For primordial black holes (PBHs) to form a considerable fraction of cold dark matter, the required amplitude of primordial scalar perturbations is quite large ($P_{\zeta }(k)\sim {10}^{-2}$) if PBH is formed in radiation epoch. In alternate cosmological histories, where additional epoch of arbitrary equation of state precede radiation epoch, the dynamics of PBH formation and relevant mass ranges can be different leading to lower requirement of primordial power at smaller scales of inflation. Moreover, this alternate history can modify the predictions for the gravitational wave (GW) spectrum, which can be probed by upcoming GW observations. In this paper we show that an early kination epoch can lead to percent level abundance of PBH for a lower amplitude of $P_{\zeta }(k)$ as compared to PBH formation in a standard radiation epoch. Moreover, we calculate the effect of early kination epoch on the GW spectrum for first and second orders in perturbation theory which show enhancement in the amplitude of the GW spectrum in a kination epoch with respect to that in a standard radiation epoch.

Recently, the NANOGrav Collaboration has reported evidence for a common-spectrum stochastic process, which might be interpreted as the first ever detection of stochastic gravitational wave (GW) background. We discuss the possibility of the signal arising from the first- and second-order GWs in nonstandard cosmological history. We show that the NANOGrav observation can be explained by first-order GWs in the nonstandard thermal history with an early matter-dominated era, whereas the parameter space required to explain the NANOGrav observation in the standard cosmology or in the nonstandard epoch of kination domination is ruled out by the big bang nucleosynthesis and cosmic microwave background observations. For the second-order GWs arising from the large primordial scalar fluctuations, we study the standard radiation domination and two specific nonstandard cases with a few forms of the primordial power spectrum $P_{\zeta }(k)$ to achieve abundant primordial black hole (PBH) production. We find that the NANOGrav observation can be explained with standard radiation domination for all of these $P_{\zeta }(k)$. Furthermore, a dustlike epoch leads to abundant PBH formation for a lower amplitude of $P_{\zeta }(k)$ than the radiation-dominated case and complies with the NANOGrav observation only for a few of the $P_{\zeta }(k)$ forms considered here, where the peak wave number is larger than the wave number range probed by NANOGrav. In this nonstandard epoch, for a broad power spectrum, PBHs are produced in a wide mass range in the planetary mass regime. A nonstandard epoch of kination domination cannot produce enough PBHs for any of the $P_{\zeta }(k)$ if the NANOGrav result is to be satisfied.

Large turns in multifield inflation can lead to a very rich phenomenology, but are difficult to realise in supergravity, and typically require large field space curvatures. In this work, we present a mechanism to realise multiple sharp turns, and therefore strong non-geodesic trajectories, from transient violations of slow-roll without the requirement of large field space curvatures in supergravity inflation. Such turning rates can strongly source the adiabatic fluctuations, resulting in an enhanced scalar power spectrum with resonant features and a large peak amplitude. If the growth of the scalar power spectrum at small scales is large enough, primordial black holes can be produced in abundance. These large scalar fluctuations induce a characteristic large spectrum of gravitational waves for a wide range of frequencies, which inherits the resonant features. We illustrate this mechanism in a supergravity model of axion monodromy, which provides the first concrete model to realise such resonant features.The model can sustain inflation for around 60 e-folds, leading to considerable production of very light primordial black holes, and large gravitational wave spectra, which could be detectable by multiple upcoming gravitational wave surveys. For the set of parameter we consider, large oscillations occur at all scales. This represents a challenge for the model at large scales and motivates further investigation to reconcile this class of models with Planck data.

We use a suite of the most recent cosmological observations to test models of dynamical dark energy motivated by quantum gravity. Specifically, we focus on hilltop quintessence scenarios, able to satisfy theoretical constraints from quantum gravity. We discuss their realisation based on axions, their supersymmetric partners, and Higgs-like string constructions, including dynamical mechanisms to set up initial conditions at the hilltops. We also examine a specific parameterisation for dynamical dark energy suitable for hilltop quintessence. We then perform an analysis based on Markov Chain Monte-Carlo to assess their predictions against CMB, galaxy surveys, and supernova data. We show to what extent current data can distinguish amongst different hilltop set-ups, providing model parameter constraints that are complementary to and synergetic with theoretical bounds from quantum gravity conjectures, as well as model comparisons across the main dark energy candidates in the literature. However, all these constraints are sensitive to priors based on theoretical assumptions about viable regions of parameter space. Consequently, we discuss theoretical challenges in refining these priors, with the aim of maximizing the informative power of current and forthcoming cosmological datasets for testing dark energy scenarios in quantum gravity.

The $\alpha$-attractor models are some of the most interesting models of inflation from the point of view of upcoming observations in cosmology and also attractive from the point of view of supergravity. We confront representative models of exponential and polynomial $\alpha$-attractors with the latest cosmological data (Planck’18+BICEP2/Keck array) to obtain predictions and best fit values of model parameters. The analysis is done by making use of ModeChord and CosmoMC plugged together via PolyChord.