous reionization from simulations in which the effects of radiative and stellar feedback effects on galaxy formation have been included. This allows to self-consistently determine the beginning ($z_iapprox 30$), the duration ($ delta zapprox 20$) and the (nonlinear) evolution of the reionization process for a critical density CDM model. In addition, from the simulated spatial distribution of ionized regions, we are able to calculate the evolution of the two-point ionization correlation function, $C_chi$, and obtain the power spectrum of the anisotropies, $C_ell$, in the range $5000 < ell < 10^6$. The power spectrum has a broad maximum around $ell approx 30000$, where it reaches the value $2times 10^{-12}$. We also show that the angular correlation function $C(theta)$ is not Gaussian, but at separation angles $% theta lower.5exhbox{ltsima} 10^{-4}$ rad it can be approximated by a modified Lorentzian shape; at larger separations an anticorrelation signal is predicted. Detection of signals as above will be possible with future mm-wavelength interferometers like ALMA, which appears as an optimum instrument to search for signatures of inhomogeneous reionization.
We study the effects of pre-recombination physics on the Stochastic Gravitational Wave Background (SGWB) anisotropies induced by the propagation of gravitons through the large-scale density perturbations and their cross-correlation with Cosmic Microwave Background (CMB) temperature and E-mode polarization ones. As examples of Early Universe extensions to the $Lambda$CDM model, we consider popular models featuring extra relativistic degrees of freedom, a massless non-minimally coupled scalar field, and an Early Dark Energy component. Assuming the detection of a SGWB, we perform a Fisher analysis to assess in a quantitative way the capability of future gravitational wave interferometers (GWIs) in conjunction with a future large-scale CMB polarization experiment to constrain such variations. Our results show that the cross-correlation of CMB and SGWB anisotropies will help tighten the constraints obtained with CMB alone, with an improvement that significantly depends on the specific model as well as the maximum angular resolution $ell_{rm max}^{rm GW}$ of the GWIs, their designed sensitivity, and the amplitude $A_*$ of the monopole of the SGWB.
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