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# A toy scenario for the dynamics of the scalar field during inflation. During the flat part of potential, universe expand exponentially. When field reaches near the minima of the potential, the field oscillates and the radiation is generated.

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In the last few decades, advances in observational cosmology have given us a standard model of cosmology.
We know the content of the universe to within a few percent. With more ambitious experiments on the way,
we hope to move beyond the knowledge of what the universe is made of, to why the universe is the way it
is. In this paper we focus on prim...

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## Citations

... However, there are many other mechanisms responsible for creating a non-Gaussian distribution of temperature fluctuations in the CMB besides the inflationary ones. These include so-called secondary effects, which involve processes that occur between the last scattering surface and the observer (see e.g [194,195]). Secondary effects can be broadly divided into scattering of the CMB ra-diation with hot gas, and classical effects mediated by gravity subsequent to the last scattering surface, such as the time-integrated SW effect [192] and gravitational lensing. ...

... Other effects that can be responsible for non-Gaussian temperature fluctuations include non-linear effects at recombination (see e.g. [194,195]). Although detection of these non-primordial effects would provide important information for distinguishing structure formation scenarios, they are often regarded as noise of the primary inflationary effects. ...

Tabletop tests of quantum gravity (QG) have long been thought to be practically impossible. However, remarkably, because of rapid progress in quantum information science (QIS), such tests may soon be achievable. Here we uncover an exciting new theoretical link between QG and QIS that also leads to a radical new way of testing QG with QIS experiments. Specifically, we find that only a quantum, not classical, theory of gravity can create non-Gaussianity, a QIS resource that is necessary for universal quantum computation, in the quantum field state of matter. This allows tests based on QIS in which non-Gaussianity in matter is used as a signature of QG. In comparison with previous studies testing QG with QIS where entanglement is used to witness QG when all other quantum interactions are excluded, our non-Gaussianity witness cannot be created by direct classical gravity interactions, facilitating tests that are not constrained by the existence of such processes. Our new signature of QG also enables tests that are based on just a single quantum system rather than a multipartite quantum system, simplifying previously considered experimental setups. We describe a tabletop test of QG that uses our non-Gaussianity signature and that is based on just a single quantum system, a Bose-Einstein condensate, in a single location. In contrast to proposals based on optomechanical setups, Bose-Einstein condensates have already been manipulated into massive nonclassical states, aiding the prospect of testing QG soon.

... For more details about specific realizations of inflationary models within each class, see the previous two Planck papers on primordial NG (PCNG13; PCNG15) and reviews (e.g. Bartolo et al. 2004a;Liguori et al. 2010;Chen 2010b;Komatsu 2010;Yadav & Wandelt 2010). We only give a more expanded description of those shapes of primordial NG analysed here for the first time with Planck data (e.g. ...

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E -mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: f NL local = −0.9 ± 5.1; f NL equil = −26 ± 47; and f NL ortho = −38 ± 24 (68% CL, statistical). These results include low-multipole (4 ≤ ℓ < 40) polarization data that are not included in our previous analysis. The results also pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and they are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, which is consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results and they give excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 σ . Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is g NL local = (−5.8 ± 6.5) × 10 ⁴ (68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of different early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g. curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

... where f NL and S(k 1 , k 2 , k 3 ) are the amplitude and the shape of non-Gaussianity, respectively (Namjoo, 2013). The three-point correlation for the CMB can also be written in the form as a function of Bardeen's curvature perturbations, Φ(k) (Yadav and Wandelt, 2010): ...

I presented a method for the detection of non-Gaussianity by implementing deep learning based estimator on non-Gaussian simulation maps with different range of fNL. Furthermore, I studied about the impact of secondary non-Gaussianities on the search for primordial non-Gaussianity and methods to discriminate these two signals. In addition, I investigated the effect of contamination of galactic emissions (foregrounds) and mask with different sky coverage on the fNL.
Abstract:
"Measurements and analysis of CMB radiation has offered a demanding test to constrain cosmological parameters to high accuracy. Planck satellite has provided a map of the CMB with temperature resolution of the order of ten part in a million (ie, 10^− 5 ). In addition, Planck full-mission combined the CMB temperature and E-mode polarization local maps analysis, obtained the constraints on primordial non-Gaussianity to be: f NL = − 0.9 ± 5.1 ( 68%CL ) . In this thesis, I generated the CMB maps containing different local non-Gaussianity in l=200 as two class of inputs for in Deep Learning models, DeepSphere. In this platform which is based upon spherical Convolutional Neural Network (spherical-CNN), the inputs are the whole sky images on the sphere generated by HEALPix python wrapper, healpy. According to the results, DeepSphere FCN (Fully Connected Network) had performed well at discriminating the CMB maps containing different levels of non-Gaussianity. This illustrates that this model have this potential to be tested with Planck SMICA CMB data and to be
ultimately used as an alternative to statistical NG estimators with high precision by the use of global regression".

... Numerous studies on non-gaussianity for CMB missions such as COBE, MAXIMA, BOOMERanG, WMAP and Planck has been done. Many of these works are based on measures such as bispectrum [4,[6][7][8][9][10][11][12], trispectrum [13][14][15][16], skewness and kurtosis [17][18][19][20], spherical Mexican hat wavelet [21][22][23][24][25][26][27][28][29][30][31][32][33], minkowski functionals [34][35][36][37][38], directional spherical real morlet wavelet analysis [27], scaling index method [39,40], method based on the N-point probability distribution function [41], skeleton statistics [42,43], spectral distortions [44], neural-network [45], multipole vector [46], genus shift parameters [47,48], bipolar spherical harmonics [49]. In many of these studies, the estimator is based on some phenomenological model and is capable of de-tecting certain types of non-gaussianity. ...

In the era of precision cosmology accurate estimation of cosmological parameters is based upon the implicit assumption of Gaussian nature of Cosmic Microwave Background (CMB) radiation. Therefore, an important scientific question to ask is whether the observed CMB map is consistent with Gaussian prediction. In this work we devise a new method where we use Rao's statistic based on sample arc-lengths to examine the validity of the hypothesis that the temperature field of the CMB is consistent with a Gaussian random field, by comprehensively testing correlations within a given $\ell$ mode and between nearby $\ell$ modes phases. This circular statistic is ordered and non-parametric. We performed our analysis on the scales limited by spherical harmonic modes $\le$ 128, to restrict ourselves to signal dominated region. To find the correlated sets of phases, we calculate the statistic for the data and 10000 Monte Carlo simulated random sets of phases and used 0.01 and 0.05 $\alpha$ levels to distinguish between statistically significant and highly significant detections. We apply our method on Planck satellite mission's final released CMB temperature anisotropy maps- COMMANDER, SMICA, NILC, and SEVEM along with WMAP 9 year released ILC map. We report that phases corresponding to some of the modes are non-uniform in these maps. We also report that most of the mode pairs are uncorrelated in each map, but a few are found to be correlated, which are different pairs in different maps. The detection of non-uniformity and correlations in the phases indicates presence of non Gaussian signals in the foreground minimized CMB maps.

... These cover a large range of physical models of the early Universe. For an elaborate review of these templates see [83,84,88,89,110]. In this study, we restrict our numerical study to the local template. ...

... These cover a large range of physical models of the early Universe. For an elaborate review of these templates see [78,79,84,85,107]. In this study, we restrict our numerical study to the local template. ...

The topology and geometry of random fields - in terms of the Euler characteristic and the Minkowski functionals - has received a lot of attention in the context of the Cosmic Microwave Background (CMB), as the detection of primordial non-Gaussianities would form a valuable clue on the physics of the early Universe. The virtue of both the Euler characteristic and the Minkowski functionals in general, lies in the fact that there exist closed form expressions for their expectation values for Gaussian random fields. However, the Euler characteristic and Minkowski functionals are summarizing characteristics of topology and geometry. Considerably more topological information is contained in the homology of the random field, as it completely describes the creation, merging and disappearance of topological features in superlevel set filtrations. In the present study we extend the topological analysis of the superlevel set filtrations of two-dimensional Gaussian random fields by analysing the statistical properties of the Betti numbers - counting the number of connected components and loops - and the persistence diagrams - describing the creation and mergers of homological features. Using the link between homology and the critical points of a function - as illustrated by the Morse-Smale complex - we derive a one-parameter fitting formula for the expectation value of the Betti numbers and forward this formalism to the persistent diagrams. We, moreover, numerically demonstrate the sensitivity of the Betti numbers and persistence diagrams to the presence of non-Gaussianities.

... Below we briefly summarize the main types of primordial NG that are constrained in this paper, providing the precise shapes that are used for data analysis. For more details about specific realizations of inflationary models within each class, see the previous two Planck papers on primordial NG (PCNG13; PCNG15) and reviews (e.g., Bartolo et al. 2004a;Liguori et al. 2010;Chen 2010b;Komatsu 2010;Yadav & Wandelt 2010). We give a more expanded description only of those shapes of primordial NG analysed here for the first time with Planck data (e.g., running of primordial NG). ...

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following results: f_NL^local = -0.9 +\- 5.1; f_NL^equil = -26 +\- 47; and f_NL^ortho = - 38 +\- 24 (68%CL, statistical). These results include the low-multipole (4 <= l < 40) polarization data, not included in our previous analysis, pass an extensive battery of tests, and are stable with respect to our 2015 measurements. Polarization bispectra display a significant improvement in robustness; they can now be used independently to set NG constraints. We consider a large number of additional cases, e.g. scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is detected with an improved significance compared to 2015, excluding the null hypothesis at 3.5 sigma. We present model-independent reconstructions and analyses of the CMB bispectrum. Our final constraint on the local trispectrum shape is g_NLl^local = (-5.8 +\-6.5) x 10^4 (68%CL, statistical), while constraints for other trispectra are also determined. We constrain the parameter space of different early-Universe scenarios, including general single-field models of inflation, multi-field and axion field parity-breaking models. Our results provide a high-precision test for structure-formation scenarios, in complete agreement with the basic picture of the LambdaCDM cosmology regarding the statistics of the initial conditions (abridged).

... Below we briefly summarize the main types of primordial NG that are constrained in this paper, providing the precise shapes that are used for data analysis. For more details about specific realizations of inflationary models within each class, see the previous two Planck papers on primordial NG (PCNG13; PCNG15) and reviews (e.g., Bartolo et al. 2004a;Liguori et al. 2010;Chen 2010b;Komatsu 2010;Yadav & Wandelt 2010). We give a more expanded description only of those shapes of primordial NG analysed here for the first time with Planck data (e.g., running of primordial NG). ...

We analyse the Planck full-mission cosmic microwave background (CMB) temperature and E-mode polarization maps to obtain constraints on primordial non-Gaussianity (NG). We compare estimates obtained from separable template-fitting, binned, and optimal modal bispectrum estimators, finding consistent values for the local, equilateral, and orthogonal bispectrum amplitudes. Our combined temperature and polarization analysis produces the following final results: f^(local)_(NL) = -0.9 ± 5.1; f^(equil)_(NL) = -26 ± 47; and f^(ortho)_(NL_ = -38 ± 24 (68% CL, statistical). These results include the low-multipole (4 ≤ ℓ < 40) polarization data, not included in our previous analysis, pass an extensive battery of tests (with additional tests regarding foreground residuals compared to 2015), and are stable with respect to our 2015 measurements (with small fluctuations, at the level of a fraction of a standard deviation, consistent with changes in data processing). Polarization-only bispectra display a significant improvement in robustness; they can now be used independently to set primordial NG constraints with a sensitivity comparable to WMAP temperature-based results, and giving excellent agreement. In addition to the analysis of the standard local, equilateral, and orthogonal bispectrum shapes, we consider a large number of additional cases, such as scale-dependent feature and resonance bispectra, isocurvature primordial NG, and parity-breaking models, where we also place tight constraints but do not detect any signal. The non-primordial lensing bispectrum is, however, detected with an improved significance compared to 2015, excluding the null hypothesis at 3:5_. Beyond estimates of individual shape amplitudes, we also present model-independent reconstructions and analyses of the Planck CMB bispectrum. Our final constraint on the local primordial trispectrum shape is g^(local)_(NL) = (-5.8 ± 6.5) x 10^4 (68% CL, statistical), while constraints for other trispectrum shapes are also determined. Exploiting the tight limits on various bispectrum and trispectrum shapes, we constrain the parameter space of di_erent early-Universe scenarios that generate primordial NG, including general single-field models of inflation, multi-field models (e.g., curvaton models), models of inflation with axion fields producing parity-violation bispectra in the tensor sector, and inflationary models involving vector-like fields with directionally-dependent bispectra. Our results provide a high-precision test for structure-formation scenarios, showing complete agreement with the basic picture of the ΛCDM cosmology regarding the statistics of the initial conditions, with cosmic structures arising from adiabatic, passive, Gaussian, and primordial seed perturbations.

... These fall into four categories: primordial sources, secondary sources, second-order gravitational terms and galactic foregrounds. Primordial non-Gaussianity offers another handle on constraining the physics of the early universe and could provide the ability to differentiate between many classes of inflationary theories, though so far it has been found to be consistent with zero (Komatsu et al. 2011;Planck Collaboration 2014e, 2016d; see Liguori et al. (2010); Yadav & Wandelt (2010); Chen (2010) for reviews of primordial non-Gaussianity. Second-order gravitational terms arise from non-linearities in the transfer function from the initial perturbations to the late time temperature fluctuations in CMB (Pettinari et al. 2013; Bartolo et al. 2006Bartolo et al. , 2007. ...

Most secondary sources of cosmic microwave background anisotropy (radio sources, dusty galaxies, thermal Sunyaev Zel'dovich distortions from hot gas, and gravitational lensing) are highly non-Gaussian. Statistics beyond the power spectrum are therefore potentially important sources of information about the physics of these processes. We use data from the Atacama Cosmology Telescope and the Planck satellite to constrain the amplitudes of a set of theoretical bispectrum templates from the thermal Sunyaev-Zeldovich (tSZ) effect, dusty star-forming galaxies (DSFGs), gravitational lensing, and radio galaxies. We make a strong detection of radio galaxies (13$\sigma$) and have hints of non-Gaussianity arising from the tSZ effect (3.2$\sigma$), DSFGs (3.8$\sigma$), from cross-correlations between the tSZ effect and DSFGs (4.2$\sigma$) and from cross-correlations among the tSZ effect, DSFGs and radio galaxies (4.6$\sigma$). These results suggest that the same halos host radio sources, DSFGs, and have tSZ signal. At current noise levels, strong degeneracies exist between the various sources; upcoming data from Advanced ACT, SPT-3G, Simons Observatory, and CMB-S4 will be able to separate the components. With these caveats, we use the tSZ bispectrum measurement to constrain the amplitude of matter fluctuations to be $\sigma_8=0.79 \pm0.07$.

... Nonlinear structure growth does not only enhance the small-scale power but also skews the distribution function of matter fluctuations, which we assume to be initially Gaussian. Thus, we do not consider primordial non-Gaussianities (see Komatsu 2010;Yadav & Wandelt 2010, for reviews) as currently favoured values of its amplitude (Planck Collaboration 2016b) suggest that its contributions to the matter bispectrum are negligible. ...

Cross-correlating the lensing signals of galaxies and comic microwave background (CMB) fluctuations is expected to provide valuable cosmological information. In particular it may help tighten constraints on parameters describing the properties of intrinsically aligned galaxies at high redshift. To access the information conveyed by the cross-correlation signal its accurate theoretical description is required. We compute the bias to CMB lensing-galaxy shape cross-correlation measurements induced by nonlinear structure growth. Using tree-level perturbation theory for the large-scale structure bispectrum we find that the bias is negative on most angular scales, therefore mimicking the signal of intrinsic alignments. Combining Euclid-like galaxy lensing data with a CMB experiment comparable to the Planck satellite mission the bias becomes significant only on smallest scales ($\ell\gtrsim 2500$). For improved CMB observations, however, the corrections amount to 10-15 per cent of the CMB lensing-intrinsic alignment signal over a wide multipole range ($10 \lesssim \ell \lesssim 2000$). Accordingly the power spectrum bias, if uncorrected, translates into $2\sigma$ and $3\sigma$ errors in the determination of the intrinsic alignment amplitude in case of CMB stage III and stage IV experiments, respectively.