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...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 B0 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.展开更多
Combining the latest Planck, Wilkinson Microwave Anisotropy Probe （WMAP）, and baryon acoustic oscillation （BAO） data, we exploit the recent cosmic microwave background （CMB） B-mode power spectra data released by...Combining the latest Planck, Wilkinson Microwave Anisotropy Probe （WMAP）, and baryon acoustic oscillation （BAO） data, we exploit the recent cosmic microwave background （CMB） B-mode power spectra data released by the BICEP2 collaboration to constrain the cosmological parameters of the ACDM model, especially the primordial power spectra parameters of the scalar and the tensor modes, ns, as, r, nt. We obtain constraints on the parameters for a lensed ACDM model using the Markov Chain -- ＋0,0307 ＋0,0061 ＋0,0105 Monte Carlo （MCMC） technique, the marginalized 68% bounds are r -0.1043 -0.0914, ns -0.9617-0.0061, as =-0.0175-0.0097, nt = 0.5198＋-0.4579. We find that a blue tilt for nt is favored slightly, but it is still well consistent with flat or even red tilt. Our r value is slightly smaller than the one obtained by the BICEP group, in that we permit nt as a free parameter without imposing the single-field slow roll inflation consistency relation. When we impose this relation, then r= 0.2130-0.06096 ＋0.0446. For most other parameters, the best fit values and measurement errors are not altered significantly by the introduction of the BICEP2 data.展开更多
In this work,we study the theory of inflation with the non-minimally coupled quadratic,standard model Higgs,and hilltop potentials,throughξφ~2R term in Palatini gravity.We first analyze observational parameters of t...In this work,we study the theory of inflation with the non-minimally coupled quadratic,standard model Higgs,and hilltop potentials,throughξφ~2R term in Palatini gravity.We first analyze observational parameters of the Palatini quadratic potential as functions ofξfor the high-N scenario.In addition to this,taking into account that the inflaton field f has a non-zero vacuum expectation value v after inflation,we display observational parameters of well-known symmetry-breaking potentials.The types of potentials considered are the Higgs potential and its generalizations,namely hilltop potentials in the Palatini formalism for the high-N scenario and the low-N scenario.We calculate inflationary parameters for the Palatini Higgs potential as functions of v for differentξvalues,where inflaton values are bothφ>v andφ<v during inflation,as well as calculating observational parameters of the Palatini Higgs potential in the induced gravity limit for high-N scenario.We illustrate differences between the Higgs potential’s effect onξversus hilltop potentials,which agree with the observations for the inflaton values forφ<v andξ,in which v<<1 for both these high and low N scenarios.For each considered potential,we also display ns-r values fitted to the current data given by the Keck Array/BICEP2 and Planck collaborations.展开更多
Could a causal discontinuity lead to an explanation of fluctuations in the CMBR radiation spectrum? Is this argument valid if there is some third choice of set structure (for instance do self-referential sets fall int...Could a causal discontinuity lead to an explanation of fluctuations in the CMBR radiation spectrum? Is this argument valid if there is some third choice of set structure (for instance do self-referential sets fall into one category or another)? The answer to this question may lie in (entangled) vortex structure of space time, along the lines of structure similar to that generate in the laboratory by Ruutu. Self-referential sets may be part of the generated vortex structure, and we will endeavor to find if this can be experimentally investigated. If the causal set argument and its violation via this procedure holds, we have the view that what we see a space time “drum” effect with the causal discontinuity forming the head of a “drum” for a region of about 10<sup>10</sup> bits of “information” before our present universe up to the instant of the big bang itself for a time region less than t~10<sup>-44 </sup>seconds in duration, with a region of increasing bits of “information” going up to 10<sup>120</sup> due to vortex filament condensed matter style forming through a symmetry breaking phase transition. We address the issue of what this has to do with Bicep 2, the question of scalar-tensor gravity versus general relativity, how to avoid the detection of dust generated Gravity wave signals as what ruined the Bicep 2 experiment and some issues information flow and causal structure has for our CMBR data as seen in an overall summary of these issues in Appendix X, of this document. Appendix XI mentions how to differentiate between scalar-tensor gravity, and general relativity whereas Appendix XII, discusses how to avoid the Bicep 2 mistake again. While Appendix VIII gives us a simple data for a graviton power burst which we find instructive. We stress again, the importance of obtaining clean data sets so as to help us in the eventual detection of gravitational waves which we regard as decisively important and which we think by 2025 or so which will be an important test to discriminate in a full experimental sense the choice of general relativity and other gravity theories, for the evolution of cosmology. Finally, Appendix VII brings up a model for production for gravitons, which is extremely simple. Based upon a formula given in a reference, by Weinberg, in 1971, we chose it due to its illustrative convenience and ties in with Bosonic particles.展开更多
In this work, we constrain the spectral index nt of the primordial gravitational wave power spectrum in a universe with sterile neutrinos by using the Planck temperature data, the WMAP 9-year polarization data, the ba...In this work, we constrain the spectral index nt of the primordial gravitational wave power spectrum in a universe with sterile neutrinos by using the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, and the BICEP2 data. We call this model the ACDM＋r＋vs＋nt model. The additional massive sterile neutrino species can significantly relieve the tension between the Planck and BICEP2 data, and thus can reduce the possible effects of this tension on the fit results of nt. To constrain the parameters of sterile neutrino, we also utilize the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, and the cosmic shear data. We find that due to the fact that the BICEP2 data are most sensitive to the multipole （ - 150 corresponding to k - 0.01 Mpc^-1, there exists a strong anticorrelation between nt and r0.0o2 in the BICEP2 data, and this further results in a strongly blue-tilt spectrum. However, a slightly red-tilt tensor power spectrum is also allowed by the BICEP2 data in the region with larger value of r0.00z. By using the full data sets, we obtain mvisterile ^eff = 0.48 -0.13^＋0.11 eV, Near = 3.73 -0.37^＋0.34, and nt = 0.96 -0.63^ ＋0.48 for the ACDM＋r＋vs＋nt model.展开更多
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 50- confidence level. If it is true,...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 50- confidence level. If it is true, this large and measurable amplitude （r - 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 nt measurements from Planck, Spider and POLARBEAR with nt as a free parameter. We quantitatively determine the signal-to-noise of the measurement in r-nt parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on r/t, but strongly depends on the true value of r.展开更多
The BICEP2 experiment confirms the existence of primordial gravitational wave with the tensor-to-scalar ratio r = 0 ruled out at 70- level. The consistency of this large value of r with the Planck data requires a larg...The BICEP2 experiment confirms the existence of primordial gravitational wave with the tensor-to-scalar ratio r = 0 ruled out at 70- level. The consistency of this large value of r with the Planck data requires a large negative running n＇s of the scalar spectral index. Herein we propose two types of the single field inflation models with simple potentials to study the possibility of the consistency of the models with the BICEP2 and Planck observations. One type of model suggested herein is realized in the supergravity model building. These models fail to provide the needed n＇s even though both can fit the tensor-to-scalar ratio and spectral index.展开更多
基金Supported by the Italian Space Agency(ASI),Through Contract Agreement I/023/12/0
文摘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 B0 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.
基金supported by the Chinese Academy of Science Strategic Priority Research Program "The Emergence of Cosmological Structures" (Grant No. XDB09000000)the National Natural Science Foundation of China (Grant Nos. 11103027, 11373030 and 11373031)the National High Technology Research and Development Program of China (Grant No. 2012AA121701)
文摘Combining the latest Planck, Wilkinson Microwave Anisotropy Probe （WMAP）, and baryon acoustic oscillation （BAO） data, we exploit the recent cosmic microwave background （CMB） B-mode power spectra data released by the BICEP2 collaboration to constrain the cosmological parameters of the ACDM model, especially the primordial power spectra parameters of the scalar and the tensor modes, ns, as, r, nt. We obtain constraints on the parameters for a lensed ACDM model using the Markov Chain -- ＋0,0307 ＋0,0061 ＋0,0105 Monte Carlo （MCMC） technique, the marginalized 68% bounds are r -0.1043 -0.0914, ns -0.9617-0.0061, as =-0.0175-0.0097, nt = 0.5198＋-0.4579. We find that a blue tilt for nt is favored slightly, but it is still well consistent with flat or even red tilt. Our r value is slightly smaller than the one obtained by the BICEP group, in that we permit nt as a free parameter without imposing the single-field slow roll inflation consistency relation. When we impose this relation, then r= 0.2130-0.06096 ＋0.0446. For most other parameters, the best fit values and measurement errors are not altered significantly by the introduction of the BICEP2 data.
文摘In this work,we study the theory of inflation with the non-minimally coupled quadratic,standard model Higgs,and hilltop potentials,throughξφ~2R term in Palatini gravity.We first analyze observational parameters of the Palatini quadratic potential as functions ofξfor the high-N scenario.In addition to this,taking into account that the inflaton field f has a non-zero vacuum expectation value v after inflation,we display observational parameters of well-known symmetry-breaking potentials.The types of potentials considered are the Higgs potential and its generalizations,namely hilltop potentials in the Palatini formalism for the high-N scenario and the low-N scenario.We calculate inflationary parameters for the Palatini Higgs potential as functions of v for differentξvalues,where inflaton values are bothφ>v andφ<v during inflation,as well as calculating observational parameters of the Palatini Higgs potential in the induced gravity limit for high-N scenario.We illustrate differences between the Higgs potential’s effect onξversus hilltop potentials,which agree with the observations for the inflaton values forφ<v andξ,in which v<<1 for both these high and low N scenarios.For each considered potential,we also display ns-r values fitted to the current data given by the Keck Array/BICEP2 and Planck collaborations.
文摘Could a causal discontinuity lead to an explanation of fluctuations in the CMBR radiation spectrum? Is this argument valid if there is some third choice of set structure (for instance do self-referential sets fall into one category or another)? The answer to this question may lie in (entangled) vortex structure of space time, along the lines of structure similar to that generate in the laboratory by Ruutu. Self-referential sets may be part of the generated vortex structure, and we will endeavor to find if this can be experimentally investigated. If the causal set argument and its violation via this procedure holds, we have the view that what we see a space time “drum” effect with the causal discontinuity forming the head of a “drum” for a region of about 10<sup>10</sup> bits of “information” before our present universe up to the instant of the big bang itself for a time region less than t~10<sup>-44 </sup>seconds in duration, with a region of increasing bits of “information” going up to 10<sup>120</sup> due to vortex filament condensed matter style forming through a symmetry breaking phase transition. We address the issue of what this has to do with Bicep 2, the question of scalar-tensor gravity versus general relativity, how to avoid the detection of dust generated Gravity wave signals as what ruined the Bicep 2 experiment and some issues information flow and causal structure has for our CMBR data as seen in an overall summary of these issues in Appendix X, of this document. Appendix XI mentions how to differentiate between scalar-tensor gravity, and general relativity whereas Appendix XII, discusses how to avoid the Bicep 2 mistake again. While Appendix VIII gives us a simple data for a graviton power burst which we find instructive. We stress again, the importance of obtaining clean data sets so as to help us in the eventual detection of gravitational waves which we regard as decisively important and which we think by 2025 or so which will be an important test to discriminate in a full experimental sense the choice of general relativity and other gravity theories, for the evolution of cosmology. Finally, Appendix VII brings up a model for production for gravitons, which is extremely simple. Based upon a formula given in a reference, by Weinberg, in 1971, we chose it due to its illustrative convenience and ties in with Bosonic particles.
基金supported by the National Natural Science Foundation of China (Grant No. 11175042)the National Ministry of Education of China (Grant No. N120505003)
文摘In this work, we constrain the spectral index nt of the primordial gravitational wave power spectrum in a universe with sterile neutrinos by using the Planck temperature data, the WMAP 9-year polarization data, the baryon acoustic oscillation data, and the BICEP2 data. We call this model the ACDM＋r＋vs＋nt model. The additional massive sterile neutrino species can significantly relieve the tension between the Planck and BICEP2 data, and thus can reduce the possible effects of this tension on the fit results of nt. To constrain the parameters of sterile neutrino, we also utilize the Hubble constant direct measurement data, the Planck Sunyaev-Zeldovich cluster counts data, the Planck CMB lensing data, and the cosmic shear data. We find that due to the fact that the BICEP2 data are most sensitive to the multipole （ - 150 corresponding to k - 0.01 Mpc^-1, there exists a strong anticorrelation between nt and r0.0o2 in the BICEP2 data, and this further results in a strongly blue-tilt spectrum. However, a slightly red-tilt tensor power spectrum is also allowed by the BICEP2 data in the region with larger value of r0.00z. By using the full data sets, we obtain mvisterile ^eff = 0.48 -0.13^＋0.11 eV, Near = 3.73 -0.37^＋0.34, and nt = 0.96 -0.63^ ＋0.48 for the ACDM＋r＋vs＋nt model.
基金supported by a CITA National Fellowship, a Starting Grant of the Eu-ropean Research Council (ERC STG Grant No. 279617)the Stephen Hawking Advanced Fellowshipfunded by BIS National E-infrastructure capital grant ST/J005673/1 and STFC grants ST/H008586/1, ST/K00333X/1
文摘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 50- confidence level. If it is true, this large and measurable amplitude （r - 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 nt measurements from Planck, Spider and POLARBEAR with nt as a free parameter. We quantitatively determine the signal-to-noise of the measurement in r-nt parameter space for the three experiments. The forecasted signal-to-noise ratio of the B-mode polarization somewhat depends on r/t, but strongly depends on the true value of r.
基金supported by the National Natural Science Foundation of China (Grant Nos. 11075194, 11135003, 11175270 and 11275246)the National Basic Research Program of China (Grant No. 2010CB833000 (TL))+1 种基金the Program for New Century Excellent Talents in University (Grant No. NCET-12-0205)the Fundamental Research Funds for the Central Universities (Grant No. 2013YQ055)
文摘The BICEP2 experiment confirms the existence of primordial gravitational wave with the tensor-to-scalar ratio r = 0 ruled out at 70- level. The consistency of this large value of r with the Planck data requires a large negative running n＇s of the scalar spectral index. Herein we propose two types of the single field inflation models with simple potentials to study the possibility of the consistency of the models with the BICEP2 and Planck observations. One type of model suggested herein is realized in the supergravity model building. These models fail to provide the needed n＇s even though both can fit the tensor-to-scalar ratio and spectral index.
