---
author:
- 'A. Del Popolo,'
- 'M. Le Delliou'
title: 'A unified solution to the small scale problems of the $\Lambda$CDM model II: introducing parent-satellite interaction'
---

Introduction
============

The $\Lambda$CDM (cosmological constant and Cold Dark Matter) model of cosmology, while describing the observations of the Universe, its large scale structure and evolution very successfully (Spergel et al. 2003, Komatsu et al. 2011; Del Popolo 2007, 2013, 2014a), retains some problems in the description of structures at small scales (e.g., Moore 1994; Moore et al. 1999; Ostriker & Steinhardt 2003; Boylan-Kolchin, Bullock, and Kaplinghat 2011, 2012; Oh et al. 2011)[^1]. These problems can be enumerated as a) the discrepancy between cuspy density profiles obtained in N-body simulations (Navarro, Frenk & White 1996, 1997 (NFW); Navarro 2010)[^2] and the flat profiles of dwarf and Low Surface Brightness galaxies (Burkert 1995; de Blok, Bosma, & McGaugh 2003; Del Popolo 2009 (DP09); Cardone et al. 2011a, 2011b; Cardone & Del Popolo 2012; Del Popolo 2012a,b (DP12a, DP12b); Oh et al. 2010, 2011; Kuzio de Naray & Kaufmann 2011), coined as the cusp/core problem (hereafter CCP) (Moore 1994; Flores & Primak 1994;Ogiya & Mori, 2011,2014; Ogiya et al. 2014), or of Galaxy Clusters 