Abstract
The enhancement of the spectrum of primordial comoving curvature perturbation R can induce the production of primordial black holes (PBH) which could account for part of present day dark matter. As an example of the effects of the modification of gravity on the production of PBHs, we investigate the effects on the spectrum of R produced by the modification of gravity in the case of G-inflation, deriving the relation between the unitary gauge curvature perturbation ζ and the comoving curvature perturbation R, and identifying a background dependent enhancement function E which can induce large differences between the two gauge invariant variables. We use this relation to derive an equation for R, showing for the presence of a momentum dependent effective sound speed (MESS), associated to the intrinsic entropy which can arise in modified gravity theories, in agreement with the model independent MESS approach to cosmological perturbations.When ζ is not constant in time it is different from R, for example on sub-horizon scales, or in models exhibiting an anomalous super-horizon growth of ζ, but since this growth cannot last indefinitely, eventually they will coincide. We derive the general condition for super-horizon growth of ζ, showing that slow-roll violation is not necessary. Since the abundance of PBHs depends on the statistics of the peaks of the comoving density contrast, which is related to the spectrum of R, it is important to take into account these effects on the PBHs abundance in modified gravity theories.
Highlights
The study of primordial perturbations is fundamental in any cosmological model, since it allows to make predictions of the conditions which provided the seeds for the anisotropies of the cosmic microwave background (CMB) radiation or for the process of structure formation
As an example of the effects of the modification of gravity on the production of primordial black holes (PBH), we investigate the effects on the spectrum of R produced by the modification of gravity in the case of G-inflation, deriving the relation between the unitary gauge curvature perturbation ζ and the comoving curvature perturbation R, and identifying a background dependent enhancement function E which can induce large differences between the two gauge invariant variables
We have computed the effective energy-stress-tensor for G-inflation theories in the comoving slices gauge and have used it to derive a general relation between the unitary gauge curvature ζ and the comoving curvature perturbation R, involving an enhancement function which depends on the evolution of the background, and which can cause a large difference between the two gauge invariant quantities
Summary
The study of primordial perturbations is fundamental in any cosmological model, since it allows to make predictions of the conditions which provided the seeds for the anisotropies of the cosmic microwave background (CMB) radiation or for the process of structure formation. The general form of the equation of curvature perturbation in comoving gauge R was derived in [10] assuming an arbitrary form of the total effective energystress tensor (EST), but no explicit calculation was given in the case of modified gravities. In this letter we compute the general relation between R and ζ and use it to derive an equation for R for G-inflation, confirming the general form predicted in [10], showing evidence of a momentum dependent effective sound speed (MESS). As an application we use the gauge transformation between R and ζ to investigate the effects of the modification of gravity on the power spectrum of R in models violating slow-roll, such as for example ultra slow-roll G-inflation [16], and its implications on the production of PBHs
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
