# Posts Tagged confidence level

## Recent Postings from confidence level

### Dimension-six anomalous $tq\gamma$ couplings in $\gamma \gamma$ collision at the LHC

We have investigated the flavor changing top quark physics on the dimension-six anomalous $tq\gamma$ ($q=u,c$) couplings through the process $pp\to p\gamma \gamma p\to p t\bar{q}p$ at the LHC by considering different forward detector acceptances. In this paper, we have taken into account and examine the effects of top quark decay. The sensitivity bounds on the anomalous couplings and, $t\to q\gamma$ branching ratio have been obtained at the $95\%$ confidence level for the effective lagrangian approach. Besides, we have investigated the effect of the anomalous couplings on single top quark spin asymmetry.

### Very Weak Primordial Gravitational Waves Signal from BICEP2 and Planck HFI 353GHz Dust Polarization

The dust polarization is parameterized as a power law form of the multipole $l$: $D^{XX}_{l}=A^{XX}l(l+1)l^{\alpha_{XX}}/(2\pi)$ ($XX$ denotes $BB$ or $EE$), where $A^{XX}$ is its amplitude with the ratio $A^{BB}/A^{EE}=0.52\pm 0.02$ and $\alpha_{BB,EE}=-2.42\pm 0.02$. Extrapolating to $150$GHz from $353$GHz yields a value of $D^{BB}_{l=80}=(1.32\pm 0.29)\times 10^{-2}\mu K^2$ (and an additional uncertainty $(+0.28,-0.24)\times 10^{-2}\mu K^2$) over the range $40<l<120$. Based on these data, in this brief paper, we report the tensor-to-scalar ratio $r=A_{t}/A_{s}$ defined at $k_0=0.05 \text{Mpc} ^{-1}$ by joining the BICEP2+{\it Planck}2013+WMAP9+BAO+HST and {\it Planck} HFI $353$GHz dust polarization and its implication to the detection of the primordial gravitational waves. Considering the $\Lambda$CDM+$r$ model, we found $r<0.108$ at $95\%$ confidence level with $\sigma_{stat}=0.29$ and $r<0.129$ at $95\%$ confidence level with $\sigma_{stat+extr}=0.29+0.28$. The results imply no significant evidence for the primordial gravitational waves in $1\sigma$ regions. However the post probability distribution of $r$ peaks at a small positive value. And $r$ moves to larger positive values when the extrapolation error bars are included. This might imply a very weak signal of the primordial gravitational waves. It also implies the crucial fact in calibrating the amplitude of the dust polarizations in detecting the primordial gravitational waves in the future.

### Evidence of $\Upsilon(1S) \to J/\psi+\chi_{c1}$ and search for double-charmonium production in $\Upsilon(1S)$ and $\Upsilon(2S)$ decays [Cross-Listing]

Using data samples of $102\times10^6$ $\Upsilon(1S)$ and $158\times10^6$ $\Upsilon(2S)$ events collected with the Belle detector, a first experimental search has been made for double-charmonium production in the exclusive decays $\Upsilon(1S,2S)\rightarrow J/\psi(\psi’)+X$, where $X=\eta_c$, $\chi_{cJ} (J=~0,~1,~2)$, $\eta_c(2S)$, and $X(3940)$. No significant signal is observed in the spectra of the mass recoiling against the reconstructed $J/\psi$ or $\psi’$ except for the evidence of $\chi_{c1}$ production with a significance of $4.6\sigma$ for $\Upsilon(1S)\rightarrow J/\psi+\chi_{c1}$. The measured branching fraction $\BR(\Upsilon(1S)\rightarrow J/\psi+\chi_{c1})$ is $(3.98\pm1.24(\rm stat.)\pm0.22 (\rm syst.))\times10^{-6}$. The $90\%$ confidence level upper limits on the branching fractions of the other modes having a significance of less than $3\sigma$ are determined. These results are consistent with theoretical calculations using the nonrelativistic QCD factorization approach.

### Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Cross-Listing]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at 95% confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.117$ at 95% confidence level. Our results imply that the chaotic inflation model is marginally disfavored at 95% confidence level. Especially, the $\half m^2\phi^2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

### Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95\%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95\%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95\%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

### Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95\%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95\%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95\%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

### Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95\%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95\%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95\%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

### Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Replacement]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at $95\%$ confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.116$ at $95\%$ confidence level. Our results imply that the inflation model with a single monomial potential is marginally disfavored at around $95\%$ confidence level. Especially, the $m^2\phi^2/2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

### Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Cross-Listing]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at 95% confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.117$ at 95% confidence level. Our results imply that the chaotic inflation model is marginally disfavored at 95% confidence level. Especially, the $\half m^2\phi^2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

### Constraint on the primordial gravitational waves from the joint analysis of BICEP2 and Planck HFI 353 GHz dust polarization data [Cross-Listing]

We make a joint analysis of BICEP2 and recently released Planck HFI 353 GHz dust polarization data, and find that there is no evidence for the primordial gravitational waves and the bound on the tensor-to-scalar ratio becomes $r<0.083$ at 95% confidence level in the base $\Lambda$CDM + tensor model. Extending to the model with running of scalar spectral index, the bound is a little bit relaxed to $r<0.117$ at 95% confidence level. Our results imply that the chaotic inflation model is marginally disfavored at 95% confidence level. Especially, the $\half m^2\phi^2$ inflation model is disfavored at more than $2\sigma$ level. However, the Starobinsky inflation model gives a nice fit.

### Search for Trilepton Nucleon Decay via $p \rightarrow e^+ \nu \nu$ and $p \rightarrow \mu^+ \nu \nu$ in the Super-Kamiokande Experiment [Cross-Listing]

The trilepton nucleon decay modes $p \rightarrow e^+ \nu \nu$ and $p \rightarrow \mu^+ \nu \nu$ violate $|\Delta (B – L)|$ by two units. Using data from a 273.4 kiloton year exposure of Super-Kamiokande a search for these decays yields a fit consistent with no signal. Accordingly, lower limits on the partial lifetimes of $\tau_{p \rightarrow e^+ \nu \nu} > 1.7 \times 10^{32}$ years and $\tau_{p \rightarrow \mu^+ \nu \nu} > 2.2 \times 10^{32}$ years at a $90 \%$ confidence level are obtained. These limits can constrain Grand Unified Theories which allow for such processes.

### Reducing the Tension Between the BICEP2 and the Planck Measurements: A Complete Exploration of the Parameter Space

A large inflationary tensor-to-scalar ratio $r_\mathrm{0.002} = 0.20^{+0.07}_{-0.05}$ is reported by the BICEP2 team based on their B-mode polarization detection, which is outside of the $95\%$ confidence level of the Planck best fit model. We explore several possible ways to reduce the tension between the two by considering a model in which $\alpha_\mathrm{s}$, $n_\mathrm{t}$, $n_\mathrm{s}$ and the neutrino parameters $N_\mathrm{eff}$ and $\Sigma m_\mathrm{\nu}$ are set as free parameters. Using the Markov Chain Monte Carlo (MCMC) technique to survey the complete parameter space with and without the BICEP2 data, we find that the resulting constraints on $r_\mathrm{0.002}$ are consistent with each other and the apparent tension seems to be relaxed. Further detailed investigations on those fittings suggest that $N_\mathrm{eff}$ probably plays the most important role in reducing the tension. We also find that the results obtained from fitting without adopting the consistency relation do not deviate much from the consistency relation. With available Planck, WMAP, BICEP2 and BAO datasets all together, we obtain $r_{0.002} = 0.14_{-0.11}^{+0.05}$, $n_\mathrm{t} = 0.35_{-0.47}^{+0.28}$, $n_\mathrm{s}=0.98_{-0.02}^{+0.02}$, and $\alpha_\mathrm{s}=-0.0086_{-0.0189}^{+0.0148}$; if the consistency relation is adopted, we get $r_{0.002} = 0.22_{-0.06}^{+0.05}$.

### Correlation between the phase and the log-amplitude of a wave through the vertical atmospheric propagation [Replacement]

Expressions of the correlation between the log-amplitude and the phase of a wavefront propagating through the atmospheric turbulence are presented. These expressions are useful to evaluate the feasibility of proposed methods to increase the confidence level of the detection of faint transient astronomical objects. The properties of the derived angular correlation functions are discussed using usual synthetic turbulence profiles. The close formulation between the phase and the log-amplitude allows an analytic formulation in the Rytov approximation. Equations contain the product of an arbitrary number of hypergeometric functions that are evaluated using the Mellin transforms integration method.

### Long-term K$_S$-band photometric monitoring of L dwarfs

(abridged) We perform photometric time-series analysis of a sample of ten early to mid-L dwarfs in the field over three years of $K_s$-band observations with the OMEGA 2000 infrared camera of the 3.5m telescope on Calar Alto Observatory between January 2010 and December 2012. We perform $K_s$-band differential photometry of our targets (with typical errors of $\pm$15-30~mmag at the 1$\sigma$ level) by subtracting a reference flux from each photometric measurement. This reference flux is computed using three nearby, probably constant stars in the target’s field-of-view. We then construct and visually inspect the light curves to search for variability, and use four different periodogram algorithms to look for possible periods in our photometric data. Our targets do not display long-term variability over 1$\sigma$ compared to other nearby stars of similar brightness, nor do the periodograms unveil any possible periodicity for these objects, with two exceptions: 2MASS~J02411151-0326587 and G196-3B. In the case of 2MASS~J02411151-0326587 (L0), our data suggest a tentative period of 307$\pm$21~days, at 40% confidence level, which seems to be associated with peak-to-peak variability of 44$\pm$10~mmag. This object may also display variability in timescales of years, as suggested by the comparison of our Ks-band photometry with 2MASS. For G196-3B (L3), we find peak-to-peak variations of 42$\pm$10~mmag, with a possible photometric period of 442$\pm$7~days, at 95% confidence level. This is roughly the double of the astrometric period reported by Zapatero Osorio (2014). Given the significance of these results, further photometric data are required to confirm the long-term variability.These results suggest that early- to mid-L dwarfs are fairly stable in the $K_s$-band within $\pm$90 mmag at the 3 $\sigma$ level over months to years, which covers hundreds to tens of thousands of rotation cycles.

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

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%.

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

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%.

### 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 [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. We forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements, with $n_{\rm t}$ as a free parameter, from a {\it Planck}-like experiment, and from Spider and POLARBEAR given the current understanding of their experimental noise and foreground contamination. 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. We forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements, with $n_{\rm t}$ as a free parameter, from a {\it Planck}-like experiment, and from Spider and POLARBEAR given the current understanding of their experimental noise and foreground contamination. 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. We forecast the precision of $r$ and the tensor spectral index $n_{\rm t}$ measurements, with $n_{\rm t}$ as a free parameter, from a {\it Planck}-like experiment, and from Spider and POLARBEAR given the current understanding of their experimental noise and foreground contamination. 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

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 $r$.

### 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.

### 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.

### 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.

### 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.

### 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 [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.

### 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.

### 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 cosmological parameters from BICEP2, Planck and WMAP [Replacement]

In this paper we constrain the cosmological parameters, in particular the tilt of tensor power spectrum, by adopting Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 (P13) and Wilkinson Microwaves Anisotropy Probe 9-year Polarization (WP) data. We find that a blue tilted tensor power spectrum is preferred at more than $3\sigma$ confidence level if the data from B2 are assumed to be totally interpreted as the relic gravitational waves, but a scale invariant tensor power spectrum is consistent with the data once the polarized dust is taken into account. The recent Planck 353 GHz HFI dust polarization data imply that the B2 data are perfectly consistent with there being no gravitational wave signal.

### Constraints on the cosmological parameters from BICEP2, Planck and WMAP [Replacement]

In this paper we constrain the cosmological parameters, in particular the tilt of tensor power spectrum, by adopting Background Imaging of Cosmic Extragalactic Polarization (B2), Planck released in 2013 (P13) and Wilkinson Microwaves Anisotropy Probe 9-year Polarization (WP) data. We find that a blue tilted tensor power spectrum is preferred at more than $3\sigma$ confidence level if the data from B2 are assumed to be totally interpreted as the relic gravitational waves, but a scale invariant tensor power spectrum is consistent with the data once the polarized dust is taken into account. The recent Planck 353 GHz HFI dust polarization data imply that the B2 data are perfectly consistent with there being no gravitational wave signal.