In this article we provide a new closed relationship between cosmic abundance of primordial gravitational waves and primordial blackholes that originated from initial inflationary perturbations for inflection-point models of inflation where inflation occurs below the Planck scale. The current Planck constraint on tensor-to-scalar ratio, running of the spectral tilt, and from the abundance of dark matter content in the universe, we can deduce a strict bound on the current abundance of primordial blackholes to be within a range, 9.99712×10−3<ΩPBHh2<9.99736×10−3

It has recently been demonstrated that the large N limit of a model of fermions charged under the global/gauge symmetry group O(N) ^q−1 agrees with the large N limit of the SYK model. In these notes we investigate aspects of the dynamics of the O(N) ^q−1 theories that differ from their SYK counterparts. We argue that the spectrum of fluctuations about the finite temperature saddle point in these theories has $$ \left(q-1\right)\frac{N^2}{2} $$ q − 1 N 2 2 new light modes in addition to the light Schwarzian mode that exists even in the SYK model, suggesting that the bulk dual description of theories differ significantly if they both exist. We also study the thermal partition function of a mass deformed version of the SYK model. At large mass we show that the effective entropy of this theory grows with energy like E ln E (i.e. faster than Hagedorn) up to energies of order N ². The canonical partition function of the model displays a deconfinement or Hawking Page type phase transition at temperatures of order 1/ln N. We derive these results in the large mass limit but argue that they are qualitatively robust to small corrections in J/m.

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.

We examine the possibility of Primordial Black Holes (PBHs) formation in single field models of inflation. Using the adiabatic or wave function renormalization scheme in the short range modes, we show that one-loop correction to the power spectrum is free from quadratic UV divergence. We consider a framework in which PBHs are produced during the transition from Slow Roll (SR) to Ultra Slow Roll (USR) followed by the end of inflation. We demonstrate that the renormalized power spectrum soften the contribution of the logarithmic IR divergence and severely restricts the possible mass range of produced PBHs in the said transition, namely, $$M_\textrm{PBH}\sim 10^{2}\,\textrm{g}$$M PBH ∼ 10 2 g $$\hat{\textrm{a}}$$a ^ la a no-go theorem. In particular, we find that the produced PBHs are short lived ( $$t^\textrm{evap}_\textrm{PBH}\sim 10^{-20}\,\textrm{s}$$t PBH evap ∼ 10 - 20 s ) and the corresponding number of e-folds in the USR region is restricted to $$\Delta {\mathcal {N}}_\textrm{USR}\approx 2$$Δ N USR ≈ 2 .

In this work, we have studied the possibility of setting up Bell’s inequality violating experiment in the context of cosmology, based on the basic principles of quantum mechanics. First we start with the physical motivation of implementing the Bell inequality violation in the context of cosmology. Then to set up the cosmological Bell violating test experiment we introduce a model independent theoretical framework using which we have studied the creation of new massive particles by implementing the WKB approximation method for the scalar fluctuations in the presence of additional time-dependent mass contribution in the cosmological perturbation theory. Here for completeness we compute the total number density and the energy density of the newly created particles in terms of the Bogoliubov coefficients using the WKB approximation method. Next using the background scalar fluctuation in the presence of a new time-dependent mass contribution, we explicitly compute the expression for the one point and two point correlation functions. Furthermore, using the results for a one point function we introduce a new theoretical cosmological parameter which can be expressed in terms of the other known inflationary observables and can also be treated as a future theoretical probe to break the degeneracy amongst various models of inflation. Additionally, we also fix the scale of inflation in a model-independent way without any prior knowledge of primordial gravitational waves. Also using the input from a newly introduced cosmological parameter, we finally give a theoretical estimate for the tensor-to-scalar ratio in a model-independent way. Next, we also comment on the technicalities of measurements from isospin breaking interactions and the future prospects of newly introduced massive particles in a cosmological Bell violating test experiment. Further, we cite a precise example of this setup applicable in the context of string theory motivated axion monodromy model. Then we comment on the explicit role of the decoherence effect and high spin on cosmological Bell violating test experiment. Finally, we provide a theoretical bound on the heavy particle mass parameter for scalar fields, gravitons and other high spin fields from our proposed setup.