In this paper, we investigate a scenario of variable gravity and apply it to the unified description of inflation and late-time cosmic acceleration dubbed quintessential inflation. The scalar field called ``cosmon,'' which in this model unifies both the concepts, reduces to the inflaton at early epochs. We calculate the slow-roll parameters, the Hubble parameter at the end of inflation, the reheating temperature, and the tensor-to-scalar ratio, and we demonstrate the agreement of the model with observations and the Planck data. As for the postinflationary dynamics, the cosmon tracks the background before it exits the scaling regime at late times. The scenario gives rise to the correct epoch sequence of standard cosmology, namely, radiative regime, matter phase, and dark energy. We show that the long kinetic regime after inflation gives rise to enhancement of the relic gravity wave amplitude, resulting in violation of the nucleosynthesis constraint at the commencement of the radiative regime in the case of an inefficient reheating mechanism, such as gravitational particle production. Instant preheating is implemented to successfully circumvent the problem. As a generic feature, the scenario gives rise to a blue spectrum for gravity waves on scales smaller than the comoving horizon scale at the commencement of the radiative regime.

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 paper, we propose a novel mechanism in 𝕋²-inflation to enhance the power spectrum large enough to seed primordial black holes (PBHs) formation. To accomplish this, we consider the coupling function between the inflaton field and 𝕋² = T_μνT^μν term. PBHs formed within this scenario can contribute partially or entirely to dark matter (DM) abundance. Furthermore, the amplification in the scalar power spectrum will concurrently produce significant scalar-induced gravitational waves (SIGWs) as a second-order effect. In addition, the energy spectrum associated with SIGWs can be compatible with the recent NANOGrav 15-year stochastic gravitational wave detection and fall into the sensitivity range of other forthcoming GW observatories.

We investigate inflationary dynamics in the framework of the Einstein-Gauss-Bonnet gravity. In the model under consideration, the inflaton field is nonminimally coupled to the Gauss-Bonnet curvature invariant, so that the latter appears to be dynamically important. We consider a quartic potential for the inflaton field, in particular, the one asymptotically connected to the Higgs inflation, and a wider class of coupling functions not considered in the earlier work. Keeping in mind the observational bounds on the parameters—the amplitude of scalar perturbations $A_s$, spectral index $n_s$ and tensor-to-scalar ratio $r$, we demonstrate that the model a quartic potential and the proposed coupling function is in agreement with observations.