Applications of the Hawking energy on lightcones in cosmology

Abstract

The past lightcone of an observer in a cosmological spacetime is the unique geometric structure directly linked to observations. After general properties of the Hawking energy along slices of the past lightcone have previously been studied, the present work continues along this path by providing explicit cosmological applications of the Hawking energy associated with a lightcone. Firstly, it is shown that amongst all two-dimensional non-trapped spheres with equal area and average matter density, a shear-free matter distribution maximizes the Hawking energy for sufficiently high densities. Secondly, a Robertson–Walker reference slice is constructed for every lightcone slice based on area and energy. Thirdly, after a few pedagogical examples in concrete FLRW spacetimes, the implications of monotonicity of the energy down the lightcone are explored, arriving at two new bounds on the cosmic fluid’s density and equation-of-state parameter.

The Hawking energy in a perturbed Friedmann-Lemaître universe

“…Here, we are mainly interested in its properties on constant redshift slices as we advance down the lightcone. According to a result by Horowitz and Schmidt [7], the Hawking Energy is positive for sufficiently small spheres in the neighbourhood of the lightcone vertex point p. As it was shown in [4], monotonicity of the function E(z) can be established in several spatially flat cases, in particular in the case of dust with a positive cosmological constant, or, more generally, for an equation of state w(z) ≥ 0.…”

“…Numerical IR-cancellations. It turns out that special care is needed when computing the monopole, because some of the terms appearing in (4.2) are IR-divergent, 4 despite their total sum being finite. In the following we present a way to ensure that all IR-divergencies cancel out explicitly, so that the numerical expression for the monopole in (4.1) is independent JCAP08(2023)033 perturbation depends on the gravitational potential.…”

“…Phenomenologically speaking, the presence of energy or mass in a spacetime, either in form of matter or gravitational waves, will affect light propagation. Because the Hawking Energy [2] is defined in terms of the expansion scalars of null congruences, it is a natural definition of energy when applied to the lightcone generators, as suggested and studied in [3] and [4]. Here, we study the Hawking Energy in the context of linearly perturbed Friedmann-Lemaître (FL) spacetimes, providing the standard JCAP08(2023)033 framework in which cosmological observations are analysed and interpreted, see e.g.…”

“…In principle our observer velocity can be measured in the CMB rest-frame[15,[31][32][33][34][35]. However the difference is expected to be within the cosmic variance[36,37] 4. The calculation of the angular power spectrum contains integrals over wavenumber k some of which, in the case of the monopole = 0, diverge for k → 0.…”

The averaging problem on the past null cone in inhomogeneous dust cosmologies

“…We remark that this backreaction term appears to bear a relationship to the Hawking-Hayward energies as defined in Refs [73,74][9,134,135]. for recent work.…”