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Register a new userOptimal constraints on primordial gravitational waves from the lensed CMB
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Julien Carron
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We demonstrate how to obtain optimal constraints on a primordial gravitational wave component in lensed Cosmic Microwave Background (CMB) data under ideal conditions. We first derive an estimator of the tensor-to-scalar ratio, $r$, by using an error-controlled close approximation to the exact posterior, under the assumption of Gaussian primordial CMB and lensing deflection potential. This combines fast internal iterative lensing reconstruction with optimal recovery of the unlensed CMB. We evaluate its performance on simulated low-noise polarization data targeted at the recombination peak. We carefully demonstrate our $r$-posterior estimate is optimal and shows no significant bias, making it the most powerful estimator of primordial gravitational waves from the CMB. We compare these constraints to those obtained from $B$-mode band-power likelihood analyses on the same simulated data, before and after map-level quadratic estimator delensing, and iterative delensing. Internally, iteratively delensed band powers are only slightly less powerful on average (by less than 10%), promising close-to-optimal constraints from a stage IV CMB experiment.
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CMB-S4---the next-generation ground-based cosmic microwave background (CMB) experiment---is set to significantly advance the sensitivity of CMB measurements and enhance our understanding of the origin and evolution of the Universe, from the highest energies at the dawn of time through the growth of structure to the present day. Among the science cases pursued with CMB-S4, the quest for detecting primordial gravitational waves is a central driver of the experimental design. This work details the development of a forecasting framework that includes a power-spectrum-based semi-analytic projection tool, targeted explicitly towards optimizing constraints on the tensor-to-scalar ratio, $r$, in the presence of Galactic foregrounds and gravitational lensing of the CMB. This framework is unique in its direct use of information from the achieved performance of current Stage 2--3 CMB experiments to robustly forecast the science reach of upcoming CMB-polarization endeavors. The methodology allows for rapid iteration over experimental configurations and offers a flexible way to optimize the design of future experiments given a desired scientific goal. To form a closed-loop process, we couple this semi-analytic tool with map-based validation studies, which allow for the injection of additional complexity and verification of our forecasts with several independent analysis methods. We document multiple rounds of forecasts for CMB-S4 using this process and the resulting establishment of the current reference design of the primordial gravitational-wave component of the Stage-4 experiment, optimized to achieve our science goals of detecting primordial gravitational waves for $r > 0.003$ at greater than $5sigma$, or, in the absence of a detection, of reaching an upper limit of $r < 0.001$ at $95%$ CL.
We show that the new precise measurements of Cosmic Microwave Background (CMB) temperature and polarization anisotropies made by the Planck satellite significantly improves previous constraints on the cosmic gravitational waves background (CGWB) at frequencies $f>10^{-15}$ Hz. On scales smaller than the horizon at the time of decoupling, primordial gravitational waves contribute to the total radiation content of the Universe. Considering adiabatic perturbations, CGWB affects temperature and polarization CMB power spectra and matter power spectrum in a manner identical to relativistic particles. Considering the latest Planck results we constrain the CGWB energy density to $Omega_{rm gw} h^2 <1.7times 10^{-6} $ at 95% CL. Combining CMB power spectra with lensing, BAO and primordial Deuterium abundance observations, we obtain $Omega_{rm gw} h^2 <1.2times 10^{-6} $ at 95% CL, improving previous Planck bounds by a factor 3 and the recent direct upper limit from the LIGO and VIRGO experiments a factor 2. A combined analysis of future satellite missions as COrE and EUCLID could improve current bound by more than an order of magnitude.
In this paper, we will give a general introduction to the project of Ali CMB Polarization Telescope (AliCPT), which is a Sino-US joint project led by the Institute of High Energy Physics (IHEP) and has involved many different institutes in China. It is the first ground-based Cosmic Microwave Background (CMB) polarization experiment in China and an integral part of Chinas Gravitational Waves Program. The main scientific goal of AliCPT project is to probe the primordial gravitational waves (PGWs) originated from the very early Universe. The AliCPT project includes two stages. The first stage referred to as AliCPT-1, is to build a telescope in the Ali region of Tibet with an altitude of 5,250 meters. Once completed, it will be the worldwide highest ground-based CMB observatory and open a new window for probing PGWs in northern hemisphere. AliCPT-1 telescope is designed to have about 7,000 TES detectors at 90GHz and 150GHz. The second stage is to have a more sensitive telescope (AliCPT-2) with the number of detectors more than 20,000. Our simulations show that AliCPT will improve the current constraint on the tensor-to-scalar ratio $r$ by one order of magnitude with 3 years observation. Besides the PGWs, the AliCPT will also enable a precise measurement on the CMB rotation angle and provide a precise test on the CPT symmetry. We show 3 years observation will improve the current limit by two order of magnitude.
We study the effects of the Gauss-Bonnet term on the energy spectrum of inflationary gravitational waves. The models of inflation are classified into two types based on their predictions for the tensor power spectrum: red-tilted ($n_T<0$) and blue-tilted spectra ($n_T>0$), respectively, and then the energy spectra of the gravitational waves are calculated for each type of model. We find that the gravitational wave spectra are enhanced depending on the model parameter if the predicted inflationary tensor spectra have a blue tilt, whereas they are suppressed for the spectra that have a red tilt. Moreover, we perform the analyses on the reheating parameters involving the temperature, the equation-of-state parameter, and the number of $e$-folds using the gravitational wave spectrum. Our results imply that the Gauss-Bonnet term plays an important role not only during inflation but also during reheating whether the process is instantaneous or lasts for a certain number of $e$-folds until it thermalizes and eventually completes.
We discuss whether an unaccounted contribution to the Cosmic Microwave Background polarization $B$-mode by primordial magnetic fields (PMFs) can bias future constraints on inflationary gravitational waves. As a case-study, we consider a scale-invariant PMF spectrum with amplitude of $approx{1},{mathrm{nG}}$ on $1,mathrm{Mpc}$ scales, compatible with current cosmological bounds. We find a degeneracy in the $B$-mode spectra between PMFs and inflationary gravitational waves. If PMFs of this amplitude are not accounted for, future CMB experiments could claim a false detection of a tensor-to-scalar ratio $rapprox 0.007$, close to the predictions of Starobinsky and $alpha$-attractor models. The degeneracy can be broken if $B$-modes are measured also at multipoles $ellgtrsim 900$: more precisely experiments like CMB-S4 or CORE-M5 would be able to discriminate PMFs from primordial GWs at high statistical significance. Experiments like LiteBIRD or PIXIE will not be able to break the degeneracy and will need complementary bounds coming, for example, from measurements of anisotropies in the Faraday rotation angle of CMB polarization. This reinforces the importance of future experimental constraints on PMFs.
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