We present a detailed exposition on the prospects of the formation of Primordial Black Holes (PBHs) during Slow Roll (SR) to Ultra Slow Roll (USR) sharp transitions in the framework of single-field inflation. We use an effective field theory (EFT) approach in order to keep the analysis model-independent and applicable to both the canonical and non-canonical cases. We show in detail how renormalizing the power spectrum to one loop order in P(X,ϕ) theories severely limits the prospects for PBH formation in a single-field inflationary framework. We demonstrate that for the allowed range of effective sound speed, 1 < c_s < 1.17, the consistency of one-loop corrected power spectrum leaves a small window for black hole masses, M _PBH∼𝒪(10²–10³)gm to have sufficient e-foldings, Δ𝒩_Total ∼ 𝒪(54–59) for inflation. We confirm that adding an SR regime after USR before the end of inflation does not significantly alter our conclusions. Our findings for sharp transition strictly rule out the possibility of generating large masses of PBHs from all possible models of single field inflation (canonical and non-canonical). Our results are at least valid for the situation where constraints from the loop effects are computed using either Late-Time (LT) or Adiabatic-Wave function (AF) scheme followed by Power Spectrum (PS) renormalization schemes.

Recently, in various theoretical works, path-breaking progress has been made in recovering the well-known page curve of an evaporating black hole with quantum extremal islands, proposed to solve the long-standing black hole information loss problem related to the unitarity issue. Motivated by this concept, in this paper, we study cosmological circuit complexity in the presence (or absence) of quantum extremal islands in negative (or positive) cosmological constant with radiation in the background of Friedmann-Lema$\widehat{i}$tre-Robertson-Walker (FLRW) space-time, i.e., the presence and absence of islands in anti de Sitter and the de Sitter space-time having SO(2, 3) and SO(1, 4) isometries, respectively. Without using any explicit details of any gravity model, we study the behavior of the circuit complexity function with respect to the dynamical cosmological solution for the scale factors for the above mentioned two situations in FLRW space-time using squeezed state formalism. By studying the cosmological circuit complexity, out-of-time ordered correlators, and entanglement entropy of the modes of the squeezed state, in different parameter space, we conclude the non-universality of these measures. Their remarkably different features in the different parameter space suggests their dependence on the parameters of the model under consideration.

We present a detailed study of the generation of large primordial non-Gaussianities during the slow-roll (SR) to ultra-slow roll (USR) transitions in the framework of Galileon inflation. We found out that due to having sharp transitions in the USR phase, which persist with a duration of Δ𝒩_USR ∼ 2 e-folds, we are able to generate the non-Gaussianity amplitude of the order: |f _NL| ∼ 𝒪(10^-2) in the SRI, -5 < f _NL < 5 in the USR, and -2 < f _NL < 2 in the SRII phases. As a result, we are able to achieve a cumulative average value of |f _NL| ∼ 𝒪(1). This implies that our results strictly satisfy Maldacena's no-go theorem in the squeezed limit only for SRI, while they strictly violate the same condition in both the USR and SRII phases. The non-renormalization theorem in the Galileon theory helps to support our results regarding the generation of large mass primordial black holes along with large non-Gaussianities, which we show to be dependent on the specific positions of the transition wave numbers fixed at low scales.

In this work, our prime objective is to study non-locality and long range effect of two body correlation using quantum entanglement from various information theoretic measure in the static patch of de Sitter space using a two body Open Quantum System (OQS). The OQS is described by a system of two entangled atoms, surrounded by a thermal bath, which is modelled by a massless probe scalar field. Firstly, we partially trace over the bath field and construct the Gorini Kossakowski Sudarshan Lindblad (GSKL) master equation, which describes the time evolution of the reduced subsystem density matrix. This GSKL master equation is characterized by two components, these are-Spin chain interaction Hamiltonian and the Lindbladian. To fix the form of both of them, we compute the Wightman functions for probe massless scalar field. Using this result alongwith the large time equilibrium behaviour we obtain the analytical solution for reduced density matrix. Further using this solution we evaluate various entanglement measures, namely Von-Neumann entropy, R $$e'$$e′ nyi entropy, logarithmic negativity, entanglement of formation, concurrence and quantum discord for the two atomic subsystem on the static patch of De-Sitter space. Finally, we have studied violation of Bell-CHSH inequality, which is the key ingredient to study non-locality in primordial cosmology.

We demonstrate the explicit realisation of the ultra-slow roll phase in the framework of the effective field theory of single-field Galileon inflation. The pulsar timing array (PTA) collaboration hints at the scalar-induced gravity waves (SIGW) from the early universe as an explanation for the origin of the observed signal, which, however, leads to an enhancement in the amplitude of the scalar power spectrum giving rise to the overproduction of primordial black holes (PBHs). In the setup under consideration, we examine the generation of SIGW consistent with PTA (NANOGrav15 and EPTA) data, in addition to which we also consider the impact from QCD crossover at the nHz frequencies and address the PBH overproduction issue assuming linear approximations for the over-density without incorporating non-Gaussian effects from the comoving curvature perturbation. The framework is shown to give rise to SIGWs well consistent with the PTA signal with comfortable PBH abundance, 10^-3≲fPBH < 1, of near solar-mass black holes.