Abstract
In this review, we investigate the question of backreaction in different approaches to cosmological perturbation theory, and with a special focus on quantum theoretical aspects. By backreaction we refer here to the effects of matter field or cosmological inhomogeneities on the homogeneous dynamical background degrees of freedom of cosmology. We begin with an overview of classical cosmological backreaction which is ideally suited for physical situations in the late time Universe. We then proceed backwards in time, considering semiclassical approaches such as semiclassical or stochastic (semiclassical) gravity which take quantum effects of the perturbations into account. Finally, we review approaches to backreaction in quantum cosmology that should apply to the very early Universe where classical and semiclassical approximations break down. The main focus is on a recently proposed implementation of backreaction in quantum cosmology using a Born–Oppenheimer inspired method.
Highlights
Using the N-body relativistic code “gevolution,” Adamek et al (2019) find that backreaction on the expansion rate in a Λ cold dark matter (ΛCDM) and an Einstein–de Sitter Universe remains small if one chooses averaging volumes related to the Poisson gauge, while when choosing comoving gauge backreaction is of the order of 15%
Semiclassical as well as stochastic gravity regard the gravitational field as a classical entity from the start while the matter fields are considered to be of quantum nature. While this represents a seminal progress to incorporating quantum effects of the matter fields in the early Universe, it can and should be questioned whether this somehow incompatible approach survives the test of future observations, and whether it should be replaced by a more consistent approach quantum gravity - at least for the earliest moments of the cosmic history
This review provides an introduction to the backreaction problem in classical, semiclassical and quantum cosmology, as well as a detailed overview of the current state of research in the respective fields
Summary
The Λ cold dark matter (ΛCDM) concordance model (Cervantes-Cota and Smoot, 2011; Deruelle and Uzan, 2018; Dodelson and Schmidt, 2021), based on the pillars of the Standard Model of particle physics and general relativity, has shaped our current view of the Universe, and has been the driving force behind many of the breakthroughs of modern cosmology, for example the prediction and the discovery of the cosmic microwave background radiation (Aghanim et al, 2019, 2020; Alpher and Herman, 1948a,b; Gamov 1948a,b; Penzias and Wilson 1965). The concordance model assumes that smallest quantum fluctuations of the primordial matter and geometry have been stretched to the present time, thereby generating the observable large scale structure. The evaluation of the Hubble constant H0 as performed by the Planck collaboration (explicitely assuming a ΛCDM model) gives a value of H0 (67.27 ± 0.60)km/(s · Mpc) (Aghanim et al, 2020), while the SH0ES collaboration finds H0 (74.03 ± 1.42)km/(s · Mpc) (Riess et al, 2019), which in turn is based on the measurements of the Hubble Space Telescope This leads to a tension at the 4.4σ level (Di Valentino et al, 2020a).
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