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Mapping the distribution of neutral atomic hydrogen (HI) in the Universe through its 21 cm emission line provides a powerful cosmological probe to map the large-scale structures and shed light on various cosmological phenomena. The Baryon Acoustic Oscillations at low redshifts can potentially be probed by sensitive HI intensity mapping experiments and constrain the properties of dark energy. However, the 21 cm signal detection faces formidable challenges due to the dominance of various astrophysical foregrounds, which can be several orders of magnitude stronger. Our current work introduces a novel and model-independent Internal Linear Combination (ILC) method in harmonic space using the principal components of the 21 cm signal for accurate foreground removal and power spectrum estimation. We estimate the principal components by incorporating prior knowledge of the theoretical 21 cm covariance matrix. We test our methodology by detailed simulations of radio observations, incorporating synchrotron emission, free-free radiation, extragalactic point sources, and thermal noise. We estimate the full sky 21 cm angular power spectrum after application of a mask on the full sky cleaned 21 cm signal by using the mode-mode coupling matrix. These full sky estimates of angular spectra can be directly used to measure the cosmological parameters. For the first time, we demonstrate the effectiveness of a foreground model-independent ILC method in harmonic space to reconstruct the 21 cm signal., Comment: 20 pages, 15 figures

An ingeniously designed autoencoder (PrimeNet) using simulated observations of future generation ECHO satellite mission recovers CMB B mode map, angular spectrum for multipoles $\ell \lesssim 9$ and tensor to scalar ratio $r$ {\it limited only by cosmic variance down to $r= 0.0001$ and below}. We use diverse, realistically complex and detailed foreground models. PrimeNet predicts accurate results even when data with $r=0$ are tested which were not used in training, implying robust and efficient predictive power. The work eliminates a major bottleneck of weak CMB B mode reconstruction and takes a leap forward for understanding fundamental physics of the primordial Universe.

In this article, we employ a machine learning (ML) approach for the estimations of four fundamental parameters, namely, the Hubble constant ($H_0$), matter ($\Omega_{0m}$), curvature ($\Omega_{0k}$) and vacuum ($\Omega_{0\Lambda}$) densities of non-flat $\Lambda$CDM model. We use $31$ Hubble parameter values measured by differential ages (DA) technique in the redshift interval $0.07 \leq z \leq 1.965$. We create an artificial neural network (ParamANN) and train it with simulated values of $H(z)$ using various sets of $H_0$, $\Omega_{0m}$, $\Omega_{0k}$, $\Omega_{0\Lambda}$ parameters chosen from different and sufficiently wide prior intervals. We use a correlated noise model in the analysis. We demonstrate accurate validation and prediction by ParamANN. ParamANN provides an excellent cross-check for the validity of the $\Lambda$CDM model. We obtain $H_0 = 68.14 \pm 3.96$ $\rm{kmMpc^{-1}s^{-1}}$, $\Omega_{0m} = 0.3029 \pm 0.1118$, $\Omega_{0k} = 0.0708 \pm 0.2527$ and $\Omega_{0\Lambda} = 0.6258 \pm 0.1689$ by using the trained network. These parameter values agree very well with the results of global CMB observations of the Planck collaboration. We compare the cosmological parameter values predicted by ParamANN with those obtained by the MCMC method. Both the results agree well with each other. This demonstrates that ParamANN is an alternative and complementary approach to the well-known Metropolis-Hastings algorithm for estimating the cosmological parameters by using Hubble measurements., Comment: 23 pages, 8 figures, 2 tables

Breakdown of rotational invariance of the primordial power spectrum manifests in the statistical anisotropy of the observed Cosmic Microwave Background (CMB) radiation. Hemispherical power asymmetry in the CMB may be caused due to a dipolar modulation, indicating the presence of a preferred direction. Appropriately re-scaled local variance maps of the CMB temperature anisotropy data effectively encapsulate this dipolar pattern. As a first-of-its-kind method, we train Artificial Neural Networks (ANNs) with such local variances as input features to distinguish statistically isotropic CMB maps from dipole modulated ones. Our trained ANNs are able to predict components of the amplitude times the unit vector of the preferred direction for mixed sets of modulated and unmodulated maps, with goodness of fit ($R^2$) scores $>0.97$ for full sky, and $>0.96$ for partial sky coverage. On all observed foreground-cleaned CMB maps, the ANNs detect the dipolar modulation signal with overall consistent values of amplitudes and directions. This detection is significant at $97.21\%-99.38\%$ C.L. for all full sky maps, and at $98.34\%-100\%$ C.L. for all partial sky maps. Robustness of the signal holds across full and partial skies, various foreground cleaning methods, inpainting algorithms, instruments and all the different periods of observation for Planck and WMAP satellites. The significant and robust detection of the signal, in addition to the consistency of values of amplitude and directions, as found independent of any pre-existing methods, further mitigates the criticisms of look-elsewhere effects and a posteriori inferences for the preferred dipole direction in the CMB., Comment: 21 pages, 16 figures

Incomplete sky analysis of cosmic microwave background (CMB) polarization spectra poses a major problem of leakage between $E$- and $B$-modes. We present a machine learning approach to remove this $E$-to-$B$ leakage using a convolutional neural network (CNN) in presence of detector noise. The CNN predicts the full sky $E$- and $B$-modes spectra for multipoles $2 \leq \ell \leq 384$ from the partial sky spectra for $N_{\rm{side}} = 256$. We use tensor-to-scalar ratio $r=0.001$ to simulate the CMB polarization maps. We train our CNN using $10^5$ full sky target spectra and an equal number of noise contaminated partial sky spectra obtained from the simulated maps. The CNN works well for two masks covering the sky area of $\sim 80\%$ and $\sim 10\%$ respectively after training separately for each mask. For the assumed theoretical $E$- and $B$-modes spectra, predicted full sky $E$- and $B$-modes spectra agree well with the corresponding target spectra and their means agree with theoretical spectra. The CNN preserves the cosmic variances at each multipole, effectively removes correlations of the partial sky $E$- and $B$-modes spectra, and retains the entire statistical properties of the targets avoiding the problem of so-called $E$-to-$B$ leakage for the chosen theoretical model., Comment: 24 pages, 13 figures

Recent CMB observations have resulted in very precise observational data. A robust and reliable CMB reconstruction technique can lead to efficient estimation of the cosmological parameters. We demonstrate the performance of our methodology using simulated temperature and polarization observations using cosmic variance limited future generation PRISM satellite mission. We generate samples from the joint distribution by implementing the CMB inverse covariance weighted internal-linear-combination (ILC) with the Gibbs sampling technique. We use the Python Sky Model (PySM), d4f1s1 to generate the realistic foreground templates. The synchrotron emission is parametrized by a spatially varying spectral index, whereas the thermal dust emission is described as a two-component dust model. We estimate the marginalized densities of CMB signal and theoretical angular power spectrum utilizing the samples from the entire posterior distribution. The best-fit cleaned CMB map and the corresponding angular power spectrum are consistent with the CMB realization and the sky angular power spectrum, implying an efficient foreground minimized reconstruction. The likelihood function estimated by making use of the Blackwell-Rao estimator is used for the estimation of the cosmological parameters. Our methodology can estimate the tensor to scalar ratio $r\ge 0.0075$ for the chosen foreground models and the instrumental noise levels. Our current work demonstrates an analysis pipeline starting from the reliable estimation of CMB signal and its angular power spectrum to the case of cosmological parameter estimation using the foreground model independent Gibbs-ILC method.

The next-generation CMB satellite missions are expected to provide robust constraints on a wide range of cosmological parameters with unprecedented precision. But these constraints on the parameters could weaken if we do not attribute dark energy to a cosmological constant. The cosmological models involving interaction between dark energy and dark matter can give rise to comparable energy densities at the present epoch, thereby alleviating the so-called cosmic coincidence problem. In the present paper, we perform a forecast analysis to test the ability of the future generation high-sensitive Cosmic Microwave Background (CMB), and Baryon Acoustic Oscillation (BAO) experiments to constrain phenomenological interacting dark energy models. We consider cosmic variance limited future CMB polarization experiment PICO along with BAO information from the DESI experiment to constrain the parameters of the interacting dark sector. Based on the stability of the cosmological perturbations, we consider two possibilities for the interaction scenario. We investigate the impact of both the coupling constant and the equation of state parameter of dark energy on the CMB temperature power spectrum, matter power spectrum, and $f\sigma_8$. We have used simulated temperature and polarization data from PICO within the multipole ranges ($\ell = 2 - 4000$), and as expected, we do see PICO alone produces better constraints than Planck on the $\Lambda$CDM parameters. With the integration of the PICO and DESI missions, we observe a significant improvement in the constraints on several cosmological parameters, especially the equation of state parameter of dark energy. However, we note that additional data is required to constrain a small positive coupling constant.

The set of cosmological density parameters ($\Omega_{0m}h_{0}^{2}$, $\Omega_{0k}h_{0}^{2}$, $\Omega_{0\Lambda}h_{0}^{2}$) and Hubble constant ($\hat{h}_{0}$) are useful for fundamental understanding of the universe from many perspectives. In this article, we propose a new procedure to estimate these parameters for $\Lambda$ cold dark matter ($\Lambda$CDM) universe in the Friedmann-Robertson-Walker (FRW) background. We generalize the two-point statistics first proposed by Sahni et al. (2008) to the three point case and estimate the parameters using currently available Hubble parameter ($H(z)$) values in the redshift range $0.07 \leq z \leq 2.36$ measured by differential age (DA) and baryon acoustic oscillation (BAO) techniques. All the parameters are estimated assuming the general case of non-flat universe. Using both DA and BAO data we obtain $\Omega_{0m}h_{0}^{2}=0.1485 \pm 0.0065$, $\Omega_{0k}h_{0}^{2}=-0.0137 \pm 0.017$, $\Omega_{0\Lambda}h_{0}^{2}=0.3126 \pm 0.0145$ and $\hat{h}_{0}=0.6689 \pm 0.0021$. These results are in satisfactory agreement with the Planck results. An important advantage of our method is that to estimate the value of any one of the independent cosmological parameters one does not need to use the values for the rest of them. Each parameter is obtained solely from the measured values of Hubble parameters at different redshifts without any need to use values of other parameters. Such a method is expected to be less susceptible to the undesired effects of degeneracy issues between cosmological parameters during their estimations. Moreover, there is no requirement of assuming spatial flatness in our method., Comment: 21 pages, 6 figures, 5 tables

Reliable extraction of cosmological information from observed cosmic microwave background (CMB) maps may require removal of strongly foreground contaminated regions from the analysis. In this article, we employ an artificial neural network (ANN) to predict the full sky CMB angular power spectrum between intermediate to large angular scales from the partial sky spectrum obtained from masked CMB temperature anisotropy map. We use a simple ANN architecture with one hidden layer containing $895$ neurons. Using $1.2 \times 10^{5}$ training samples of full sky and corresponding partial sky CMB angular power spectra at Healpix pixel resolution parameter $N_{side} = 256$, we show that predicted spectrum by our ANN agrees well with the target spectrum at each realization for the multipole range $2 \leq l \leq 512$. The predicted spectra are statistically unbiased and they preserve the cosmic variance accurately. Statistically, the differences between the mean predicted and underlying theoretical spectra are within approximately $3\sigma$. Moreover, the probability densities obtained from predicted angular power spectra agree very well with those obtained from `actual' full sky CMB angular power spectra for each multipole. Interestingly, our work shows that the significant correlations in input cut-sky spectra, due to mode-mode coupling introduced on the partial sky, are effectively removed since the ANN learns the hidden pattern between the partial sky and full sky spectra preserving the entire statistical properties. The excellent agreement of statistical properties between the predicted and the ground-truth demonstrates the importance of using artificial intelligence systems in cosmological analysis more widely., Comment: 17 pages, 15 figures

Statistical Isotropy of the Cosmic Microwave Background (CMB) radiation has been studied and debated extensively in recent years. Under this assumption, the hot spots and cold spots of the CMB are expected to be uniformly distributed over a 2-sphere. We use the orientation matrix, first proposed by Watson (1965) and Scheidegger (1965) and associated shape and strength parameters (Woodcock, 1977) to analyse whether the hot and cold spots of the observed CMB temperature anisotropy field are uniformly placed. We demonstrate the usefulness of our estimators by using simulated toy models containing non-uniform data. We apply our method on several foreground minimized CMB maps observed by WMAP and Planck over large angular scales. The shape and strength parameters constrain geometric features of possible deviations from uniformity (isotropy) and the power of the anomalous signal. We find that distributions of hot or cold spots in cleaned maps show no unusual signature of clustering or girdling. Instead, we notice a strikingly uniform distribution of hot spots over the full sky. The signal remains robust with respect to the four cleaned maps used and presence or absence of the non-Gaussian cold spot (NGCS). On the partial sky with WMAP KQ75 and Planck U73 masks we find anomalously low strength of non-uniformity for cold spots which is found to be robust with respect to various cleaning methods, masks applied, instruments, frequencies, and the presence or absence of the NGCS. Interestingly we find that the signal of anomalously weak non-uniformity could be due to contributions from the quadrupole and octupole and may be related with the low CMB temperature variance anomaly., Comment: 25 pages, 11 figures

In this article we present a formalism to incorporate the partial-sky maps to the Gibbs ILC algorithm to estimate the joint posterior density of the Cosmic Microwave Background (CMB) signal and the theoretical CMB angular power spectrum given the observed CMB maps. In order to generate the partial-sky maps we mask all the observed CMB maps provided by WMAP and Planck satellite mission using a Gaussian smoothed mask formed on the basis of thermal dust emissions in Planck 353 GHz map. The central galactic region from all the input maps is removed after the application of the smoothed mask. While implementing the Gibbs ILC method on the partial-sky maps, we convert the partial-sky cleaned angular power spectrum to the full-sky angular power spectrum using the mode-mode coupling matrix estimated from the smoothed mask. The main products of our analysis are partial-sky cleaned best-fit CMB map and an estimate of the underlying full-sky theoretical CMB angular power spectrum along with their error estimates. We validate the methodology by performing detailed Monte Carlo simulations after using realistic models of foregrounds and detector noise consistent with the WMAP and Planck frequency channels used in our analysis. We can estimate the posterior density and full-sky theoretical CMB angular power spectrum, without any need to explicitly model the foreground components, from partial-sky maps using our method. Another important feature of this method is that the power spectrum results along with the error estimates can be directly used for cosmological parameter estimations.

The cosmological models exhibiting tracker properties have great significance in the context of dark energy as they can reach the present value of dark energy density from a wide range of initial conditions, thereby alleviating both the fine-tuning and the cosmic coincidence problem. The $\alpha$-attractors, which are originally discussed in the context of inflation, can exhibit the properties of dark energy as they can behave like cosmological trackers at early times and show the late time behaviour of a cosmological constant. In the present paper, we study the Oscillatory Tracker Model (OTM), which belongs to the family of $\alpha$-attractor dark energy models. Using the current observational data sets like Cosmic Microwave Background (CMB), Baryon Acoustic Oscillation (BAO) and type 1a supernova data (Pantheon compilation), we constrain the parameters of the model and estimate both the mean and best-fit values. Although the oscillatory tracker model contains a larger set of parameters than the usual LCDM model, the common set of parameters of both agree within $1\, \sigma$ error limits. Our observations using both high redshift and low redshift data supports Hubble parameter value $H_0 = 67.4$ Kms$^{-1}$Mpc$^{-1}$. We study the effect of the OTM on the CMB temperature and polarization power spectra, matter power spectrum and $f \sigma_8$. Our analysis of the CMB power spectrum and matter power spectrum suggests that the oscillatory tracker dark energy model has noticeable differences from usual LCDM predictions. Yet, in most cases, the agreement is very close.

Genetic Algorithm (GA) -- motivated by natural evolution -- is a robust method to estimate the global optimal solutions of problems involving multiple objective functions. In this article, for the first time, we apply GA to reconstruct the CMB temperature anisotropy map over large angular scales of the sky using (internal) linear combination (ILC) of the final-year WMAP and Planck satellite observations. To avoid getting trapped into a local minimum, we implement the GA with generous diversity in the populations by selecting pairs with diverse fitness coefficients and by introducing a small but significant amount of mutation of genes. We find that the new GA-ILC method produces a clean map which agrees very well with that obtained using the exact analytical expression of weights in ILC. By performing extensive Monte Carlo simulations of the CMB reconstruction using the GA-ILC algorithm, we find that residual foregrounds in the cleaned map are minimal and tend to occupy localized regions along the galactic plane. The CMB angular power spectrum shows no indication of any bias in the entire multipole range $2 \leq \ell \leq 32$ studied in this work. The error in the CMB angular power spectrum is also minimal and given entirely by the cosmic-variance-induced error. Our results agree well with those obtained by various other reconstruction methods by different research groups. This problem-independent robust GA-ILC method provides a flexible way towards the complex and challenging task of CMB component reconstruction in cosmology.

Accurate estimation of the Cosmic Microwave Background (CMB) angular power spectrum is enticing due to the prospect for precision cosmology it presents. Galactic foreground emissions, however, contaminate the CMB signal and need to be subtracted reliably in order to lessen systematic errors on the CMB temperature estimates. Typically bright foregrounds in a region lead to further uncertainty in temperature estimates in the area even after some foreground removal technique is performed and hence determining the underlying full-sky angular power spectrum poses a challenge. We explore the feasibility of utilizing artificial neural networks to predict the angular power spectrum of the full sky CMB temperature maps from the observed angular power spectrum of the partial sky in which CMB temperatures in some bright foreground regions are masked. We present our analysis at large angular scales with two different masks. We produce unbiased predictions of the full-sky angular power spectrum and recover the underlying theoretical power spectrum using neural networks. Our predictions are also uncorrelated to a large extent. We further show that the multipole-space covariances of the predictions of full-sky spectra made by the ANNs are much smaller than those of the estimates obtained using the pseudo-$C_\ell$ method., Comment: 10 pages, 11 figures; altered methodology, added links to references, updated analysis using latest available data, modified the write-up accordingly

If the principle of statistical isotropy is valid, then the angular power spectrum (APS) of cosmic microwave background (CMB) radiation is uncorrelated between different multipoles. We propose a novel technique to analyse any possible correlations of the foreground cleaned CMB temperature angular power spectrum (APS) measures ($C_{\ell}$ and $\mathcal{D}_\ell=\frac{\ell(\ell+1)}{2\pi}C_\ell$). This is motivated by the behaviour of level spacings between random matrix eigenvalues. The method helps distinguish uncorrelated statistically isotropic CMB APS from correlated APS, where the latter can arise due to breakdown of isotropy or presence of some residual systematics in the foreground cleaned CMB maps. Spacings of statistically isotropic CMB $C_\ell$'s and $\mathcal{D}_\ell$'s are seen to closely obey Poisson statistics and introduction of correlations changes the distribution to appropriate Wigner-Dyson statistics. For foreground cleaned CMB, we employ the average spacing of consecutive multipole APS for multipoles $\in [2,31]$. This estimator is sensitive to departures from the null hypothesis of zero correlations between the APS measures of statistically isotropic CMB. We study full sky WMAP 9 year ILC and 2018 Planck foreground cleaned maps (Commander, NILC and SMICA). Sans parity distinctions, average spacings are in good agreement with theoretical expectation. With parity distinctions, even multipoles indicate unusually low average spacings for both $C_\ell$'s (at $\geq 98.86\%$ C.L.) and $\mathcal{D}_\ell$'s (at $\geq 95.07\%$ C.L.). We use an inpainting method based on constrained Gaussian realisations and show that for the Planck $U73$ and WMAP $KQ75$ masks, all the foreground cleaned inpainted CMB maps robustly confirm the existence of such unusually low average spacings of even multipole APS. In addition, this signal is independent of the non-Gaussian cold spot., Comment: 16 pages, 9 figures

Semiconductor quantum dots (QDs) are being regarded as the primary unit for a wide range of advanced and emerging technologies including electronics, optoelectronics, photovoltaics and biosensing applications as well as the domain of q-bits based quantum information processing. Such QDs are suitable for several novel device applications for their unique property of confining carriers 3-dimensionally creating discrete quantum states. However, the realization of such QDs in practice exhibits serious challenge regarding their fabrication in array with desired scalability and repeatability as well as control over the quantum states at room temperature. In this context, the current work reports the fabrication of an array of highly scaled Ge-nanowire (radius ~25 nm) based vertical metal-oxide-semiconductor devices that can operate as voltage tunable quantum dots at room temperature. The electrons in such nanowire experience a geometrical confinement in the radial direction, whereas, they can be confined axially by tuning the applied bias in order to manipulate the quantum states. Such quantum confinement of electrons has been confirmed from the step-like responses in the room temperature capacitance-voltage (C-V) characteristics at relatively low frequency (200 kHz). Each of such steps has observed to encompass convolution of the quantized states occupying ~6 electronic charges. The details of such carrier confinement are analyzed in the current work by theoretically modeling the device transport properties based on non-equilibrium Green's function (NEGF) formalism.

The Cosmic Microwave Background (CMB) radiation B mode polarization signal contains the unique signature of primordial metric perturbations produced during the inflation. The separation of the weak CMB B-mode signal from strong foreground contamination in observed maps is a complex task, and proposed new generation low noise satellite missions compete with the weak signal level of this gravitational background. In this article, for the first time, we employ a foreground model-independent internal linear combination (ILC) method to reconstruct the CMB B mode signal using simulated observations over large angular scales of the sky of 6 frequency bands of future generation CMB mission Probe of Inflation and Cosmic Origins (PICO). We estimate the joint CMB B mode posterior density following the interleaving Gibbs steps of B mode angular power spectrum and cleaned map samples using the ILC method. We extend and improve the earlier reported Bayesian ILC method to analyze weak CMB B mode reconstruction by introducing noise bias corrections at two stages during the ILC weight estimation. By performing $200$ Monte Carlo simulations of the Bayesian ILC method, we find that our method can reconstruct the CMB signals and the joint posterior density accurately over large angular scales of the sky. We estimate Blackwell-Rao statistics of the marginal density of CMB B mode angular power spectrum and use them to estimate the joint density of scalar to tensor ratio $r$ and a lensing power spectrum amplitude $A^{\textrm{lens}}$. Using $200$ Monte Carlo simulations of the delensing approach, we find that our method can achieve an unbiased detection of the primordial gravitational wave signal $r$ with more than 8$\sigma$ significance for levels of $r \geqslant 0.01$., Comment: 12 pages,13 figures,1 table

Ever since Cosmic Microwave Background (CMB) signal is being measured by various satellites based observations with increasing experimental accuracies there has been a parallel increase in the demand for a CMB reconstruction technique which can provide accurate estimates of CMB signal and the theoretical angular power spectrum along with reliable statistical error estimates associated with them. In this work, we estimate the joint posterior of CMB E mode signal (S) and corresponding theoretical angular power spectrum (C^E_l) over large angular scales given the simulated polarization observations of future generation COrE satellite mission. To generate samples from the joint distribution we employ the ILC technique with prior information of CMB E mode covariance matrix augmented by a Gibbs sampling technique. We estimate the marginalized densities of S and C^E_l using the samples from full-posterior. The best fit cleaned E mode map and the corresponding angular power spectrum agree well with the input E mode map and the sky power spectrum implying accurate reconstruction using COrE like observations. Using the samples C^E_l of all Gibbs chains we estimate the likelihood function P(C^E_l|D) of any arbitrary C^E_l given simulated observed maps (D) of COrE mission following Blackwell-Rao estimator. The likelihood function can be seamlessly integrated to the cosmological parameter estimation method. Apart from producing an accurate estimate of E mode signal over large angular scales our method also builds a connection between the component reconstruction and reliable cosmological parameter estimation using CMB E mode observations over large angular scales. The entire method does not assume any explicit models for E mode foreground components in order to remove them, which is an attractive property since foreground modelling uncertainty does not pose as a challenge in this case., Comment: 11 figures and 14 pages

In the recent years, the internal-linear-combination (ILC) method was investigated extensively in the context of reconstruction of Cosmic Microwave Background (CMB) temperature anisotropy signal using observations obtained by WMAP and Planck satellite missions. In this article, we, for the first time, apply the ILC method to reconstruct the large scale CMB E mode polarization signal, which serves as the unique probe of ionization history of the Universe, using simulated observations of 15 frequency CMB polarization maps of future generation COrE satellite mission. We find that usual ILC cleaned E mode map is highly erroneous due to presence of a chance-correlation between CMB and astrophysical foreground components in the empirical covariance matrix which is used to estimate the weight factors. The cleaned angular power spectrum for E mode is strongly biased and erroneous due to these chance correlation factors. In order to address the issues of bias and errors we extend and improve the usual ILC method for CMB E mode reconstruction by incorporating prior information of theoretical E mode angular power spectrum while estimating the weights for linear combination of input maps. Using the E mode covariance matrix effectively suppresses the CMB-foreground chance correlation power leading to an accurate reconstruction of cleaned CMB E mode map and its angular power spectrum. We provide a comparative study of the performance of the usual ILC and the new method over large angular scales of the sky and show that the later produces significantly statistically improved results than the former. The new E mode CMB angular power spectrum contains neither any significant negative bias at the low multipoles nor any positive foreground bias at relatively higher mutlipoles. The error estimates of the cleaned spectrum agree very well with the cosmic variance induced error., Comment: 29 pages, 10 figures

In this article, we extend previous studies based on CMB spherical harmonic phases (SHP) to examine the validity of the hypothesis that the temperature field of the CMB is consistent with a Gaussian random field (GRF). The null hypothesis is that the corresponding CMB SHP are independent and identically distributed in terms of a uniform distribution in the interval [0, 2$\pi$] \citep{1986ApJ...304...15B,2013rossmanith}. We devise a new model-independent method where we use ordered and non-parametric Rao's statistic, based on sample arc-lengths to comprehensively test uniformity and independence of SHP. We performed our analysis on the scales limited by spherical harmonic modes $\le$ 128, to restrict ourselves to signal-dominated regions. To find the non-uniform or dependent sets of SHP, we calculate the statistic for the data and 10000 Monte Carlo simulated uniformly random sets of SHP and use 0.05 and 0.001 $\alpha$ levels to distinguish between statistically significant and highly significant detections. We first establish the performance of our method using simulated Gaussian, non-Gaussian CMB temperature maps, along with observed non-Gaussian 100 and 143 GHz Planck channel maps. We find that our method performs efficiently and accurately in detecting phase correlations generated in all of the non-Gaussian simulations and observed foreground contaminated 100 and 143 GHz Planck channel temperature maps. We apply our method on the 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 SHP corresponding to some of the $m$-modes is non-uniform, some of the $\ell$ mode SHP and neighboring mode pair SHP are correlated in cleaned CMB maps. The detection of non-uniformity or correlation in the SHP indicates the presence of non-Gaussian signals in the foreground minimized CMB maps., Comment: 42 pages, 23 figures, 6 tables

Residual error in calibration coefficients corresponding to observed CMB maps is an important issue while estimating a pure CMB signal. A component separation method, if these errors in the input foreground contaminated CMB maps are not properly taken into account, may lead to bias in the cleaned CMB map and estimated CMB angular power spectrum. But the inability to exactly determine the calibration coefficients corresponding to each observed CMB map from any CMB experiment makes it very difficult to incorporate their exact and actual values in a component separation analysis. Hence the effect of any random and residual calibration error on the cleaned CMB map and its angular power spectrum of a component separation problem can only be understood by performing detailed Monte Carlo simulations. In this paper, we investigate the impact of using input foreground contaminated CMB maps with random calibration errors on posterior density of cleaned CMB map and theoretical CMB angular power spectrum over large angular scales of the sky following the Gibbs ILC method proposed by \cite{Sudevan:2018qyj}. By performing detailed Monte Carlo simulations of WMAP and Planck temperature anisotropy observations with calibration errors compatible with them we show that the best-fit map corresponding to posterior maximum is minimally biased in Gibbs ILC method by a CMB normalization bias and residual foreground bias. The bias in best-fit CMB angular power spectrum with respect to the case where no calibration error is present are $\sim 28 \mu K^2$ and $-4.7 \mu K^2$ respectively between $2 \le \ell \le 15$ and $16 \le \ell \le 32$. The calibration error induced error in best-fit power spectrum causes an overall $6\%$ increase of the net error when added in quadrature with the cosmic variance induced error., Comment: 8 pages, 4 figures

The inflationary epoch and the late time acceleration of the expansion rate of universe can be explained by assuming a gravitationally coupled scalar field. In this article, we propose a new method of finding exact solutions in the background of flat Friedmann-Robertson-Walker (FRW) cosmological models by considering both scalar field and matter where the scalar field potential is a function of the scale factor. Our method provides analytical expressions for equation of state parameter of scalar field, deceleration parameter and Hubble parameter. This method can be applied to various other forms of scalar field potential, to the early radiation dominated epoch and very early scalar field dominated inflationary dynamics. Since the method produces exact analytical expression for $H(a)$ (i.e., H(z) as well), we then constrain the model with currents data sets, which includes-Baryon Acoustic Oscillations, Hubble parameter data and Type 1a Supernova data (Pantheon Dataset). As an extension of the method, we also consider the inverse problem of reconstructing scalar field potential energy by assuming any general analytical expression of scalar field equation of state parameter as a function of scale factor., Comment: 21 pages, 7 figures

In this work, we formalize a new technique to investigate joint posterior density of Cosmic Microwave Background (CMB) signal and its theoretical angular power spectrum given the observed data, using the global internal-linear-combination (ILC) method first proposed by Sudevan & Saha (2017). We implement the method on low resolution CMB maps observed by WMAP and Planck satellite missions, using Gibbs sampling, assuming that the detector noise is negligible on large angular scales of the sky. The main products of our analysis are best fit CMB cleaned map and its theoretical angular power spectrum along with their error estimates. We validate the methodology by performing Monte Carlo simulations that includes realistic foreground models and noise levels consistent with WMAP and Planck observations. Our method has an unique advantage that the posterior density is obtained without any need to explicitly model foreground components. Secondly, the power spectrum results with the error estimates can be directly used for cosmological parameter estimations., Comment: 10 pages, 8 figures

We propose a new internal linear combination (ILC) method in the pixel space, applicable on large angular scales of the sky, to estimate a foreground minimized Cosmic Microwave Background (CMB) temperature anisotropy map by incorporating prior knowledge about the theoretical CMB covariance matrix. Usual ILC method in pixel space, on the contrary, does not use any information about the underlying CMB covariance matrix. The new approach complements the usual pixel space ILC technique specifically at low multipole region, using global information available from theoretical CMB covariance matrix as well as from the data. Since we apply our method over the large scale on the sky containing low multipoles we perform foreground minimization globally. We apply our methods on low resolution Planck and WMAP foreground contaminated CMB maps and validate the methodology by performing detailed Monte-Carlo simulations. Our cleaned CMB map and its power spectrum have significantly less error than those obtained following usual ILC technique at low resolution that does not use CMB covariance information. Another very important advantage of our method is that the cleaned power spectrum does not have any negative bias at the low multipoles because of effective suppression of CMB-foreground chance correlations on large angular scales of the sky. Our cleaned CMB map and its power spectrum match well with those estimated by other research groups., Comment: 11 pages, 12 figures