Cosmological Particle Production in Quantum Gravity

Quantum theory of a test field on a quantum cosmological spacetime may be viewed as a theory of the test field on an emergent classical background. In such a case, the resulting dressed metric for the field propagation is a function of the quantum fluctuations of the original geometry. When the backreaction is negligible, massive modes can experience an anisotropic Bianchi type I background. The field modes propagating on such a quantum-gravity-induced spacetime can then unveil interesting phenomenological consequences of the super-Planckian scales, such as gravitational particle production. The aim of this paper is to address the issue of gravitational particle production associated with the massive modes in such an anisotropic dressed spacetime. By imposing a suitable adiabatic condition on the vacuum state and computing the energy density of the created particles, the significance of the particle production on the dynamics of the universe in Planck era is discussed.

A comparison theorem for cosmological lightcones

Let (M, g) denote a cosmological spacetime describing the evolution of a universe which is isotropic and homogeneous on large scales, but highly inhomogeneous on smaller scales. We consider two past lightcones, the first, $${{\mathcal {C}}_{L}^{-}}(p, g)$$ C L - ( p , g ) , is associated with the physical observer $$p\in \,M$$ p ∈ M who describes the actual physical spacetime geometry of (M, g) at the length scale L, whereas the second, $${\mathcal {C}_{L}^{-}}(p, \hat{g})$$ C L - ( p , g ^ ) , is associated with an idealized version of the observer p who, notwithstanding the presence of local inhomogeneities at the given scale L, wish to model (M, g) with a member $$(M, \hat{g})$$ ( M , g ^ ) of the family of Friedmann–Lemaitre–Robertson–Walker spacetimes. In such a framework, we discuss a number of mathematical results that allows a rigorous comparison between the two lightcones $${\mathcal {C}_{L}^{-}}(p, g)$$ C L - ( p , g ) and $${\mathcal {C}_{L}^{-}}(p, \hat{g})$$ C L - ( p , g ^ ) . In particular, we introduce a scale-dependent (L) lightcone-comparison functional, defined by a harmonic type energy, associated with a natural map between the physical $${\mathcal {C}_{L}^{-}}(p, g)$$ C L - ( p , g ) and the FLRW reference lightcone $${\mathcal {C}_{L}^{-}}(p, \hat{g})$$ C L - ( p , g ^ ) . This functional has a number of remarkable properties, in particular it vanishes iff, at the given length-scale, the corresponding lightcone surface sections (the celestial spheres) are isometric. We discuss in detail its variational analysis and prove the existence of a minimum that characterizes a natural scale-dependent distance functional between the two lightcones. We also indicate how it is possible to extend our results to the case when caustics develop on the physical past lightcone $${\mathcal {C}_{L}^{-}}(p, g)$$ C L - ( p , g ) . Finally, by exploiting causal diamond theory, we show how the distance functional is related (to leading order in the scale L) to spacetime scalar curvature in the causal past of the two lightcones, and briefly illustrate a number of its possible applications.

Black hole solutions in a cosmological spacetime background

We propose and analyze a new metric that has two conformal factors a(t) and b(t) that combine the expansion of the universe and its effects on the spatial and temporal part of the Schwarzschild metric in isotropic coordinates. We present the solutions, their descriptions and we comment on their shortcomings. In the spatially flat case of an expanding universe, we derive from the proposed metric the special solutions of the field equations for the dust approximation and the McVittie metric. We show that the presence of a black hole does not modify the a(t)αt2/3 law for dust and H = const. for dark energy.

THE COSMOLOGICAL SPACETIME

We present here the transformations required to recast the Robertson–Walker metric and Friedmann–Robertson–Walker equations in terms of observer-dependent coordinates for several commonly assumed cosmologies. The overriding motivation is the derivation of explicit expressions for the radius Rh of our cosmic horizon in terms of measurable quantities for each of the cases we consider. We show that the cosmological time dt diverges for any finite interval ds associated with a process at R → Rh, which therefore represents a physical limit to our observations. This is a key component required for a complete interpretation of the data, particularly as they pertain to the nature of dark energy. With these results, we affirm the conclusion drawn in our earlier work that the identification of dark energy as a cosmological constant does not appear to be consistent with the data.

Testing the local spacetime dynamics by heliospheric radiocommunication methods

According to general relativistic theories, cosmological spacetime is dynamic. This prediction is in excellent agreement with the huge majority of astronomical observations on large cosmic scales, especially the observations of cosmological redshifts of distant galaxies. However, on scales of heliospheric distances, verifications of general relativistic effects are based on Schwarzschild metric tests or kinetical corrections, such as the perihelion motion of Mercury, photon deflection at the Sun and gravitational photon redshifts in central gravity fields. As we will show in this paper, there is, however, a chance to detect new cosmologically relevant features on heliospheric scales by careful study of photon propagations in the local spacetime metrics, based on red- or blueshifts as a clear, but up to now overlooked, signature of the local spacetime dynamics. Thus, we propose the challenging possibility of carrying out experiments of cosmological relevance by simply using high-precision radio tracking of heliospheric spaceprobes, as already practised in cases like Pioneer-10/11, Galileo and Ulysses.