AR-2019-2020

obtained by varying the corresponding effective action S T 2 eff [ C ] turns out to be precisely that of the ‘in-in’ formalism. Therefore, one obtains a path integral based approach for deriving the correct backreaction prescription, which: (i) is causal and (ii) has the effect of particle production correctly taken into account. Cosmology and Structure Formation Primordial black holes from a tiny bump or dip in the inflaton potential The existence of primordial black holes (PBHs) has been a subject of considerable interest ever since this possibility was suggested by Zeldovich and Novikov in 1967. Subsequently Hawking (1974) showed that quantum evaporation would leave behind PBHs with masses greater than about 10 15 g, smaller black holes having completely evaporated by the present epoch. Interest in PBHs grew quite rapidly following these two seminal papers. It was soon realized that PBHs created in the early history of our universe could be of considerable importance since they might: 1. Seed the formation of supermassive black holes (BHs) in the nuclei of galaxies and AGN’s. 2. Influence the ionization history of the universe. 3. Contribute to the dark matter (DM) density in the universe. One might add that since particle dark matter in the form of WIMPs or an axion has not yet been compellingly discovered either by accelerator experiments or by direct DM searches, the possibility that a significant component of DM may consist of primordial black holes presents an entirely plausible and even alluring possibility. Interest in PBHs received a major boost with the discovery by LIGO of gravitational radiation from merging BHs (event GW150914) with a mass of about 30 M . This discovery was supported by additional events, and at the time of writing, the number of black hole merger events exceeds ten, with many more expected to follow from future runs of LIGO, Virgo and KAGRA. The precise physical mechanism responsible for PBH formation has been a subject of considerable debate. Early models of PBH production included: formation during bubble collision in a first order phase transition, the collapse of topological defects such as domain walls and cosmic strings, etc. Within the context of inflation, it was suggested that an enhancement of perturbations leading to PBH formation would occur if the inflationary spectrum had a significant blue tilt and/or non- Gaussianity, or if the inflaton rolled extra slowly for a duration of time which was much shorter than the full inflationary epoch. In the context of single-field models, PBHs can form if the potential contains a near inflection point, or a saddle type region, which slows the motion of the inflaton field and leads to a spike in the perturbation spectrum. Alternatively, the inflaton can also slow down by climbing a small local bump-like feature in the base inflationary potential. As demonstrated by Swagat Mishra and Varun Sahni by locally slowing the motion of the scalar field, the bump behaves like a speed-breaker and leads to a sharp increase in the amplitude of the curvature perturbation R . An interesting example of a local speed-breaker arises if a term such as V b ( φ ) ε ( φ ) ( ε 1), localised at φ = φ 0 , is added to the base inflationary potential V b ( φ ). Applying this simple prescription with a Gaussian speed-breaker Δ( φ − φ 0 ) to the string theory based KKLT model and to α -attractor potentials, the authors find a sharp local enhancement of primordial perturbations at φ 0 , which can result in a significant abundance of PBHs at the present epoch. The local nature of the speed-breaker permits the generation of PBHs in a wide mass ranging from the ultra-light 10 − 17 M to the super-heavy 10 2 M without significantly affecting the scalar spectral index n S and the tensor-to-scalar ratio r on scales measured by the Cosmic Microwave Background (CMB). This stands in marked contrast