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While the standard, six-parameter, spatially flat ΛCDM model has been highly successful, certain anomalies in the cosmic microwave background bring out a tension between this model and observations. The statistical significance of any one anomaly is small. However, taken together, the presence of two or more of them imply that according to standard inflationary theories we live in quite an exceptional Universe. We revisit the analysis of the PLANCK collaboration using loop quantum cosmology, where an unforeseen interplay between the ultraviolet and the infrared makes the primordial power spectrum scale dependent at very small k. Consequently, we are led to a somewhat different ΛCDM Universe in which anomalies associated with large scale power suppression and the lensing amplitude are both alleviated. The analysis also leads to new predictions for future observations. This article is addressed both to cosmology and loop quantum gravity communities, and we have attempted to make it self-contained. 

Gravitational waveforms for compact binary coalescences (CBCs) have been invaluable for detections by the LIGO-Virgo collaboration. They are obtained by a combination of semi-analytical models and numerical simulations. So far systematic errors arising from these procedures appear to be less than statistical ones. However, the significantly enhanced sensitivity of the new detectors that will become operational in the near future will require waveforms to be much more accurate. This task would be facilitated if one has a variety of cross-checks to evaluate accuracy, particularly in the regions of parameter space where numerical simulations are sparse. Currently errors are estimated by comparing the candidate waveforms with the numerical relativity (NR) ones, which are taken to be exact. The goal of this paper is to propose a qualitatively different tool. We show that full non-linear general relativity (GR) imposes an infinite number of sharp constraints on the CBC waveforms. These can provide clear-cut measures to evaluate the accuracy of candidate waveforms against exact GR, help find systematic errors, and also provide external checks on NR simulations themselves. 

Certain anomalies in the CMB bring out a tension between the six-parameter flat ΛCDM model and the CMB data. We revisit the PLANCK analysis with loop quantum cosmology (LQC) predictions and show that LQC alleviates both the large-scale power anomaly and the tension in the lensing amplitude. These differences arise because, in LQC, the primordial power spectrum is scale dependent for small k, with a specific power suppression. We conclude with a prediction of larger optical depth and power suppression in the B-mode polarization power spectrum on large scales.