# Posts Tagged confidence level

## Recent Postings from confidence level

### Higgs couplings and Naturalness in the littlest Higgs model with T-parity at the LHC and TLEP

Motivated by the recent LHC Higgs data and null results in searches for any new physics, we investigate the Higgs couplings and naturalness in the littlest Higgs model with T-parity. By performing the global fit of the latest Higgs data, electroweak precise observables and $R_{b}$ measurements, we find that the scale $f$ can be excluded up to 600 GeV at $2\sigma$ confidence level. The expected Higgs coupling measurements at the future collider TLEP will improve this lower limit to above 3 TeV. Besides, the top parnter mass $m_{T_{+}}$ can be excluded up to 880 GeV at $2\sigma$ confidence level. The future HL-LHC can constrain this mass in the region $m_{T_{+}} < 2.2$ TeV corresponding to the fine-tuning being lager than 1\%.

### A study of electroweak vacuum metastablity with a singlet scalar dark matter

We study several aspects of electroweak vacuum metastability when an extra gauge singlet scalar, a viable candidate for a dark matter particle, is added to the standard model of particle physics, which is assumed to be valid up to the Planck scale. Phase diagrams are drawn for different parameter spaces, and based on that, we graphically demonstrate how the confidence level, at which stability of electroweak vacuum is excluded, depends on such new physics parameters.

### Weighing neutrinos in $f(R)$ gravity in light of BICEP2

We constrain the neutrino mass in $f(R)$ gravity using the latest observations from the Planck, BAO and BICEP2 data. We find that the measurement on the B-modes can break the degeneracy between the massive neutrinos and the $f(R)$ gravity. We find a non-zero value of the Compton wavelengths $B_{0}$ at a $68\%$ confidence level for the $f(R)$ model in the presence of massive neutrinos when the BICEP2 data is used. Furthermore, the tension on the tensor-to-scalar ratios between the measured values from Plank and BICEP2 is significantly reconciled in our model.

### A search for decay $\eta' \rightarrow 4 \pi^{0}$ with GAMS-$4\pi$ Setup [Cross-Listing]

A search for rare decay $\eta’ \rightarrow 4 \pi^{0}$ has been performed with GAMS-4$\pi$ Setup. The new upper limit for decay was established $BR(\eta’ \rightarrow 4 \pi^{0}) < 3.2 \cdot 10^{-4}$ at 90\% confidence level. The $\pi^{-} p$ charge-exchange reaction at 32.5 GeV/c was used as a source of $1.3\cdot 10^{6}$ $\eta’$ mesons. Experiment carried out at the IHEP U-70 accelerator.

### Precision of future experiments measuring primordial tensor fluctuation

Recently the second phase of Background Imaging of Cosmic Extragalactic Polarization (BICEP2) claimed a detection of the tensor-to-scalar ratio ($r$) of primordial fluctuation at $5\sigma$ confidence level. If it is true, this large and measurable amplitude ($r \simeq 0.2$) of B-mode polarization indicates that it is possible to measure the shape of CMB B-mode polarization with future experiments. Given the current understanding of the experimental noise and foreground contamination, we forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements from Planck, Spider and POLARBEAR with $n_{\rm t}$ as a free parameter. We quantitatively determine the signal-to-noise of the measurement in $r$-$n_{\rm t}$ parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on $n_{\rm t}$, but strongly depends on the true value of $r$.

### Precision of future experiments measuring primordial tensor fluctuation [Cross-Listing]

Recently the second phase of Background Imaging of Cosmic Extragalactic Polarization (BICEP2) claimed a detection of the tensor-to-scalar ratio ($r$) of primordial fluctuation at $5\sigma$ confidence level. If it is true, this large and measurable amplitude ($r \simeq 0.2$) of B-mode polarization indicates that it is possible to measure the shape of CMB B-mode polarization with future experiments. Given the current understanding of the experimental noise and foreground contamination, we forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements from Planck, Spider and POLARBEAR with $n_{\rm t}$ as a free parameter. We quantitatively determine the signal-to-noise of the measurement in $r$-$n_{\rm t}$ parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on $n_{\rm t}$, but strongly depends on the true value of $r$.

### Precision of future experiments measuring primordial tensor fluctuation [Cross-Listing]

Recently the second phase of Background Imaging of Cosmic Extragalactic Polarization (BICEP2) claimed a detection of the tensor-to-scalar ratio ($r$) of primordial fluctuation at $5\sigma$ confidence level. If it is true, this large and measurable amplitude ($r \simeq 0.2$) of B-mode polarization indicates that it is possible to measure the shape of CMB B-mode polarization with future experiments. Given the current understanding of the experimental noise and foreground contamination, we forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements from Planck, Spider and POLARBEAR with $n_{\rm t}$ as a free parameter. We quantitatively determine the signal-to-noise of the measurement in $r$-$n_{\rm t}$ parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on $n_{\rm t}$, but strongly depends on the true value of $r$.

### Precision of future experiments measuring primordial tensor fluctuation [Replacement]

Recently the second phase of Background Imaging of Cosmic Extragalactic Polarization (BICEP2) claimed a detection of the tensor-to-scalar ratio ($r$) of primordial fluctuation at $5\sigma$ confidence level. If it is true, this large and measurable amplitude ($r \simeq 0.2$) of B-mode polarization indicates that it is possible to measure the shape of CMB B-mode polarization with future experiments. Given the current understanding of the experimental noise and foreground contamination, we forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements from Planck, Spider and POLARBEAR with $n_{\rm t}$ as a free parameter. We quantitatively determine the signal-to-noise of the measurement in $r$-$n_{\rm t}$ parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on $n_{\rm t}$, but strongly depends on the true value of $r$.

### Precision of future experiments measuring primordial tensor fluctuation [Replacement]

Recently the second phase of Background Imaging of Cosmic Extragalactic Polarization (BICEP2) claimed a detection of the tensor-to-scalar ratio ($r$) of primordial fluctuation at $5\sigma$ confidence level. If it is true, this large and measurable amplitude ($r \simeq 0.2$) of B-mode polarization indicates that it is possible to measure the shape of CMB B-mode polarization with future experiments. Given the current understanding of the experimental noise and foreground contamination, we forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements from Planck, Spider and POLARBEAR with $n_{\rm t}$ as a free parameter. We quantitatively determine the signal-to-noise of the measurement in $r$-$n_{\rm t}$ parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on $n_{\rm t}$, but strongly depends on the true value of $r$.

### Precision of future experiments measuring primordial tensor fluctuation [Replacement]

Recently the second phase of Background Imaging of Cosmic Extragalactic Polarization (BICEP2) claimed a detection of the tensor-to-scalar ratio ($r$) of primordial fluctuation at $5\sigma$ confidence level. If it is true, this large and measurable amplitude ($r \simeq 0.2$) of B-mode polarization indicates that it is possible to measure the shape of CMB B-mode polarization with future experiments. Given the current understanding of the experimental noise and foreground contamination, we forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements from Planck, Spider and POLARBEAR with $n_{\rm t}$ as a free parameter. We quantitatively determine the signal-to-noise of the measurement in $r$-$n_{\rm t}$ parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on $n_{\rm t}$, but strongly depends on the true value of $r$.

### Constraints on Dark Energy from New Observations including Pan-STARRS [Replacement]

In this paper, we set the new limits on the equation of state parameter (EoS) of dark energy with the observations of cosmic microwave background radiation (CMB) from Planck satellite, the type Ia supernovae from Pan-STARRS and the baryon acoustic oscillation (BAO). We consider two parametrization forms of EoS: a constant $w$ and time evolving $w(a)=w_0+w_a(1-a)$. The results show that with a constant EoS, $w=-1.141\pm{0.075}$ ($68\%~C.L.$), which is consistent with $\Lambda$CDM at about $2\sigma$ confidence level. For a time evolving $w(a)$ model, we get $w_0=-1.09^{+0.16}_{-0.18}$ ($1\sigma~C.L.$), $w_a=-0.34^{+0.87}_{-0.51}$ ($1\sigma~C.L.$), and in this case $\Lambda$CDM can be comparable with our observational data at $1\sigma$ confidence level. In order to do the parametrization independent analysis, additionally we adopt the so called principal component analysis (PCA) method, in which we divide redshift range into several bins and assume $w$ as a constant in each redshift bin (bin-w). In such bin-w scenario, we find that for most of the bins cosmological constant can be comparable with the data, however, there exists few bins which give $w$ deviating from $\Lambda$CDM at more than $2\sigma$ confidence level, which shows a weak hint for the time evolving behavior of dark energy. To further confirm this hint, we need more data with higher precision.

### Constraints on Dark Energy from New Observations including Pan-STARRS

In this paper, we set the new limits on the equation of state parameter (EoS) of dark energy with the observations of cosmic microwave background radiation (CMB) from Planck satellite, the type Ia supernovae from Pan-STARRS and the baryon acoustic oscillation (BAO). We consider two parametrization forms of EoS: a constant $w$ and time evolving $w(a)=w_0+w_a(1-a)$. The results show that with a constant EoS, $w=-1.141\pm{0.075}$ ($68\%~C.L.$), which is consistent with $\Lambda$CDM at about $2\sigma$ confidence level. For a time evolving $w(a)$ model, we get $w_0=-1.09^{+0.16}_{-0.18}$ ($1\sigma~C.L.$), $w_a=-0.34^{+0.87}_{-0.51}$ ($1\sigma~C.L.$), and in this case $\Lambda$CDM can be comparable with our observational data at $1\sigma$ confidence level. In order to do the parametrization independent analysis, additionally we adopt the so called principal component analysis (PCA) method, in which we divide redshift range into several bins and assume $w$ as a constant in each redshift bin (bin-w). In such bin-w scenario, we find that for most of the bins cosmological constant can be comparable with the data, however, there exists few bins which give $w$ deviating from $\Lambda$CDM at more than $2\sigma$ confidence level, which shows a weak hint for the time evolving behavior of dark energy. To further confirm this hint, we need more data with higher precision. Moreover, we also forecast the constraint on bin-w from the future supernova observation of WFIRST.

### Detecting chiral gravity with the pure pseudospectrum reconstruction of the cosmic microwave background polarized anisotropies

We consider the possible detection of parity violation at the linear level in gravity using polarized anisotropies of the cosmic microwave background. Since such a parity violation would lead to non-zero TB and EB correlations, this makes those odd-parity angular power spectra a potential probe of parity violation in the gravitational sector. These spectra are modeled incorporating the impact of lensing and we explore their possible detection in the context of small-scale (balloon-borne or ground-based) experiments and a future satellite mission dedicated to B-mode detection. We assess the statistical uncertainties on their reconstruction using mode-counting and a (more realistic) pure pseudospectrum estimator approach. Those uncertainties are then translated into constraints on the level of parity asymmetry. We found that detecting chiral gravity is impossible for ongoing small-scale experiments. However, for a satellite-like mission, a parity asymmetry of at least 50% could be detected at 68% of confidence level, and a parity asymmetry of 100% is measurable with at least a confidence level of 95%. We also assess the impact of a possible miscalibration of the orientation of the polarized detectors, leading to spurious TB and EB cross-correlations. We show that in the context of pseudospectrum estimation of the angular power spectra, self-calibration of this angle could significantly reduce the statistical significance of the measured level of parity asymmetry (by e.g. a factor ~2.4 for a miscalibration angle of 1 degree). For chiral gravity and assuming a satellite mission dedicated to primordial B-mode, a non detection of the TB and EB correlation would translate into an upper bound on parity violation of 39% at 95% confidence level for a tensor-to-scalar ratio of 0.2, excluding values of the (imaginary) Barbero-Immirzi parameter comprised between 0.2 and 4.9 at 95% CL.

### Detecting chiral gravity with the pure pseudospectrum reconstruction of the cosmic microwave background polarized anisotropies [Replacement]

We consider the possible detection of parity violation at the linear level in gravity using polarized anisotropies of the cosmic microwave background. Since such a parity violation would lead to non-zero TB and EB correlations, this makes those odd-parity angular power spectra a potential probe of parity violation in the gravitational sector. These spectra are modeled incorporating the impact of lensing and we explore their possible detection in the context of small-scale (balloon-borne or ground-based) experiments and a future satellite mission dedicated to B-mode detection. We assess the statistical uncertainties on their reconstruction using mode-counting and a (more realistic) pure pseudospectrum estimator approach. Those uncertainties are then translated into constraints on the level of parity asymmetry. We found that detecting chiral gravity is impossible for ongoing small-scale experiments. However, for a satellite-like mission, a parity asymmetry of at least 50% could be detected at 68% of confidence level, and a parity asymmetry of 100% is measurable with at least a confidence level of 95%. We also assess the impact of a possible miscalibration of the orientation of the polarized detectors, leading to spurious TB and EB cross-correlations. We show that in the context of pseudospectrum estimation of the angular power spectra, self-calibration of this angle could significantly reduce the statistical significance of the measured level of parity asymmetry (by e.g. a factor ~2.4 for a miscalibration angle of 1 degree). For chiral gravity and assuming a satellite mission dedicated to primordial B-mode, a non detection of the TB and EB correlation would translate into an upper bound on parity violation of 39% at 95% confidence level for a tensor-to-scalar ratio of 0.2, excluding values of the (imaginary) Barbero-Immirzi parameter comprised between 0.2 and 4.9 at 95% CL.

### Robustness of $H_0$ determination at intermediate redshifts [Replacement]

The most recent Hubble constant ($H_0)$ estimates from local methods (z << 1), $H_0=73.8\pm 2.4$ km s$^{-1}$ Mpc$^{-1}$, and the one from high redshifts $H_0=67.3\pm 1.2$ km s$^{-1}$ Mpc$^{-1}$, are discrepant at $2.4 \sigma$ confidence level. Within this context, Lima & Cunha (LC) derived a new determination of $H_0$ using four cosmic probes at intermediate redshifts ($0.1<z<1.8$) based on the so-called flat $\Lambda$CDM model. They obtained $H_0=74.1\pm 2.2$ km s$^{-1}$ Mpc$^{-1}$, in full agreement with local measurements. In this Letter, we explore the robustness of the LC result searching for systematic errors and its dependence from the cosmological model used. We find that the $H_0$ value from this joint analysis is very weakly dependent on the underlying cosmological model, but the morphology adopted to infer the distance to galaxy clusters changes the result sizeably, being the main source of systematic errors. Therefore, a better understanding of the cluster morphology is paramount to transform this method into a powerful cross-check for $H_0$.

### Robustness of $H_0$ determination at intermediate redshifts [Cross-Listing]

The most recent Hubble constant $(H_0)$ estimates from local methods ($z<<1$), $H_0=73.8\pm 2.4$ km s$^{-1}$ Mpc$^{-1}$, and the one from high redshits (Planck Collaboration 2013), $H_0=67.3\pm 1.2$ km s$^{-1}$ Mpc$^{-1}$, are discrepant at $2.4 \sigma$ confidence level. Within this context, Lima & Cunha (LC) (ApJL 781, 38, 2014) derived a new determination of $H_0$ using four cosmic probes at intermediate redshifts ($0.1<z<1.8$) based on the so-called flat $\Lambda$CDM model. They obtained $H_0=74.1\pm 2.2$ km s$^{-1}$ Mpc$^{-1}$, in full agreement with local measurements. In this letter, we explore the robustness of the LC result searching for systematic errors and its dependence from the cosmological model used. We find that the $H_0$ value from this joint analysis is very weakly dependent on the underlying cosmological model, but the morphology adopted to infer the distance to galaxy clusters changes the result sizeably, being the main source of systematic errors.

### Robustness of $H_0$ determination at intermediate redshifts

The most recent Hubble constant $(H_0)$ estimates from local methods ($z<<1$), $H_0=73.8\pm 2.4$ km s$^{-1}$ Mpc$^{-1}$, and the one from high redshits (Planck Collaboration 2013), $H_0=67.3\pm 1.2$ km s$^{-1}$ Mpc$^{-1}$, are discrepant at $2.4 \sigma$ confidence level. Within this context, Lima & Cunha (LC) (ApJL 781, 38, 2014) derived a new determination of $H_0$ using four cosmic probes at intermediate redshifts ($0.1<z<1.8$) based on the so-called flat $\Lambda$CDM model. They obtained $H_0=74.1\pm 2.2$ km s$^{-1}$ Mpc$^{-1}$, in full agreement with local measurements. In this letter, we explore the robustness of the LC result searching for systematic errors and its dependence from the cosmological model used. We find that the $H_0$ value from this joint analysis is very weakly dependent on the underlying cosmological model, but the morphology adopted to infer the distance to galaxy clusters changes the result sizeably, being the main source of systematic errors.

### Reconstruction of the primordial power spectra with Planck and BICEP2 [Replacement]

By using the cubic spline interpolation method, we reconstruct the shape of the primordial scalar and tensor power spectra from the recently released {\it Planck} temperature and BICEP2 polarization cosmic microwave background data. We find that the vanishing scalar index running ($\dd n_s/\dd\ln k$) model is strongly disfavored at more than $3\sigma$ confidence level on the $k=0.0002$ Mpc$^{-1}$ scale. Furthermore, the power-law parameterization gives a blue-tilt tensor spectrum, no matter using only the first 5 bandpowers $n_t = 1.20^{+0.56}_{-0.64} (95% {\rm CL})$ or the full 9 bandpowers $n_t = 1.24^{+0.51}_{-0.58} (95% {\rm CL})$ of BICEP2 data sets. Unlike the large tensor-to-scalar ratio value ($r\sim0.20$) under the scale-invariant tensor spectrum assumption, our interpolation approach gives $r_{0.002} < 0.060 (95% {\rm CL})$ by using the first 5 bandpowers of BICEP2 data. After comparing the results with/without BICEP2 data, we find that {\it Planck} temperature with small tensor amplitude signals and BICEP2 polarization data with large tensor amplitude signals dominate the tensor spectrum reconstruction on the large and small scales, respectively. Hence, the resulting blue tensor tilt actually reflects the tension between {\it Planck} and BICEP2 data.

### Reconstruction of the primordial power spectra with Planck and BICEP2

By using the cubic spline interpolation method, we reconstruct the shape of the primordial scalar and tensor power spectra from the recently released {\it Planck} temperature and BICEP2 polarization cosmic microwave background data. We find that the vanishing scalar index running ($\dd n_s/\dd\ln k$) model is strongly disfavored with more than $3\sigma$ confidence level on the $k=0.0002$ Mpc$^{-1}$ scale. Furthermore, the power-law parameterization gives a blue-tilt tensor spectrum, no matter using only the first 5 bandpowers $n_t = 1.20^{+0.56}_{-0.64}~(95\% {\rm CL})$ or the full 9 bandpowers $n_t = 1.24^{+0.51}_{-0.58}~(95\% {\rm CL})$ of BICEP2 data sets. Compared with the large tensor-to-scalar ratio value ($r\sim0.20$) under the scale-invariant tensor spectrum assumption, our interpolation approach gives $r_{0.002} < 0.060~(95\% {\rm CL})$ by using the first 5 bandpowers of BICEP2 data.

### Reconstruction of the primordial power spectra with Planck and BICEP2 [Cross-Listing]

By using the cubic spline interpolation method, we reconstruct the shape of the primordial scalar and tensor power spectra from the recently released {\it Planck} temperature and BICEP2 polarization cosmic microwave background data. We find that the vanishing scalar index running ($\dd n_s/\dd\ln k$) model is strongly disfavored with more than $3\sigma$ confidence level on the $k=0.0002$ Mpc$^{-1}$ scale. Furthermore, the power-law parameterization gives a blue-tilt tensor spectrum, no matter using only the first 5 bandpowers $n_t = 1.20^{+0.56}_{-0.64}~(95\% {\rm CL})$ or the full 9 bandpowers $n_t = 1.24^{+0.51}_{-0.58}~(95\% {\rm CL})$ of BICEP2 data sets. Compared with the large tensor-to-scalar ratio value ($r\sim0.20$) under the scale-invariant tensor spectrum assumption, our interpolation approach gives $r_{0.002} < 0.060~(95\% {\rm CL})$ by using the first 5 bandpowers of BICEP2 data.

### Reconstruction of the primordial power spectra with Planck and BICEP2 [Replacement]

By using the cubic spline interpolation method, we reconstruct the shape of the primordial scalar and tensor power spectra from the recently released {\it Planck} temperature and BICEP2 polarization cosmic microwave background data. We find that the vanishing scalar index running ($\dd n_s/\dd\ln k$) model is strongly disfavored at more than $3\sigma$ confidence level on the $k=0.0002$ Mpc$^{-1}$ scale. Furthermore, the power-law parameterization gives a blue-tilt tensor spectrum, no matter using only the first 5 bandpowers $n_t = 1.20^{+0.56}_{-0.64} (95% {\rm CL})$ or the full 9 bandpowers $n_t = 1.24^{+0.51}_{-0.58} (95% {\rm CL})$ of BICEP2 data sets. Unlike the large tensor-to-scalar ratio value ($r\sim0.20$) under the scale-invariant tensor spectrum assumption, our interpolation approach gives $r_{0.002} < 0.060 (95% {\rm CL})$ by using the first 5 bandpowers of BICEP2 data. After comparing the results with/without BICEP2 data, we find that {\it Planck} temperature with small tensor amplitude signals and BICEP2 polarization data with large tensor amplitude signals dominate the tensor spectrum reconstruction on the large and small scales, respectively. Hence, the resulting blue tensor tilt actually reflects the tension between {\it Planck} and BICEP2 data.

### Constraints on the extensions to the base $\Lambda$CDM model from BICEP2, Planck and WMAP [Cross-Listing]

Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0\sigma$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $\Lambda$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a positive running of running of spectral index is preferred at $1.7\sigma$ level from the combination of B2, P13 and WMAP Polarization data.

### Constraints on the extensions to the base $\Lambda$CDM model from BICEP2, Planck and WMAP [Cross-Listing]

Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0\sigma$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $\Lambda$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a positive running of running of spectral index is preferred at $1.7\sigma$ level from the combination of B2, P13 and WMAP Polarization data.

### Constraints on the extensions to the base $\Lambda$CDM model from BICEP2, Planck and WMAP [Replacement]

Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0\sigma$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $\Lambda$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a positive running of running of spectral index is preferred at $1.7\sigma$ level from the combination of B2, P13 and WMAP Polarization data.

### Constraints on the extensions to the base $\Lambda$CDM model from BICEP2, Planck and WMAP [Cross-Listing]

Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0\sigma$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $\Lambda$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a positive running of running of spectral index is preferred at $1.7\sigma$ level from the combination of B2, P13 and WMAP Polarization data.

### Constraints on the extensions to the base $\Lambda$CDM model from BICEP2, Planck and WMAP [Replacement]

Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0\sigma$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $\Lambda$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a positive running of running of spectral index is preferred at $1.7\sigma$ level from the combination of B2, P13 and WMAP Polarization data.

### Constraints on the extensions to the base $\Lambda$CDM model from BICEP2, Planck and WMAP

Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0\sigma$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $\Lambda$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a positive running of running of spectral index is preferred at $1.7\sigma$ level from the combination of B2, P13 and WMAP Polarization data.

### Constraints on the extensions to the base $\Lambda$CDM model from BICEP2, Planck and WMAP [Replacement]

Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0\sigma$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $\Lambda$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a positive running of running of spectral index is preferred at $1.7\sigma$ level from the combination of B2, P13 and WMAP Polarization data.

### Constraints on the extensions to the base $\Lambda$CDM model from BICEP2, Planck and WMAP [Replacement]

Recently Background Imaging of Cosmic Extragalactic Polarization (B2) discovered the relic gravitational waves at $7.0\sigma$ confidence level. However, the other cosmic microwave background (CMB) data, for example Planck data released in 2013 (P13), prefer a much smaller amplitude of the primordial gravitational waves spectrum if a power-law spectrum of adiabatic scalar perturbations is assumed in the six-parameter $\Lambda$CDM cosmology. In this paper, we explore whether the $w$CDM model and the running spectral index can relax the tension between B2 and other CMB data. In particular, we find that a positive running of running of spectral index is preferred at $1.7\sigma$ level from the combination of B2, P13 and WMAP Polarization data.

### Taking Halo-Independent Dark Matter Methods Out of the Bin

We develop a new halo-independent strategy for analyzing emerging DM hints, utilizing the method of extended maximum likelihood. This approach does not require the binning of events, making it uniquely suited to the analysis of emerging DM direct detection hints. It determines a preferred envelope, at a given confidence level, for the DM velocity integral which best fits the data using all available information and can be used even in the case of a single anomalous scattering event. All of the halo-independent information from a direct detection result may then be presented in a single plot, allowing simple comparisons between multiple experiments. This results in the halo-independent analogue of the usual mass and cross-section plots found in typical direct detection analyses, where limit curves may be compared with best-fit regions in halo-space. The method is straightforward to implement, using already-established techniques, and its utility is demonstrated through the first unbinned halo-independent comparison of the three anomalous events observed in the CDMS-Si detector with recent limits from the LUX experiment.

### Reconstructing the Local Potential of Inflation with BICEP2 data [Replacement]

We locally reconstruct the inflationary potential by using the current constraints on $r$ and $n_{\rm s}$ from BICEP2 data. Assuming small and negligible $\alpha_{\rm s}$, the inflationary potential is approximately linear in $\Delta\phi\sim M_{\rm pl}$ range but becomes non-linear in $\Delta\phi\sim 10 M_{\rm pl}$ range. However if we vary the value of $\alpha_{\rm s}$ within the range given by constraints from {\it Planck} measurement, the local reconstruction is only valid in the range of $\Delta\phi\sim 0.4 M_{\rm pl}$, which challenges the inflationary background from the point of view of effective field theory. We show that, within the range of $\Delta \phi \sim 0.4 M_{\rm pl}$, the inflation potential can be precisely reconstructed. With the current reconstruction, we show that $V(\phi) \sim \phi^{2}$ and $\phi^{3}$ are consistent, while $\phi$ model is ruled out by $95\%$ confidence level of the reconstructed range of potential. This sets up a strong limit of large-field inflation models.

### Reconstructing the Local Potential of Inflation with BICEP2 data [Replacement]

We locally reconstruct the inflationary potential by using the current constraints on $r$ and $n_{\rm s}$ from BICEP2 data. Assuming small and negligible $\alpha_{\rm s}$, the inflationary potential is approximately linear in $\Delta\phi\sim M_{\rm pl}$ range but becomes non-linear in $\Delta\phi\sim 10 M_{\rm pl}$ range. However if we vary the value of $\alpha_{\rm s}$ within the range given by constraints from {\it Planck} measurement, the local reconstruction is only valid in the range of $\Delta\phi\sim 0.4 M_{\rm pl}$, which challenges the inflationary background from the point of view of effective field theory. We show that, within the range of $\Delta \phi \sim 0.4 M_{\rm pl}$, the inflation potential can be precisely reconstructed. With the current reconstruction, we show that $V(\phi) \sim \phi^{2}$ and $\phi^{3}$ are consistent, while $\phi$ model is ruled out by $95\%$ confidence level of the reconstructed range of potential. This sets up a strong limit of large-field inflation models.

### Investigation of dark matter-dark energy interaction cosmological model

In this paper, we test the dark matter-dark energy interacting cosmological model with a dynamic equation of state $w_{DE}(z)=w_{0}+w_{1}z/(1+z)$, using type Ia supernovae (SNe Ia), Hubble parameter data, baryonic acoustic oscillation (BAO) measurements, and the cosmic microwave background (CMB) observation. This interacting cosmological model has not been studied before. The best-fitted parameters with $1 \sigma$ uncertainties are $\delta=-0.022 \pm 0.006$, $\Omega_{DM}^{0}=0.213 \pm 0.008$, $w_0 =-1.210 \pm 0.033$ and $w_1=0.872 \pm 0.072$ with $\chi^2_{min}/dof = 0.990$. At the $1 \sigma$ confidence level, we find $\delta<0$, which means that the energy transfer prefers from dark matter to dark energy. We also find that the SNe Ia are in tension with the combination of CMB, BAO and Hubble parameter data. The evolution of $\rho_{DM}/\rho_{DE}$ indicates that this interacting model is a good approach to solve the coincidence problem, because the $\rho_{DE}$ decrease with scale factor $a$. The transition redshift is $z_{tr}=0.63 \pm 0.07$ in this model.

### First measurement of $\sigma_8$ using supernova magnitudes only [Replacement]

A method was recently proposed which allows the conversion of the weak-lensing effects in the supernova Hubble diagram from noise into signal. Such signal is sensitive to the growth of structure in the universe, and in particular can be used as a measurement of $\sigma_8$ which is independent from more traditional methods such as those based on the CMB, cosmic shear or cluster abundance. We extend here that analysis to allow for intrinsic non-Gaussianities in the supernova PDF, and discuss how this can be best modelled using the Bayes Factor. Although it was shown that a precise measurement of $\sigma_8$ requires ~$10^5$ supernovae, current data already allows an important proof of principle. In particular we make use of the 732 supernovae with z < 1 of the recent JLA catalog and show that a simple treatment of intrinsic non-Gaussianities with a couple of nuisance parameters is enough for our method to yield the values $\sigma_8 = 0.84^{+0.28}_{-0.65}$ or $\sigma_8 < 1.45$ at a $2\sigma$ confidence level. This result is consistent with mock simulations and it is also in agreement with independent measurements and presents the first ever measurement of $\sigma_8$ using supernova magnitudes alone.

### First measurement of $\sigma_8$ using supernova data only

A method was recently proposed which allows the conversion of the weak-lensing effects in the supernova Hubble diagram from noise into signal. Such signal is sensitive to the growth of structure in the universe, and in particular can be used as a measurement of $\sigma_8$ which is independent from more traditional methods such as those based on the CMB, cosmic shear or cluster abundance. We extend here that analysis to allow for intrinsic non-Gaussianities in the supernova PDF, and discuss how this can be best modelled using the Bayes Factor. Although it was shown that a precise measurement of $\sigma_8$ requires ~$10^5$ supernovae, current data already allows an important proof of principle. In particular we make use of the 732 supernovae with z < 1 of the recent JLA catalog and show that a simple treatment of intrinsic non-Gaussianities with a couple of nuisance parameters is enough for our method to yield the values $\sigma_8 = 0.84^{+0.28}_{-0.65}$ or $\sigma_8 < 1.45$ at a $2\sigma$ confidence level. This result is consistent with mock simulations and it is also in agreement with independent measurements and presents the first ever measurement of $\sigma_8$ using supernova data alone.

### First measurement of $\sigma_8$ using supernova magnitudes only [Replacement]

A method was recently proposed which allows the conversion of the weak-lensing effects in the supernova Hubble diagram from noise into signal. Such signal is sensitive to the growth of structure in the universe, and in particular can be used as a measurement of $\sigma_8$ which is independent from more traditional methods such as those based on the CMB, cosmic shear or cluster abundance. We extend here that analysis to allow for intrinsic non-Gaussianities in the supernova PDF, and discuss how this can be best modelled using the Bayes Factor. Although it was shown that a precise measurement of $\sigma_8$ requires ~$10^5$ supernovae, current data already allows an important proof of principle. In particular we make use of the 732 supernovae with z < 1 of the recent JLA catalog and show that a simple treatment of intrinsic non-Gaussianities with a couple of nuisance parameters is enough for our method to yield the values $\sigma_8 = 0.84^{+0.28}_{-0.65}$ or $\sigma_8 < 1.45$ at a $2\sigma$ confidence level. This result is consistent with mock simulations and it is also in agreement with independent measurements and presents the first ever measurement of $\sigma_8$ using supernova magnitudes alone.

### Reconciling the cosmic age problem in the R_h=ct Universe

Many dark energy models fail to pass the cosmic age test. In this paper, we investigate the cosmic age problem associated with 20 extremely red and massive galaxies at very high redshift from Castro-Rodr{\’i}guez and Lopez-Corredoira (2012) in the $R_h=ct$ Universe. These old galaxies and the $R_h=ct$ Universe have not been used to study the cosmic age problem in previous literature. By evaluating the age of the $R_h=ct$ Universe with the observational constraints from the Type Ia supernovae, and Hubble parameter, we find that the $R_h=ct$ Universe can accommodate the 20 old galaxies and quasar APM 08279+5255 at redshift $z=3.91$ at more than $3\sigma$ confidence level. So, unlike other cosmological models, the $R_h=ct$ Universe does not suffer the cosmic age problem.

### Molecular hydrogen absorption systems in SDSS

We present a systematic search for molecular hydrogen absorption systems at high redshift in quasar spectra from the Sloan Digital Sky Survey (SDSS) II Data Release 7 and SDSS-III Data Release 9. We have selected candidates using a modified profile fitting technique taking into account that the Ly$\alpha$ forest can effectively mimic H$_2$ absorption systems at the resolution of SDSS data. To estimate the confidence level of the detections, we use two methods: a Monte-Carlo sampling and an analysis of control samples. The analysis of control samples allows us to define regions of the spectral quality parameter space where H$_2$ absorption systems can be confidently identified. We find that H$_2$ absorption systems with column densities $\log {\rm N_{H_2}} > 19$ can be detected in only less than 3% of SDSS quasar spectra. We estimate the upper limit on the detection rate of saturated H$_2$ absorption systems ($\log {\rm N_{H_2}} > 19$) in Damped Ly-$\alpha$ (DLA) systems to be about 7%. We provide a sample of 23 confident H$_2$ absorption system candidates that would be interesting to follow up with high resolution spectrographs. There is a 1$\sigma$ $r-i$ color excess and non-significant $A_{\rm V}$ extinction excess in quasar spectra with an H$_2$ candidate compared to standard DLA-bearing quasar spectra. The equivalent widths (EWs) of C II, Si II and Al III (but not Fe II) absorptions associated with H$_2$ candidate DLAs are larger compared to standard DLAs. This is probably related to a larger spread in velocity of the absorption lines in the H$_2$ bearing sample.

### Molecular hydrogen absorption systems in Sloan Digital Sky Survey [Replacement]

We present a systematic search for molecular hydrogen absorption systems at high redshift in quasar spectra from the Sloan Digital Sky Survey (SDSS) II Data Release 7 and SDSS-III Data Release 9. We have selected candidates using a modified profile fitting technique taking into account that the Ly$\alpha$ forest can effectively mimic H$_2$ absorption systems at the resolution of SDSS data. To estimate the confidence level of the detections, we use two methods: a Monte-Carlo sampling and an analysis of control samples. The analysis of control samples allows us to define regions of the spectral quality parameter space where H$_2$ absorption systems can be confidently identified. We find that H$_2$ absorption systems with column densities $\log {\rm N_{H_2}} > 19$ can be detected in only less than 3% of SDSS quasar spectra. We estimate the upper limit on the detection rate of saturated H$_2$ absorption systems ($\log {\rm N_{H_2}} > 19$) in Damped Ly-$\alpha$ (DLA) systems to be about 7%. We provide a sample of 23 confident H$_2$ absorption system candidates that would be interesting to follow up with high resolution spectrographs. There is a 1$\sigma$ $r-i$ color excess and non-significant $A_{\rm V}$ extinction excess in quasar spectra with an H$_2$ candidate compared to standard DLA-bearing quasar spectra. The equivalent widths (EWs) of C II, Si II and Al III (but not Fe II) absorptions associated with H$_2$ candidate DLAs are larger compared to standard DLAs. This is probably related to a larger spread in velocity of the absorption lines in the H$_2$ bearing sample.

### Probing Quintessence Potential with Future Cosmological Surveys [Replacement]

Quintessence, a scalar field model, has been proposed to account for the acceleration of the Universe at present. We discuss how accurately quintessence models are discriminated by future cosmological surveys, which include experiments of CMB, galaxy clustering, weak lensing, and the type Ia SNe surveys, by making use of the conventional parameterized dark energy models. We can see clear differences between the thawing and the freezing quintessence models at more than $1\sigma$ ($2\sigma$) confidence level as long as the present equation of state for quintessence is away from $-1$ as $w_X \gtrsim -0.95 (-0.90)$. However, it is found to be difficult to probe the effective mass squared for the potential in thawing models, whose signs are different between the quadratic and the cosine-type potentials. This fact may require us to invent a new estimator to distinguish quintessence models beyond the thawing and the freezing ones.

### Probing Quintessence Potential with Future Cosmological Surveys [Cross-Listing]

Quintessence, a scalar field model, has been proposed to account for the acceleration of the Universe at present. We discuss how accurately quintessence models are discriminated by future cosmological surveys, which include experiments of CMB, galaxy clustering, weak lensing, and the type Ia SNe surveys, by making use of the conventional parameterized dark energy models. We can see clear differences between the thawing and the freezing quintessence models at more than $1\sigma$ ($2\sigma$) confidence level as long as the present equation of state for quintessence is away from $-1$ as $w_X \gtrsim -0.95 (-0.90)$. However, it is found to be difficult to probe the effective mass squared for the potential in thawing models, whose signs are different between the quadratic and the cosine-type potentials. This fact may require us to invent a new estimator to distinguish quintessence models beyond the thawing and the freezing ones.

### Probing Quintessence Potential with Future Cosmological Surveys [Replacement]

Quintessence, a scalar field model, has been proposed to account for the acceleration of the Universe at present. We discuss how accurately quintessence models are discriminated by future cosmological surveys, which include experiments of CMB, galaxy clustering, weak lensing, and the type Ia SNe surveys, by making use of the conventional parameterized dark energy models. We can see clear differences between the thawing and the freezing quintessence models at more than $1\sigma$ ($2\sigma$) confidence level as long as the present equation of state for quintessence is away from $-1$ as $w_X \gtrsim -0.95 (-0.90)$. However, it is found to be difficult to probe the effective mass squared for the potential in thawing models, whose signs are different between the quadratic and the cosine-type potentials. This fact may require us to invent a new estimator to distinguish quintessence models beyond the thawing and the freezing ones.

### Probing Quintessence Potential with Future Cosmological Surveys [Cross-Listing]

Quintessence, a scalar field model, has been proposed to account for the acceleration of the Universe at present. We discuss how accurately quintessence models are discriminated by future cosmological surveys, which include experiments of CMB, galaxy clustering, weak lensing, and the type Ia SNe surveys, by making use of the conventional parameterized dark energy models. We can see clear differences between the thawing and the freezing quintessence models at more than $1\sigma$ ($2\sigma$) confidence level as long as the present equation of state for quintessence is away from $-1$ as $w_X \gtrsim -0.95 (-0.90)$. However, it is found to be difficult to probe the effective mass squared for the potential in thawing models, whose signs are different between the quadratic and the cosine-type potentials. This fact may require us to invent a new estimator to distinguish quintessence models beyond the thawing and the freezing ones.

### Probing Quintessence Potential with Future Cosmological Surveys [Replacement]

Quintessence, a scalar field model, has been proposed to account for the acceleration of the Universe at present. We discuss how accurately quintessence models are discriminated by future cosmological surveys, which include experiments of CMB, galaxy clustering, weak lensing, and the type Ia SNe surveys, by making use of the conventional parameterized dark energy models. We can see clear differences between the thawing and the freezing quintessence models at more than $1\sigma$ ($2\sigma$) confidence level as long as the present equation of state for quintessence is away from $-1$ as $w_X \gtrsim -0.95 (-0.90)$. However, it is found to be difficult to probe the effective mass squared for the potential in thawing models, whose signs are different between the quadratic and the cosine-type potentials. This fact may require us to invent a new estimator to distinguish quintessence models beyond the thawing and the freezing ones.

### Probing Quintessence Potential with Future Cosmological Surveys

Quintessence, a scalar field model, has been proposed to account for the acceleration of the Universe at present. We discuss how accurately quintessence models are discriminated by future cosmological surveys, which include experiments of CMB, galaxy clustering, weak lensing, and the type Ia SNe surveys, by making use of the conventional parameterized dark energy models. We can see clear differences between the thawing and the freezing quintessence models at more than $1\sigma$ ($2\sigma$) confidence level as long as the present equation of state for quintessence is away from $-1$ as $w_X \gtrsim -0.95 (-0.90)$. However, it is found to be difficult to probe the effective mass squared for the potential in thawing models, whose signs are different between the quadratic and the cosine-type potentials. This fact may require us to invent a new estimator to distinguish quintessence models beyond the thawing and the freezing ones.

### Cosmological parameter estimation from CMB and X-ray clusters after Planck

We update the cosmological parameter estimation for three non-vanilla models by a joint analysis of \CCCP\ X-ray cluster, the newly released \Planck\ CMB data as well as some external data sets, such as baryon acoustic oscillation measurements from the 6dFGS, SDSS DR7 and BOSS DR9 surveys, and Hubble Space Telescope $H_0$ measurement. First of all, we find that X-ray cluster data sets strongly favor a non-zero summed neutrino mass at more than 3$\sigma$ confidence level in these non-vanilla models. And then, we reveal some tensions between X-ray cluster and {\it Planck} data in some cosmological parameters. For the matter power spectrum amplitude $\sigma_8$, X-ray cluster data favor a lower value compared with {\it Planck}. Because of the strong $\sigma_8-\sum m_{\nu}$ degeneracy, this tension could beyond 2$\sigma$ confidence level when the summed neutrino mass $\sum m_{\nu}$ is allowed to vary. For the CMB lensing amplitude $A_L$, the addition of X-ray cluster data results in a 3$\sigma$ deviation from the vanilla model. Furthermore, {\it Planck}+X-ray data prefer a large Hubble constant and phantom-like dark energy equation of state, which are in $2\sigma$ tension with those from WMAP7+X-ray data. Finally, we find that these tensions/descrepencies could be relaxed in some sense by adding a $9\%$ systematic shift in the cluster mass functions.

### Cosmological parameter estimation from CMB and X-ray clusters after Planck [Replacement]

We update the cosmological parameter estimation for three non-vanilla models by a joint analysis of \CCCP\ X-ray cluster, the newly released \Planck\ CMB data as well as some external data sets, such as baryon acoustic oscillation measurements from the 6dFGS, SDSS DR7 and BOSS DR9 surveys, and Hubble Space Telescope $H_0$ measurement. First of all, we find that X-ray cluster data sets strongly favor a non-zero summed neutrino mass at more than 3$\sigma$ confidence level in these non-vanilla models. And then, we reveal some tensions between X-ray cluster and {\it Planck} data in some cosmological parameters. For the matter power spectrum amplitude $\sigma_8$, X-ray cluster data favor a lower value compared with {\it Planck}. Because of the strong $\sigma_8-\sum m_{\nu}$ degeneracy, this tension could beyond 2$\sigma$ confidence level when the summed neutrino mass $\sum m_{\nu}$ is allowed to vary. For the CMB lensing amplitude $A_L$, the addition of X-ray cluster data results in a 3$\sigma$ deviation from the vanilla model. Furthermore, {\it Planck}+X-ray data prefer a large Hubble constant and phantom-like dark energy equation of state, which are in $2\sigma$ tension with those from WMAP7+X-ray data. Finally, we find that these tensions/descrepencies could be relaxed in some sense by adding a $9\%$ systematic shift in the cluster mass functions.

### Estimating the uncorrelated dark energy evolution in the Planck era

The equation of state (EOS), $w(z)$, is the most important parameter of dark energy. We reconstruct the evolution of this EOS in a model-independent way using the latest cosmic microwave background (CMB) data from Planck and other observations, such as type Ia supernovae (SNe Ia), the baryonic acoustic oscillation measurements (SDSS, 6dF, BOSS, and WiggleZ), and the Hubble parameter value $H(z)$. The results show that the EOS is consistent with the cosmological constant at the $2\sigma$ confidence level, not preferring a dynamical dark energy. The uncorrelated EOS of dark energy constraints from Planck CMB data are much tighter than those from the WMAP 9-year CMB data.

### Search for a Stochastic Gravitational-wave Background using a pair of Torsion-bar Antennas

We have set a new upper limit on the stochastic gravitational wave background (SGWB) using two prototype Torsion-bar Antennas (TOBAs). TOBA is a low-frequency gravitational-wave detector with bar-shaped test masses rotated by the tidal force of gravitational waves. As a result of simultaneous 7-hour observations with TOBAs in Tokyo and Kyoto in Japan, our upper limit with a confidence level of 95% is $\Omega_{\rm gw}h_0^2 < 1.9 \times 10^{17}$ at 0.035 – 0.830 Hz, where $h_{0}$ is the Hubble constant in units of 100 km/s/Mpc and $\Omega_{\rm gw}$ is the gravitational wave energy density per logarithmic frequency interval in units of the closure density. We successfully updated the upper limit and extended the explored frequency band.

### Search for a Stochastic Gravitational-wave Background using a pair of Torsion-bar Antennas [Cross-Listing]

We have set a new upper limit on the stochastic gravitational wave background (SGWB) using two prototype Torsion-bar Antennas (TOBAs). TOBA is a low-frequency gravitational-wave detector with bar-shaped test masses rotated by the tidal force of gravitational waves. As a result of simultaneous 7-hour observations with TOBAs in Tokyo and Kyoto in Japan, our upper limit with a confidence level of 95% is $\Omega_{\rm gw}h_0^2 < 1.9 \times 10^{17}$ at 0.035 – 0.830 Hz, where $h_{0}$ is the Hubble constant in units of 100 km/s/Mpc and $\Omega_{\rm gw}$ is the gravitational wave energy density per logarithmic frequency interval in units of the closure density. We successfully updated the upper limit and extended the explored frequency band.

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